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\begin{document}

\trnum{9202}
\date{April 1992}
\title{Essays on Darwinism \\2: Organismic Darwinism}
\maketitle

\begin{abstract}
{\em Artificial Life\/} is, by its nature, an interdisciplinary
research programme; it will involve biologists, of course, but
also philosophers, mathematicians, chemists, computer
scientists---and perhaps even (as in my case) engineers. Success
in our endeavours will require some of us, at least, to venture
into foreign territory. This essay is a log of my personal
expedition into evolutionary biology. I attempt to provide a
comprehensive review of Darwinism in the biological world, and to
do so as an {\em outsider\/}---a non-professional in the field.
My purpose is twofold.  Firstly, I hope that real biologists may
take this opportunity to correct at least the worst of my errors.
Secondly, I offer this to other non-specialists as a sort of
map---a record of my particular exploration.  I hope it might at
least provide some insight into the kinds of questions which need
to be asked, even if the particular answers suggested here are
less than satisfactory.  Above all, I want to convince any who
may be in doubt that {\em Darwinism\/} encompasses a complex and subtle
system of interrelated theories, whose substantive
transplantation to any artificial medium will be very far from
easy.

This essay draws on abstract concepts introduced in a previous
essay \cciteAD{McMullin:DarwinianOntology}; the two essays are
therefore best read in conjunction.
\end{abstract}

\pagenumbering{roman}
\tableofcontents

\pagenumbering{arabic}
%\draft

\section{Introduction}

\begin{quote}
  Another curious aspect of the theory of evolution is that
  everybody thinks he understands it!

  Jacques Monod\\
  (Quoted by \ociteAD[p.~18]{Dawkins:NewSelfishGene})
\end{quote}

This essay provides a review of \mbox{(neo-)Darwinian} theory, in its
native, biological, setting.  I suggest that this is an essential
pre-requisite for any attempt to apply Darwinian principles
outside their original context. The essential idea is to view the
biological world as an example of what I have previously called a
{\em D-system\/} \cciteAD{McMullin:DarwinianOntology}, with
biological organisms as {\em D-actors\/}---hence {\em
Organismic\/} Darwinism.\footnote{My
  usage of ``organismic'' here is loosely related to the {\em
  Organismic Evolution\/} of
  \citeAD{Beurton:OrganismicEvolution}, and the {\em Organismic
  Selection\/} of \citeAD{Wright:GenicAndOrganismic}.}

I make a distinction between two questions: firstly, whether
there exists an evolutionary or phylogenetic {\em tree\/}; and
secondly, given the existence of such a tree, the elucidation of
particular aspects of it---preeminently, the emergence of
``adaptive complexity'' (or knowledge). It is the latter question
which is of critical interest and importance, and which Darwin
sought to answer with his theory of natural selection.

I discuss the detailed structure of the theory of Organismic
Darwinism, establishing that some components may be much more
easily tested and corroborated than others.

I review the various theories which seem to be plausible
alternatives or competitors to Organismic Darwinism, but conclude
that none of these currently provides a significant challenge.

I consider the {\em scientific status\/} of Organismic
Darwinism---particularly claims that it may be tautological and/or
metaphysical.  I argue that these suggestions are mistaken, but
{\em not\/} trivially so.  Consideration of them will clarify some
further important aspects of Organismic Darwinism. The resulting
claim is that Organismic Darwinism is {\em incomplete\/} (as a
theory or explanation of the growth of adaptive complexity) but
that, in an essential sense, it is {\em incompletable}, even in
principle.  It is asserted that a complete or universal theory of
the growth of adaptive organismic complexity would amount to a
logic of induction, and will therefore remain forever beyond our
grasp.  This may be of relatively little significance within
biology; it is, however, of crucial importance to any research
programme aimed at realising the spontaneous growth, by Darwinian
means, of adaptive complexity in {\em artificial\/} systems.

\section{On the Origin of Species\ldots}
\subsection{Two Theories}
\label{origin}
\begin{quote}
  In considering the Origin of Species, it is quite conceivable
  that a naturalist, reflecting on the mutual affinities of
  organic beings, on their embryological relations, their
  geographical distribution, geological succession, and other
  such facts, might come to the conclusion that each species had
  not been independently created, but had descended, like
  varieties, from other species\ldots\

  \citeAD[Introduction]{Darwin:TheOriginOfSpecies}
\end{quote}
\label{sec:evo}

This is Darwin's original statement both of the theory of evolution, and
the problem(s) which it is intended to solve. Remarkably, this is as
valid and incisive a formulation today as when Darwin first presented
it; indeed, it is still widely quoted (e.g.\
\ociteAD{Lewontin:Adaptation}).
Nonetheless, Darwin's sheer economy of expression disguises its
subtlety. Therefore I should like to dissect it carefully,
restating and/or elaborating the various elements.

First, Darwin summarises the problem, which is:
\begin{description}
\item[\pr{b} (Biology):] To explain the various {\em regularities\/}
  which are manifested in the biological world, especially the
  relationships which exist between species,\footnote{There are
    difficulties with the exact interpretation of {\em species\/}
    in biology; for my purposes it will be sufficient to take the
    fairly simplistic line that a species is a set of
    organisms whose members can be reliably identified in some
    (unstated) fashion.}
  both as they exist now, and as they have existed in the past.

\end{description}

Then Darwin introduces two theories which may compete to solve this
problem:
\begin{description}
\item[\th{t} (Phylogenetic Tree):] Species arise by descent from
  other different species.\footnote{I shall speak, loosely, of
  species descending from other species, as a shorthand way of
  saying that organisms of one species are (ultimately) descended
  from organisms of another species. I postpone any consideration
  of how many generations may be required to complete such a
  speciation event.}

In this case there must exist a unique evolutionary
(phylogenetic) tree, ultimately leading back to a single common
ancestor of all species. The process by which this putative
original species came into existence is left open.

\item[\th{c} (Creation):] All species arise {\em separately},
and are immutable (cannot give rise to other species by
descent). The process by which species do, in fact, arise, is
left open.

The distinguishing feature of this theory is that organisms of
any one species are not related {\em by descent} to organisms of any
other species.

\end{description}

\th{t} is, precisely, what I had in mind when I said that Darwin had
here stated {\em the theory of evolution}. It is worth emphasizing that
Darwin did not {\em originate\/} \th{t}---any more than he originated
\th{c}---and nor did he claim to. As Burrow put it, in his
editor's introduction to a modern reprinting of {\it The
Origin\/}:
\begin{quote}
  The theory of evolution was already an old, even a discredited
  one.  Darwin, in later editions of {\it The Origin}, listed
  over thirty predecessors and was still accused of lack of
  generosity.

  \citeAD[p.~27]{Burrow:DarwinsOrigin}
\end{quote}

In any case, I shall avoid any further reference to ``the theory of
evolution'', as such, and will use the more austere ``\th{t}'' instead.
I do this for several distinct reasons:
\begin{enumerate}
\item Darwin himself did not originally use the word
  ``evolution'' at all, because, at that time, both conventional
  and technical usage of this word was quite different from
  Darwin's notion of descent (with modification). This has been
  discussed in detail by
  \citeAD[Essay~3]{Gould:EverSinceDarwin}.

\item \th{t} prescribes only that new species may arise from earlier
  species by descent; it does not specify that this process is
  necessarily incremental or gradual---i.e.\ that it is literally
  {\em evolutionary\/} as the term is now commonly understood. In
  particular, the fossil record (Darwin's ``geological
  succession'') does not offer direct evidence capable of
  deciding this issue with precision (even assuming that there is
  a single ``right'' answer).

\item Although I have characterised the two theories as involving
  {\em creation\/} versus {\em descent}, {\em both} theories have
  to posit {\em some\/} ``creation'' event(s)---in the technical sense
  of species coming into existence {\em other\/} than by descent
  from earlier species. The significant feature of \th{t}
  relative to \th{c} is not that it eschews creation altogether,
  but that creation is invoked only in a relatively minor,
  secondary, \role. As we will see, this is decisive for the
  comparison between the two theories.

\item Finally, phrases like ``the theory of evolution'' (or
  perhaps ``The Theory of Evolution''), ``evolutionary theory'',
  and even just ``evolution'', have become vague and
  confusing through popular use and abuse.  Thus, for example,
  \citeAD[Essay~19]{Gould:HensTeeth} argues forcefully
  for the view that the object I have identified as \th{t} should
  {\em not\/} be called a ``theory'' at all but rather a
  ``fact''---on the basis that it has been ``confirmed to such a
  degree that it would be perverse to withhold provisional
  assent''. Gould reserves the term ``theory'' in this context
  for hypotheses relating to the {\em mechanisms\/} regulating
  the development of the phylogenetic tree.  I do not disagree
  with the substance of Gould's position, but, for the purposes
  of discussing whether or not something is a ``fact'' in his
  sense, we must first formulate it, and it is, at that stage,
  only a ``theory''---and that is the stage I am at in this
  section, so to start off by using Gould's terminology would,
  itself, be perverse.

\end{enumerate}

At this point I should like to compare \th{t} and \th{c}---to decide,
if possible, which we should {\em prefer}. To do this, I shall
rely (albeit loosely) on Popper's notion of {\em degree of
corroboration} (Popper \ociteD{Popper:LScD}; \ociteD{Popper:Realism}).

First let us consider the relative {\em corroborability\/} of the two
theories---that is, the {\it a priori\/} degree to which they {\em
might\/} be corroborated. This is equivalent to their {\em testability},
which, in turn, is more or less determined by their {\em information
content}---the sets of non-tautologous consequences which flow from
them.

Now, as it happens, \th{c} has zero corroborability---there are {\em
no\/} non-tautologous consequences of it. That is, if we suppose that
all species arise separately, and not by descent, then, in the
(self-imposed) absence of some theory of the creation mechanism itself,
we cannot predict {\em anything\/} about what relationships should exist
between species, present and/or past; which is to say that \th{c}
does not (yet) address \pr{b} at all. In Darwin's formulation, this
aspect is implied by his reference to {\em independent\/} creation.

\th{t}, on the other hand, makes some fairly definite, non-tautologous,
predictions, and is therefore testable and corroborable. The basic
prediction is that some single, unique, phylogenetic tree must be
compatible with {\em all\/} manifestations of that tree. These
manifestations are, precisely, the regularities cited in \pr{b}.
\th{t} is, at least, confronting our problem, if not actually solving
it.

So, \th{t} has a higher corroborability than \th{c}. Indeed,
there exists a sort of continuum of theories, between \th{c}
and \th{t}, parameterized by the number of ``original'' species
which are posited; the corroborability is (more or less)
inversely related to this. I have deliberately placed \th{t} at
the limit of this range; that is, in the strongest, boldest,
form of stating that {\em all\/} species, present and past, are
descended from just {\em one\/} original species. This may
seem stronger than necessary---but there is no particular
merit in caution {\em at this stage\/} (i.e.\ unless and until
\th{t} fails one or more critical tests).  This is
essentially the position originally adopted by Darwin himself:
\begin{quote}
  I believe that animals have descended from at most only four or
  five progenitors, and plants from an equal or lesser number.

  Analogy would lead me one step further, namely to the belief
  that all animals and plants have descended from some one
  prototype. But analogy may be a deceitful guide.  Nevertheless
  all living things have much in common, in their chemical
  composition, their germinal vesicles, their cellular structure,
  and their laws of growth and reproduction.  We see this even in
  so trifling a circumstance as that the same poison often
  similarly affects plants and animals; or that the poison
  secreted by the gallfly produces produces monstrous growths on
  the wild rose or oak-tree. Therefore {\em I should infer from
  analogy that probably all the organic beings which have ever
  lived on this earth have descended from some one primordial
  form,} into which life was first breathed.

  Darwin\\
  \cciteD[Chapter~XIV, emphasis added]{Darwin:TheOriginOfSpecies}

\end{quote}

Now it is important to note that, even though \th{t} has a higher
corroborability than \th{c} this is, as yet, of limited significance;
we have not yet spoken of the degree to which \th{t} has {\em
withstood} its tests to date---i.e.\ its actual (as opposed to
potential) degree of corroboration. In particular, even though \th{c}
is pre-scientific (metaphysical), we should still prefer it if \th{t}
fared very badly in its tests (if, in effect, \th{t} was {\em refuted}).

Technically, while \th{c} has zero corroborability, and therefore zero
corroboration, \th{t} could have a {\em negative} corroboration
(ultimately, if it were decisively refuted, the corroboration would be
exactly $-1$); we could thus find ourselves actually {\em preferring\/}
\th{c}.

Of course, our response to such a situation would depend on
the exact manner of \th{t}'s refutation; we might be able to rescue it
simply by moving a little way along the continuum toward \th{c}.
However, if the refutation were profound or extensive, such {\em ad
hoc\/} immunization, though always possible, would be counterproductive.
In that situation we would want to confront \th{c}, by augmenting it
with some specific theories of the ``creation'' process---theories which
{\em would\/} make some definite predictions relating to \pr{b}, and
would thus have non-zero corroborability.

In any case, this is something of a digression, because \th{t} has, in
fact, withstood its tests very well, and I should say that it is
currently ``well'' corroborated.

This conclusion includes, of course, the fossil evidence. As
Dawkins has recently put it: ``If a single, well-verified mammal
skull were to turn up in 500 million year-old rocks, our whole
modern theory of evolution would be utterly destroyed''
\cciteAD[Chapter~9, p.~225]{Dawkins:BlindWatchmaker}. On the
other hand, the fossil record is by no means complete, and this
limits the severity of the testing by this means---as was known
and acknowledged by Darwin himself
\cciteAD[Chapter~IX]{Darwin:TheOriginOfSpecies}.  In fact, the
primary tests of \th{t} are not based on fossil evidence, but on
evidence from the observed evolution of species, from
biogeography, and from the hierarchical structure of organismic
taxonomy. These are essentially the same kinds of tests as Darwin
himself formulated, although the contemporary versions have
become a good deal more severe, as discussed in detail by
\citeAD{Ridley:WhoDoubtsEvolution}.

Additionally, it has recently become possible to test \th{t} in a
manner which would not even have been intelligible in Darwin's
time---by the comparison of protein sequences in putatively
related species.  \th{t} has, in fact, continued to withstand
these even more severe tests (see
\ociteAD{Penny:TestingTheTheoryOfEvolution}).

So we can conclude that we should rationally prefer \th{t} to \th{c},
because of its decisively greater degree of corroboration; but let me
reiterate, one last time, that this is nothing to do either with some
{\em inherent\/} ``implausibility'' of \th{c}, nor with some refutation of it.
\th{c}, as it stands, {\em cannot} be refuted, and it would be pointless
to pretend otherwise. Granted, \th{c} is not (yet) scientific; but it
could be elaborated into a variety of scientific theories. Our reason
for not pursuing that avenue is simply that \th{t} is {\em already\/} a
stronger (scientific) theory, which {\em is\/} successfully solving the
relevant problems (i.e.\ has not been refuted). We will {\em
need\/} to re-assess this position only if, or when, some
additional elements are added into the problem situation.

All of this extended argument, now coerced into the Popperian model of
scientific discourse, was, then, already implicit in Darwin's
straightforward assertion that it is ``quite conceivable'' that one
would prefer \th{t} to \th{c}, as a solution to \pr{b}.
Nonetheless, I believe that, in the intervening years, there has
been such a degree of confusion if not obfuscation of this original
argument, that the detailed analysis offered here is justified.

\subsection{Two Digressions}

\subsubsection{Creationism}

At this point, I should like to briefly digress to relate the
development so far to the doctrine of {\em Creationism}.

First consider what I shall call {\em Biblical Creationism} i.e.\
a more or less literal interpretation of the Book of Genesis.
Note that this is {\em not\/} equivalent to \th{c}; it is
stronger than \th{c}, and is, in fact, a perfectly good
scientific theory (in the sense of having testable consequences).

In particular, Biblical Creationism posits that all biological species
were created concurrently and more or less instantaneously (for
my purposes it does not matter how, why, or when), and that the
only change since then has been the possible extinction of some
of the originally created species.

Certainly, this leaves a lot of questions open (particularly as
regards the nature of the creation event), but, insofar as it
goes, it is still clear and testable. Specifically, it entails
clear predictions about what we should expect the fossil record
to look like (the {\em only\/} allowed change over time would be a
thinning out of the varieties of fossil observed). Since the
fossil record has been found, repeatedly and consistently, to
refute this prediction, this theory has been decisively refuted
(relative to, among others, \th{t}).

Now, the theory could be saved by dropping the requirement for
instantaneous, or simultaneous, creation (albeit, we would have to
sacrifice our literal conformity to Genesis, to do this). But
such a {\em Creeping Creationism\/} as it might be called,
essentially {\em is\/} identical to \th{c}; and, as we have seen,
\th{c} is not (currently) a serious competitor to \th{t}. Of
course, Creeping Creationism is typically dressed up a lot
more than \th{c}---by saying, for example, that the creation
events have been decided or determined by some god, in her
infinite wisdom; but, in the absence of a (testable) theory of
the powers and motivations of this god, this is not logically
distinguishable from \th{c}---it is merely more verbose.

Of course (and this really {\em is\/} a bold leap!) we could
still hypothesize, in effect, that we are the hapless (but
rational) victims of some diabolical practical joke---that
Biblical Creationism really is true, but that some agent, with a
rather warped sense of humour, has deliberately contrived the
assorted empirical evidence which contributes to the refutation
of Biblical Creationism and the corroboration of \th{t}.
Presumably, such an elaborate hoax would have been designed with
the specific {\em intention\/} of tricking us mere mortals into
erroneously adopting \th{t}. Such an idea seems to me to be on a
par with the theological speculations of Douglas Adam's fictional
philosopher {\em Oolon Colluphid\/}.\footnote{Well known author
  of the trilogy of philosophical blockbusters {\em Where God
  Went Wrong,} {\em Some More of God's Greatest Mistakes\/} and
  {\em Who is this God Person Anyway?}
  \cciteAD{Adams:HitchhikersGuide}.}
On the other hand, there has apparently been at least one serious
proposal to this general effect (reported by
\ociteAD{Little:Evolution}).

In any case, I suggest that it serves no useful purpose to
unilaterally {\em deny} or denigrate theories like \th{c} (e.g.\
by {\em insisting\/} on describing \th{t} as a fact, as
discussed with reference to Gould in the previous section), or to
pretend that they can be (or have already been) absolutely
refuted. I consider that it is better simply to observe that such
(metaphysical) theories {\em cannot\/} be refuted, that some such
theory {\em may}, in fact, be true, but that, notwithstanding all
that, \th{t} can and should be rationally {\em preferred} to
them.

\subsubsection{Saltationism}

\label{saltation1}

{\em Within\/} the scope of \th{t} we can identify various
more specific theories distinguished by claims about the ``rate''
of evolution.

Firstly we may consider {\em gradualism} which asserts that
species are formed gradually and cumulatively over many
generations---i.e.\ the differences which may arise between
parent and offspring in any {\em single\/} generation are much
smaller than the differences which ultimately distinguish or
separate species.  In contrast to gradualism, we may consider
{\em saltationism\/} which asserts that new species can arise in
a small number of generations, perhaps even just one. Darwin
certainly adopted the former, gradualist, view (particularly by
his invocation of the slogan {\em Natura non facit saltum}, or
{\em nature does not make leaps\/}; the slogan is usually
attributed originally to Linnaeus---see, for example,
\ociteAD[Essay~17]{Gould:PandasThumb}). For the moment I simply
note that the fossil record is too fragmentary to decide this
issue, but that other sources of evidence (observed evolution,
biogeography) seem to favour something closer to gradualism than
saltationism.

Secondly we may consider whether the rate of evolution is itself
constant, or varies significantly.  Here we encounter the theory
of {\em punctuated equilibria\/} of Eldredge and Gould
\cciteAD{Eldredge:PunctuatedEquilibria,%
Gould:TempoOfEvolution}.  This
asserts that the rate of evolution varies greatly, and that
species remain static for most of the time
(equilibrium), but with occasional bursts (punctuations) of
relatively rapid evolution and/or speciation. The key phrase here
is ``relatively rapid''.  Eldredge and Gould are not
saltationists---they are operating within the framework of
gradual, cumulative change over a large number of generations.
This question of punctuated equilibrium versus constant speed
evolution has been reviewed in depth by
\citeAD[Chapter~9]{Dawkins:BlindWatchmaker}.  The conclusion is
that the weight of the evidence favours something closer to
punctuated equilibrium rather than constant speed evolution
(although with some exceptions).  The point for my purposes here
is simply to note that punctuated equilibrium is not in any sense
an alternative or competitor to \th{t}; it is rather a further
refinement within the gradualist version of \th{t}.

\section{\ldots\ by Means of Natural Selection}
\subsection{Darwin's Problem (\pr{d})}

\label{dprob}
\begin{quote}
  \ldots\ Nevertheless, such a conclusion [\th{t}], even if well
  founded, would be unsatisfactory, until it could be shown how
  the innumerable species inhabiting this world have been
  modified, so as to acquire that perfection of structure and
  coadaptation which most justly excites our admiration.

  \citeAD[Introduction]{Darwin:TheOriginOfSpecies}
\end{quote}

With this continuation of the earlier quotation from Darwin
(section~\ref{origin}) the problem situation is now extended, in
a crucial way, beyond \pr{b}. We arrive at what I shall term {\em
Darwin's Problem\/}:

\begin{description}
\item[\pr{d} (Darwin):] Given that species descend from other
species (i.e.\ given \th{t}), how is it that, in some cases at
least, this descent has been accompanied by an increase in
adaptive complexity?

\end{description}

I introduce the term {\em adaptive complexity\/} here, following
Maynard Smith:
\begin{quote}
  The main task of any theory of evolution ({\it sic\/}) is to
  explain adaptive complexity, i.e.\ to explain the same set of
  facts which Paley used as evidence of a Creator.  Thus if we
  look at an organism, we find that it is composed of organs
  which are at the same time of great complexity and of a kind
  which ensures the survival and/or reproduction of their
  possessor.  Evolution theory must explain the origin of such
  adaptations.

  \citeAD[p.~82]{MaynardSmith:StatusOfNeoDarwinism}

\end{quote}

\citeAD{Popper:EmergenceOfMind} has similarly formulated a
version of \pr{d} by reference to Paley's famous ``argument from
design''---i.e.\ that the appearance of ``Design'' in the
biological world ``proves'' the pre-existence of a designer or
creator (which is to say, {\em God\/}). Popper emphasizes that
Darwin himself acknowledged a strong influence from Paley's
formulation (and attempted solution) of this problem.  At one
point Popper explicitly calls this ``Paley's problem'' (p.~345);
but elsewhere in this same paper he refers to ``Paley's and
Darwin's problem'' (p.~342), which is thus consistent with my
designation of \pr{d} as ``Darwin's Problem''.  I shall
consistently use the latter name; partly because I have used
Darwin's formulation, rather than Paley's, to introduce it; but
mainly because there is a subtle difference between the problem
as {\em originally conceived\/} by Paley, and as {\em actually
solved\/} by Darwin. In my construction (\pr{d}), the
(conjectured) truth of \th{t} (the existence of the phylogenetic
tree) is part of the problem situation; whereas, for Paley, the
truth of \th{t} was neither a necessary part of (nor even
particularly relevant to) the problem situation. I shall return
to this point below.

Dawkins has adopted the terminology of ``adaptive complexity''
from Maynard Smith \cciteAD[p.~404]{Dawkins:UniversalDarwinism},
and I shall use this phrase freely in what follows, but I shall
also synonymously (?), and sometimes preferentially, refer to
``inate'' or ``inborn'' {\em knowledge\/} in the sense introduced
(somewhat separately) by Popper:
\begin{quote}
  I assert that every animal is born with expectations or
  anticipations, which could be framed as hypotheses; a kind of
  hypothetical knowledge.  And I assert that we have, in this
  sense, some degree of inborn knowledge from which we may begin,
  even though it may be quite unreliable.  This inborn knowledge,
  these inborn expectations, will, if disappointed, create {\em
  our first problems\/}; and the ensuing [somatic time] growth of
  our knowledge may therefore be described as consisting
  throughout of corrections and modifications of previous
  knowledge.

  \citeAD[pp.~258--259]{Popper:TreeOfKnowledge}
\end{quote}

A more comprehensive and formal analysis of the idea of an {\em
anticipatory system\/} has been independently developed by
\citeAD{Rosen:AnticipatorySystems}.

\pr{d} refers to an increase or growth of adaptive complexity. I
thus implicitly assume some notion of ``degree'' of adaptive
complexity; but I require only that this can be defined {\it a
posteriori}. That is, {\em given} two systems, I suppose that I
will, in general, be able to rank them (at least roughly) in terms of
relative adaptive complexity. I specifically eschew any attempt
to define an {\it a priori\/} measure of adaptive complexity. To
this extent I shall be following Rosen:
\begin{quote}
  \ldots complexity is not just complication, to be described by
  another number (e.g., the dimension of a state space or the
  length of a program), but a whole new theoretical world, with a
  whole new physics associated with it.

  \citeAD[p.~202]{Rosen:OrganismsAsCausalSystems}
\end{quote}

However, I should add that I shall not attempt to use
``complexity'' in precisely the strict technical sense intended
here by Rosen.

von~Neumann has described a similar idea as follows:
\begin{quote}
  There is a concept which will be quite useful here, of which we
  have a certain intuitive idea, but which is vague,
  unscientific, and imperfect \ldots\ I know no adequate name for
  it, but it is best described by calling it ``complication.''
  It is effectivity in complication, or the potentiality to do
  things.  I am not thinking about how involved the object is,
  but how involved its {\em purposive operations\/} are.  In this
  sense, an object is of the highest degree of complexity if it
  can do very difficult and involved things.

  \citeAD[Fifth Lecture, p.~78, emphasis added]{vonNeumann:TSRAutomata}
\end{quote}

Maynard Smith has similarly endorsed this somewhat loose
approach:
\begin{quote}

  At the outset we are faced with a difficulty: we have no way of
  measuring the degree of complexity of a structure.  Thus
  although most of us would readily agree that the organs of a
  man are more complex than those of an amoeba, and those of an
  amoeba more complex than those of a bacterium, we have no
  agreed criteria on which to base this decision, and no way of
  deciding by how much one organism is more complex than another.

  It may therefore seem odd to start formulating a theory of
  evolution by introducing a term which cannot be fully defined.
  However, I see no escape from doing so.  {\em If organisms were
  not both complicated and adapted, living matter would not
  differ from dead matter, and evolution theory would have
  nothing to explain.}

  Maynard Smith\\
  \cciteD[pp.~82--83, emphasis added]{MaynardSmith:StatusOfNeoDarwinism}

\end{quote}

I consider that \pr{d} is the central, perhaps even the
defining, problem of evolutionary biology, and is the problem
Darwin hoped to solve with his theory of Natural Selection.  To
this extent, the title of Darwin's book, {\em The Origin of
Species} may be slightly misleading---it directs attention
specifically at the phenomenon of {\em speciation}, rather than
at the growth of adaptive complexity.  While speciation is
certainly an important issue we can say nonetheless that it is of
secondary importance compared to the question of adaptive
complexity. Diversity of species as such would be of relatively
little interest if all species were equally rudimentary;
conversely, even if there were only one species which displayed
adaptive complexity, this one species would be of overwhelming
interest.\footnote{This is not, of course, to argue that
  speciation and the growth of adaptive complexity are {\em
  independent\/} phenomena, but merely that I shall concentrate
  on the latter.}

Before attempting to solve \pr{d} we must be clear as to how
\pr{d} goes beyond \pr{b}; that is, in what respect(s) \th{t}
fails to address (much less solve) \pr{d}.

\pr{b} was solely concerned with {\em relationships\/} of
various sorts between species---it took species (current and
extinct) as {\em given\/} and asked why they should exhibit the
various patterns of similarity and divergence which they do.
\th{t} solved this problem by postulating the existence of a
phylogenetic tree, involving more or less close relationships of
common descent among all species; by a suitable choice of this
tree (and \th{t} conjectures precisely that such a choice is
possible) then all the other relationships can be correlated with
({\em reduced to,} if you will) the single relationship of common
descent.

\pr{d}, on the other hand, then goes on to ask why the
phylogenetic tree has the particular structure that it has? Why,
above all else, does it display at least some cases of
increasing adaptive complexity?

Note that the claim here is not that {\em all\/} evolutionary
lineages have involved increasing adaptive complexity, but merely
that at least {\em some\/} have. Similarly, even for those
evolutionary lineages where there has been a net increase of
adaptive complexity, there is no claim that this increase has
occurred at a steady rate, or that it has been monotonic, or (most
especially) that it will continue into the future.

\pr{d} thus cannot even be properly formulated {\em except}
in the context of adopting (always {\em tentatively\/}) \th{t}.
\pr{d} may be viewed, in this sense, as a {\em consequence} of
the particular solution we have adopted to \pr{b}.\footnote{We
  \label{sec:popschema}
  have here a typical illustration of Popper's schema for the
  growth of scientific knowledge
  \cciteAD[Essay~3]{Popper:ObjectiveKnowledge}:
    \[ P_1 \rightarrow TT \rightarrow EE \rightarrow P_2 \]
  $P_1$ denotes some ``initial'' problem situation (in our case,
  \pr{b}); $TT$ denotes the tentative theories invented (somehow)
  as candidate solutions (\th{t}, \th{c}, and, in fact, the
  entire continuum between them); $EE$ denotes the process of
  criticism, testing, and error elimination (whereby we concluded
  that \th{t} was, for the time being at least, decisively
  better corroborated than any of its competitors); finally, this
  results in the establishment of a {\em new\/} problem situation
  $P_2$ (identified here with the emergence, and recognition, of
  \pr{d}).}
This is essentially the point made earlier, that the problem
situation perceived by Paley was not (necessarily) quite
identical with that perceived by Darwin.

Contrariwise, for a Creationist (in the sense of one who rejects \th{t}),
\pr{d} simply does not arise; some {\em other\/} problem(s)
certainly do arise, but not \pr{d}. To this extent, the
Creationist ``debate'', whatever its subject matter, is not about
\pr{d}; and especially, it is not about deciding between
competing solutions to \pr{d}.  So, Creationism {\it simpliciter}
will play no further \role\ in this discussion (though some
related theories will still have to be considered).
\citeAD[Essay~17, p.~234]{Gould:Urchin} has previously made
essentially this same point.

I shall present the proposed solution to Darwin's problem based
on the abstract formulation of Darwinism given in
\cciteAD{McMullin:DarwinianOntology} (I rely particularly on the
notion of a {\em Similarity-lineage\/}, or {\em S-lineage,}
introduced there; the discussion which follows will be
almost unintelligible except by reference to that concept). I claim
that this is essentially the solution offered by Darwin himself.
However, for reasons which should become clear, I do not proceed
directly to this solution, but instead build up to it in a number
of distinct steps.

\subsection{Contemporary Selection (\th{cs})}

\begin{quote}
  However, Darwin's own most important contribution to the theory
  of evolution, his theory of natural selection, is difficult to
  test.  There are some tests, even some experimental tests; and
  in some cases, such as the famous phenomenon known as
  ``industrial melanism'', we can observe natural selection
  happening under our very eyes, as it were.  Nevertheless,
  really severe tests of the theory of natural selection are hard
  to come by, much more so than tests of otherwise comparable
  theories in physics or chemistry.

  \citeAD[p.~344]{Popper:EmergenceOfMind}
\end{quote}

Consider the following:
\begin{description}

\item[\th{cs} (Contemporary Selection):] The {\em
contemporary\/} biological world is such that, with organisms
regarded as {\em actors}, these actors form coherent S-lineages,
with well defined S-values,\footnote{S-value is my term for what
  is conventionally called {\em fitness\/} in population
  genetics.  It is a quantitative measure of the ``reproductive
  success'' of an S-lineage, given particular environmental
  constraints. It must have the property that, when all other
  conditions for S-lineage selection are satisfied, the
  difference in S-values of the competing S-lineages is
  predictive of both the direction and the rate of selective
  displacement. The term is originally defined in
  \cciteAD{McMullin:DarwinianOntology}.}
 which can (and do) selectively displace each other.

\end{description}

Informally, \th{cs} amounts to the claim that Darwinian (S-lineage)
selection is now occurring in the biological world, with
biological organisms as actors.  For the moment I make no comment
about the nature of S-creation (except that some such events
occur).  In particular I do not (yet) specify that it is {\em
unjustified}. In my terms, this is the distinction between an
actor {\it per se\/} and a {\em Darwinian\/} actor (D-actor). I
shall return to this in section~\ref{unjustified} below.

I stipulate certain things (which seem relatively uncontentious)
without further discussion:
\begin{itemize}

\item Organisms do procreate---indeed, they provide the
paradigmatic case of procreation.

\item Organisms are capable, in suitable
circumstances, of exhibiting the required (Malthusian) growth.

\item Their numbers are, in fact, limited by resource
availabilities (possibly among other things).  It follows that
there must be competition between, and especially within,
species, for at least some resources.

\end{itemize}

In themselves, of course, these facts do not establish that
S-lineage selection occurs. To begin with, we further require
that there must exist S-classes---which is to say classifications
of organisms such that:
\begin{itemize}

\item With ``high'' frequency, an offspring organism should be a
member only of S-classes to which at least one of its parent(s)
belong (S-founders should be relatively rare, but must occur
occasionally). This guarantees the ongoing formation of coherent
S-lineages, between which selection {\em may\/} (or may not)
operate.

\item At least some S-classes should be such that corresponding
S-lineages will selectively displace each other, in a manner which is
at least approximately deterministic (in given environmental
conditions); which is to say that selection will, in fact, operate.

\end{itemize}

The satisfaction of the first of these conditions depends
crucially on the nature of inheritance in biological organisms.
The modern theory of biological inheritance, grounded in
molecular biology, is elaborate and complex.  For my immediate
purposes I shall consider just the following relatively simple
form:
\begin{description}

\item[\th{i} (Inheritance):] Organisms exhibit at
least some characteristics (termed {\em heritable characters\/})
which have the following properties: with ``high'' frequency, an
organism will exhibit one of these characters {\em only\/}
if at least one of its parent(s) were similarly characterised;
however, with ``low'' frequency an organism may exhibit a
completely novel character, i.e.\ one not exhibited by any
of its parent(s) (but which can, nonetheless, be inherited by its
offspring).

\end{description}

In this form, \th{i} consists in little more than the assertion
that there do, in fact, exist characteristics of biological
organisms which, if used to classify the organisms, will satisfy
the {\em inheritance\/} condition for S-classification, and the
{\em novelty\/} condition for continuing evolution of a
\mbox{(D-)lineage.} However there are some subtle ideas concealed behind
the apparent simplicity of this formulation of \th{i}.

First note carefully that there {\em is\/} some worthwhile
empirical content in \th{i}: it need not be true (even though it
is ``almost'' inherent in our very conception of what a
biological organism is). For example, we can (just about) conceive
of a world in which there are living organisms, and in which the
organisms procreate, but where there are {\em no\/}
characteristics whose inheritance is consistently (with ``high
frequency'') constrained in the way prescribed by \th{i}---for
example, if ``elephants'' gave ``birth'' to ``mice'' or
``bacteria'' (or arbitrary other ``classes'' of organism) more or
less as commonly as to other ``elephants''.  Somewhat more
plausibly, we can imagine that there could be characteristics
whose inheritance is constrained as required by \th{i} (which is
to say, there would exist coherent S-lineages), but where
no {\em new\/} characteristics of this sort ever come into existence.
This would effectively amount to the existence of static or
immutable biological species, contrary to \th{t}; to this extent,
\th{i} can be viewed as being, at least partially, a consequence
of \th{t}.

Secondly, note that \th{i} takes the form of a {\em
prohibition\/} on the nature of inheritance, rather that a
positive affirmation.  That is, we do not explicitly say that
heritable characters {\em will\/} be inherited by offspring
(not even if {\em both\/} parents share a particular
character); rather we say that novelty (of heritable
characters) is rare---that, almost always, an organism will
{\em not\/} exhibit a character unless at least one parent
already exhibited it.  Of course, given that, in practise, an
offspring has to exhibit {\em some\/} complement of heritable
characters (in order to qualify as an organism---a member of a
particular class of biological actors---at all), it will be the
case that, almost always, an offspring will exhibit some (perhaps
even ``most'') parental characters; the point is simply that
\th{i} does not require that any {\em particular\/} character be
inherited by any {\em particular\/} offspring.

Indeed, there could, in principle, be good, heritable, characters,
satisfying \th{i}, which are nonetheless ``rarely'' inherited by
offspring; this would simply mean that an S-lineage identified by
such a character would have relatively low S-fecundity---which
may mean that it is not viable at all (i.e.\ be incapable of
exhibiting Malthusian growth, in {\em any\/} circumstances), or
that it will be displaced relatively easily by competitors.  However,
none of this would detract from the heritable nature of such a
character.

Finally, note that I am deliberately using the term {\em
character\/} here, and not the modern term {\em gene} which might
seem to be essentially equivalent.  This is a fine terminological
distinction, but an important one.

``Character'' is the term introduced in Mendel's original paper
(or, more accurately, introduced in the English translation of
that paper, made by the Royal Horticultural Society of London,
\ociteAD{Mendel:PlantHybridization}).  By this Mendel
meant simply {\em any\/} characteristic of an organism which ({\it
inter alia\/}) satisfies \th{i} (there are additional constraints
on what I shall subsequently call {\em Mendelian\/} characters,
but that will be clarified in due course).  He did {\em not\/}
speculate as to the underlying {\em mechanisms\/} whereby such
characteristics are exhibited by organisms, or are inherited.
Davern makes this point in his introduction to the reprinting of
Mendel's paper, cited above:
\begin{quote}

  \ldots\ as Robert C.~Olby has recently pointed out \ldots\
  Mendel did not infer the existence of {\em
  determinants\/} of heredity that {\em conserved their
  integrity\/} in hybrids and successive generations.  Instead,
  Mendel argued that the parental characteristics {\it per se\/}
  were conserved in the hybrid generations.  While he apparently
  failed to distinguish between the potential and actual when it
  came to accounting for the manifestation of parental
  characteristics, his discoverers in 1900 certainly made this
  distinction.  They explained the phenomenon of dominance and
  the patterns of segregation for a contrasting characteristic
  pair in the hybrid generations in terms of genetic determinants
  or {\em genes}, thus clearly distinguishing between genotype
  and phenotype.

  \citeAD[p.~6, emphasis added]{Davern:Heredity}
\end{quote}

Contrary to the confident tone struck here by Davern, I take the
view that the step from overt characteristics of organisms to
supposed ``determinants'' of these characteristics is distinctly
problematical; it is associated, in Jensen's terms, with a
dangerous (if not actually erroneous) ``reification'' of the gene
\cciteAD{Jensen:Preconditions}.  This is a complex topic which I
shall not, however, pursue here; for the moment, it is sufficient
to note that I make no claims (in \th{i} or otherwise) about the
underlying mechanisms whereby heritable characters are exhibited
and/or inherited.

It follows, incidentally, that I do not restrict ``character'' to
denote the nucleotide sequence of some fragment of DNA (i.e.\
what is now typically regarded as a ``gene''). My ``character'' {\em
could\/} refer to a gene in this sense, but it could equally
refer to at least some ``phenotypic traits''.  The exhibition of
a character, in my terms, could (for example) correspond to the
presence of a particular protein or a particular organ, or the
performance of a particular behaviour etc.  In these cases there
may be some simple correlation between what I call a character
and a gene, but this is not necessarily the case.  Thus, for
example, karyotypic characteristics (such as chromosome number)
could be heritable characters in my terms. I require {\em only\/}
that it be rare for an organism to exhibit such a character
unless at least one of its parents already exhibited it.  This is
sufficient for the establishment of S-lineages (though it does
not, in itself, guarantee S-lineage {\em selection}).

I shall take it that \th{i} is well corroborated.

The next question is whether any S-lineages, based on heritable
characters, can potentially ``compete'' with each other, such
that one can competitively eliminate the other.  This requires
three conditions:
\begin{enumerate}

\item S-lineages should be limited in S-size by availability of
some resources.

\item At least some S-lineages should be so limited by
the {\em same\/} resources.

\item At least some such S-lineages should be constrained such that
their memberships cannot (completely) converge.  That is to say,
their memberships are constrained not to be equal.

\end{enumerate}

Together these three conditions ensure that there exist some
S-lineages whose S-sizes are so related that, {\em if\/} one
persistently increases, the other must, at some point, reduce and
thus be ultimately eliminated---i.e.\ some S-lineages may
selectively displace others.  Note that these conditions are thus
necessary but not sufficient for S-lineage selection.

I take it that the validity of the first two of these conditions
is unproblematic in the biological world and does not require
further discussion.  However, the third condition requires much
more careful consideration.

We can certainly say that if certain S-lineages are inherently
disjoint (their intersections are empty) then, trivially, their
memberships cannot be equal.  Thus, for asexually reproducing
organisms (i.e.\ where S-procreation is unimodal), where the
S-lineages are, by definition, disjoint, we can say that
condition~3 above will be satisfied.  More generally, if the
S-lineages consist of organisms from distinct (sexually
reproducing) species (where distinct species are taken to be
reproductively isolated, by definition), then, by a similar
argument, they will be disjoint, and condition~3 will again be
satisfied.  I therefore take it that {\em at least\/} these kinds
of exclusion between S-lineages can occur in the biological world
(though, of course, these are precisely the cases where it may be
difficult to establish that the S-lineages involved rely on the
same resources).

The situation of S-lineages within a single (sexually
reproducing) species is more complex, though it is (arguably) the
more important. Certainly, such S-lineages will, almost by
definition, share many of the same resources, which is to say
that condition~2 above can be almost trivially satisfied.  But
since these S-lineages are not reproductively isolated from each
other, they need not, and generally will not, be disjoint; so it
is not at all clear that condition~3 can be satisfied in such
cases.

If it were the case that heritable characters could, in
general, be divided into sets such that the characters in
any single set are mutually exclusive (i.e.\ any given organism
could exhibit only one of the characteristics in the set), then
S-classes defined by reference to distinct elements of any such
set would be disjoint, and so also would be the corresponding
S-lineages.  Again, condition~3 would be satisfied.
Unfortunately (?) it turns out that heritable characteristics do
{\em not}, in general, satisfy such mutual exclusion
conditions under sexual reproduction.\footnote{There are, of
  course, exceptions; for example, in species with fully
  differentiated sexes ({\em dioecious\/}
  species---\ociteAD[p.~236]{MaynardSmith:EvolutionaryGenetics}),
  the heritable characters ``male'' and ``female'' do generally
  satisfy a simple mutual exclusion condition, and do establish
  disjoint lineages. This is true even though, from a genetic
  point of view, the heterogametic (typically male) sex carries
  genes ``for'' both sexes.}

However, it transpires that at least some heritable characters
show a relationship which, although it is weaker than mutual
exclusion, can still be shown to suffice for condition~3 to be
satisfied (in suitable circumstances).  I shall discuss only the
simplest case, but emphasize that this is only an example:
similar reasoning may well apply to different and/or more complex
cases. This simplest case corresponds essentially to a pair of
what I shall call strictly {\em Mendelian\/} characters, in
diploid organisms.  These are heritable characters which are
associated or correlated with distinct (Mendelian) genes at a
single genetic locus, in a species of sexually reproducing
diploid organisms.

A pair of such Mendelian characters is distinguished by the
following properties:
\begin{itemize}

\item Firstly, every organism (of the given species) exhibits at
least one of the pair, and may exhibit both. I denote the two
characters as A and B; thus any given organism can be labelled
AA (exhibits A but not B), BB (exhibits B but not A) or AB
(exhibits both A and B). In conventional genetic terms, AA and BB
correspond to the two homozygotes, AB to the heterozygote. I
assume the heterozygote to be distinguishable as such (in the
case of ``complete'' dominance of one gene over the other, this
may require a relatively elaborate process, such as a
generation of controlled breeding, or DNA
sequencing etc.; such methodological difficulties, though
possibly severe, have no conceptual significance here).

\item Secondly, the character(s) exhibited by an offspring are
found to be randomly distributed, approximately according to
table~\ref{mendeltab} (the distributions in this simplest case are
symmetrical with respect to the two parents; redundant entries
are therefore omitted from the table).

\end{itemize}

\begin{table}
\begin{center}
\begin{tabular}{|l|l||l|l|l|} \hline
  \multicolumn{2}{|c||}{PARENTS}  &
  \multicolumn{3}{c|}{OFFSPRING} \\ \hline
  \multicolumn{2}{|c||}{ }
        & AA   & AB   & BB   \\ \hline
AA & AA & 1.00 & 0.00 & 0.00 \\
AA & AB & 0.50 & 0.50 & 0.00 \\
AA & BB & 0.00 & 1.00 & 0.00 \\ \hline
AB & AB & 0.25 & 0.50 & 0.25 \\
AB & BB & 0.00 & 0.50 & 0.50 \\ \hline
BB & BB & 0.00 & 0.00 & 1.00 \\ \hline
\end{tabular}

\caption{Mendelian Inheritance}
\label{mendeltab}
\end{center}
\end{table}

We see that, according to table~\ref{mendeltab}, the characters A
and B do satisfy \th{i}, namely that an offspring will generally
exhibit A (or B) only if at least one parent exhibited A (or B).
Again, note carefully that I do not assert that {\em all\/}
heritable characters obey a table such as the above (are
Mendelian); there are many possible complications which I shall
not pursue.  I merely claim that at least {\em some\/} heritable
characters (namely, those called Mendelian) behave in this way.

Formally, this table could be interpreted as a stronger or more
explicit form of \th{i}, for the case of sexually reproducing
diploid organisms.  I shall take it that this augmentation
of \th{i} is well corroborated and need not be critically
examined here.\footnote{I note, in passing, that the results of
  Mendel's own original, pea breeding, experiments
  \cciteAD{Mendel:PlantHybridization} actually provided almost
  ``too'' good a corroboration, to the extent that there has been
  some suspicion that Mendel adjusted some doubtful or
  intermediate results so as to yield just the expected outcome;
  but that, in any case, the theory has effectively withstood
  very severe subsequent, independent, tests
  (\ociteAD[pp.~88--89]{Hardy:LivingStream};
  \ociteAD[pp.~33--34]{Gribbin:DoubleHelix}).}

I can now adopt the following (putative) S-classes:
\begin{description}

\item[S-class A:] All organisms exhibiting A (i.e.\ all organisms
labelled AA or AB).

\item[S-class B:] All organisms exhibiting B (i.e.\ all organisms
labelled BB or AB).

\end{description}

By inspection of the table, we can see that these S-classes then
satisfy the inheritance condition on S-classification, namely
that an offspring will generally be a member only of S-class(es)
of which at least one S-parent is a member (S-creation will be
relatively rare).  Note that this would not hold if, say, we
considered AA, BB, and AB organisms to define distinct classes: for
if AA mates with BB (for example) the outcome will be consistently
(probability 1) AB i.e.\ of a different class to either parent
relative to such a classification.

As anticipated, the proposed S-classes are not disjoint, and so
the corresponding S-lineages will not, in general, be disjoint
either.  However, changes in the S-sizes of the two S-lineages
{\em will\/} be more or less coupled, according to the
restrictions implied by the table above.  Our problem is to
establish whether this coupling is such that condition~3 above for
S-lineage selection (non convergence of S-lineages) can be
satisfied.

The exact effect of the coupling will be stochastic and will also
depend on the mating pattern (e.g.\ are AA organisms more likely
to mate with other AA organisms than AB or BB?). However, for my
immediate purposes I require only to establish the {\em
possibility\/} that this coupling can prevent convergence of
the two S-lineages.  This can be achieved by considering just a
single (plausible?) case: random mating, in a population which is
large enough that the proportions of offspring will be more or
less deterministically related to the probabilities indicated on
the table.  In this case it can be shown that the {\em
relative\/} proportions of organisms produced in each generation
will consistently be in a so-called {\em Hardy-Weinberg\/}
ratio \cciteAD[Chapter~3]{MaynardSmith:EvolutionaryGenetics}; that
is, the (relative) numbers of organisms labelled AA, AB and BB will
consistently be in ratios which are of the form
$p^2 : 2pq : q^2$ respectively, where $p$ and $q$ are parameters of the
population which are potentially time varying but are always such
that $0 \leq p,q \leq 1$ and $p + q = 1$. $p, q$ would normally
be interpreted as the total relative densities of the {\em
genes}, with which the characters are (putatively) correlated, in
the {\em gene-pool}.

Note that, as pointed out by Maynard Smith, the Hardy-Weinberg
form of ratio will be achieved after one generation of random
mating, even if the parents were not in this ratio. It will
therefore be consistently maintained (as measured by the relative
numbers of offspring {\em born}, as opposed to, say, surviving to
maturity), even while $p$ and $q$ are changing---for example due
to selection.  My claim here---that a ratio of the Hardy-Weinberg
{\em form\/} will be consistently maintained, even while
selection is in progress---should not be confused with the
closely related, but distinct, idea that the {\em specific\/}
Hardy-Weinberg ratio will be stable (the Hardy-Weinberg {\em
equilibrium\/}) if $p$ and $q$ remain constant.

I assume that there is a single S-lineage present of each of the
two S-classes (A and B). Let $S_A$ and $S_B$ denote the relative
S-sizes of these two S-lineages (i.e.\ as fractions of the total
population of organisms; for simplicity, I assume this total
population size to be fixed).  Let $R_{AA}, R_{AB}, R_{BB}$ denote
the relative proportions of AA, AB and BB organisms respectively.
Note that, because the two S-lineages are not disjoint, we {\em
cannot\/} say that $S_A + S_B = 1$, and thus cannot (directly)
conclude that an increase in one must necessarily be associated
with a reduction in the other. Conversely, note that classes
based on AA, AB, and BB {\em would\/} be mutually exclusive, and
we {\em can\/} say that $R_{AA} + R_{AB} + R_{BB} = 1$; but,
since these do not serve to label S-classes (i.e.\ do not give
rise to coherent S-lineages) we cannot use this as our basis for
establishing the possibility of S-lineage selection.

However, we {\em can\/} now argue as follows:
\begin{eqnarray*}
R_{AA}  & =     & p^2 \\
R_{AB}  & =     & 2pq \\
        & =     & 2p(1-p) \\
R_{BB}  & =     & q^2 \\
        & =     & (1-p)^2
\end{eqnarray*}

\begin{eqnarray*}
S_A     & =     & R_{AA} + R_{AB} \\
        & =     & p^2 + 2p(1-p) \\
        & =     & 2p-p^2 \\
\Rightarrow \dd{S_A}{p}     & = & 2-2p
\end{eqnarray*}

\begin{eqnarray*}
S_B     & =     & R_{AB} + R_{BB} \\
        & =     & 2p(1-p) + (1-p)^2 \\
        & =     & 1-p^2 \\
\Rightarrow p^2                 & =     & 1-S_B \\
\Rightarrow 2p \dd{p}{S_B}      & =     & -1 \\
\Rightarrow \dd{p}{S_B}         & =     & -1/2p
\end{eqnarray*}

\begin{eqnarray*}
\dd{S_A}{S_B}   & =     & \dd{S_A}{p} \cdot \dd{p}{S_B} \\
                & =     & (2-2p)(-1/2p) \\
                & =     & 1-1/p \\
                & \leq  & 0 \;\;\forall\; p \leq 1
\end{eqnarray*}

That is, for any pair of S-lineages whose relative S-sizes are
(for example) consistently constrained by the Hardy-Weinberg
ratio, a change in the S-size of either one will necessarily be
accompanied by an opposite (though generally unequal) change in
the S-size of the other.  This means precisely that the two
S-lineages, though they may intersect, cannot converge. Thus, for
such S-lineages (at least), condition~3 above, for the
possibility of S-lineage selection (non-convergence of the
S-lineages) will be satisfied.

To review briefly: the discussion so far has established that, under
our current, well corroborated, theory of inheritance (\th{i}) in
biological organisms, there exists the {\em possibility\/} for
the formation of coherent S-lineages whose sizes are so coupled
that they {\em could\/} exhibit S-lineage selection.  This is
true in general of S-lineages whose organisms are not
interbreeding (because they are asexual, or of different sexual
species), and is true for at least {\em some\/} S-lineages within
single interbreeding (sexual, single species)
populations---namely where the characters are Mendelian; I
emphasize again that I have not argued, and do not claim, that
strictly Mendelian characters provide the {\em only\/}
possibility for S-lineage selection within interbreeding
populations.

But this is not yet sufficient to establish that S-lineage
selection either can or does take place in the biological world.
We further require that at least some heritable characters be
sufficiently well correlated with the S-values of the
corresponding S-lineages that the S-sizes of some will grow more
or less deterministically (at the expense of others).  That is,
we must recognise that there could exist characteristics which
are heritable (perhaps even Mendelian) but yet have no particular
effect, one way or another, on the relative S-mortality or
S-fecundity of the S-lineages which are so distinguished. Such
S-lineages would, of course, still grow or shrink but these
effects would be essentially capricious (so-called {\em random
drift\/}), and could not be interpreted as examples of S-lineage
{\em selection.}

This is a very difficult question to answer; and one must beware
of accepting a simplistic answer which effectively avoids the
problem.  Thus, it has been established, by experiments involving
artificial selection, that biological organisms exhibit a very
wide range of heritable characters;\footnote{I accept this fact,
  but caution against its exaggeration; thus, for example, I
  doubt that the following claim could be effectively defended:
  ``The fact that artificial selection works almost every time it
  is attempted indicates that there is genetic variation in
  populations {\em for virtually every characteristic of the
  organism}'' \cciteAD[emphasis
  added]{Ayala:MechanismsOfEvolution}.  I say this simply because
  a phrase like ``virtually every characteristic of the
  organism'' seems to me hardly meaningful.}
but this does not, {\em in itself,\/} guarantee that any of them
are such as to result in selection.

Indeed, we should be wary of {\em any\/} argument based directly
or exclusively on this kind of artificial selection experiment,
{\em if\/} the experiment relies on amplifying some pre-existing variation
in a population; for the whole point of selection (as {\em I\/}
have used the word at any rate) is that, if it operates, it {\em
eliminates\/} certain variations; so variations we now observe
cannot {\em generally\/} be variations which have supported
selection in the past.  In evaluating the significance of such
experiments we should strictly restrict attention to only those
heritable characters which have been experimentally observed to
arise ``spontaneously'' (i.e.\ S-creation events).  Darwin
himself implied something of this sort when he wrote:
\begin{quote}

  This preservation of favourable variations and the rejection of
  injurious variations, I call Natural Selection.  Variations
  neither useful nor injurious would not be affected by natural
  selection, {\em and would be left a fluctuating element,} as
  perhaps we see in the species called polymorphic.

  Darwin\\
  \cciteD[Chapter~IV, emphasis added]{Darwin:TheOriginOfSpecies}

\end{quote}

However, the decisive corroboration of the {\em possibility\/}
of S-lineage selection (in the biological world) does not, in
fact, rely on artificial selection experiments of this sort.  It
relies instead on the actual observation of the phenomenon in
{\em natural\/} biological populations. Various cases have now
been very well corroborated; the examples most commonly cited
are the spontaneous development of industrial melanism, and of
insecticide resistance (e.g.\
\ociteAD[pp.~90--92]{Stebbins:OrganicEvolution};
\ociteAD[pp.~42--45]{MaynardSmith:EvolutionaryGenetics}).

I take it, in conclusion, that the occurrence of S-lineage
selection, based on S-classes identified by reference to
heritable characters (in the sense of \th{i}), is very well
corroborated; which is to say, that \th{cs} has withstood the
most severe tests to which it has been (so far) subjected.

\subsection{Historical Selection (\th{hs})}

\label{hstry}

Consider now the following extension of \th{cs}:
\begin{description}

\item[\th{hs} (Historical Selection):]  The biological world has
{\em always\/} been such that, with organisms regarded as {\em
actors\/}, these actors have formed coherent S-lineages, with
well defined S-values, which have selectively displaced displaced
each other. All (inate) organismic attributes which have shown
sustained growth in the phylogenetic tree, have done so by virtue
of being positively correlated (directly or otherwise) with
S-value.

\end{description}

\th{hs} thus tentatively extends the scope of \th{cs}, from its
(relatively) well corroborated application in the present, into
the indefinite past.
This kind of extension of present causes into the past was a
central element in the {\em uniformitarianism\/} of the geologist
Charles Lyell and, subsequently, Darwin himself (see, for
example, \ociteAD[Essay~9]{Gould:HensTeeth}).

This step is, of course, essential if we are ultimately to
address \pr{d}, for that problem is explicitly concerned with the
historical formation of the phylogenetic tree.  Nonetheless, it
is well to keep \th{cs} and \th{hs} clearly separated, for
they require quite different approaches to their corroboration.

I have termed \th{hs} an extension of \th{cs}, which is to say
that \th{cs} is entailed by \th{hs}, and, were it to be refuted,
\th{hs} would likewise also be refuted; but given that \th{cs}
has, so far, withstood its tests, we must then consider to what
extent \th{hs} can be {\em separately\/} tested or corroborated.
That is, is there any specific means of testing, not just that
selection is operating now, but that it has operated into the
indefinite past? The answer to this rests on whether we can make
any predictions about observable attributes of organisms (either
living now, or fossilised) based solely on \th{hs}.

To achieve this, note that \th{hs} explicitly affords no means
for the sustained, cumulative, growth of any organismic (or, more
properly, S-lineage) attribute {\em except\/} that it be
correlated with S-value.  Or, to put it another way, if it could
be established that any organismic attribute had shown sustained,
cumulative, phylogenetic growth, but was either uncorrelated, or
negatively correlated, with S-value, then this would, {\it ipso
facto}, be a refutation of \th{hs}. As Darwin put it (where his
``species'' should, in this particular case at least, be read as
equivalent to my ``S-lineage''):
\begin{quote}
  If it could be proved that any part of the structure of any one
  species had been formed for the exclusive good of another
  species, it would annihilate my theory, for such could not have
  been produced by natural selection.

  \citeAD[Chapter~VI, pp.~228--229]{Darwin:TheOriginOfSpecies}
\end{quote}

In a similar vein, Maynard Smith has offered the following
scenarios:
\begin{quote}

\ldots\ if someone discovers a deep-sea fish with varying numbers
of luminous dots on its tail, the number at any one time having
the property of being always a prime number, I should regard this
as rather strong evidence against neo-Darwinism.  And if the dots
took up in turn the exact configuration of the various heavenly
constellations, I should regard it as an adequate disproof.

\citeAD[p.~86]{MaynardSmith:StatusOfNeoDarwinism}

\end{quote}

So \th{hs} is, in principle at least, potentially refutable.

Noting that no organisms with the clearcut peculiarities
suggested by Maynard Smith have, in fact, been reliably reported
we may say that, to this extent, \th{hs} has successfully stood
up to testing.  Indeed, we can go somewhat further, and note that
many organismic characteristics {\em can\/} plausibly be
interpreted as being positively correlated with S-value.  As
Maynard Smith points out:
\begin{quote}
  \ldots if it were not the case that most organs can readily be
  understood as contributing to survival [reduced S-mortality] or
  reproduction [increased S-fecundity], Darwinism would never
  have been accepted by biologists in the first place\ldots

  \citeAD[p.~87]{MaynardSmith:StatusOfNeoDarwinism}
\end{quote}

Alternatively, we can also approach this question from the other
direction and ask whether there exist organismic attributes whose
existence seems inexplicable {\em except\/} by an hypothesized
correlation with S-value.  This was a point emphasized by Darwin,
presumably because he had in mind the possibility of competing
theistic theories---which could easily account for the existence
of ``perfection'' in the biological world, but could offer no
explanation for evident ``imperfection''.  Thus, we have his
comment:
\begin{quote}

  Nor ought we to marvel if all the contrivances in nature be
  not, as far as we can judge, absolutely perfect; and if some of
  them be abhorrent to our ideas of fitness.  We need not marvel
  at the sting of the bee causing the bee's own death; at drones
  being produced in such vast numbers for one single act, and
  being then slaughtered by their sterile sisters; at the
  astonishing waste of pollen by our fir-trees;  at the
  instinctive hatred of the queen bee for her own fertile
  daughters; at ichneumonidae feeding within the live bodies of
  caterpillars; and at other such cases. The wonder indeed is, on
  the theory of natural selection, that more cases of the want of
  absolute perfection have not been observed.

  \citeAD[p.~445]{Darwin:TheOriginOfSpecies}

\end{quote}

However, notwithstanding these various facts, we must be somewhat
wary in evaluating the degree to which \th{hs} can be
successfully corroborated in such a manner.

A first problem is that there {\em do\/} exist evolutionary
phenomena which are {\it prima facie\/} refutations of \th{hs}, in
the form of so-called {\em orthogenetic trends}. These are trends
in organism lineages which seem to continue up to and beyond a point
where they are ``obviously'' detrimental to the organisms (and
thus the S-lineages) involved; if this is a correct interpretation
then it is definitely inconsistent with \th{hs}.\footnote{I
  restrict the use of the term ``orthogenesis'' to these cases,
  where the trend supposedly persists to the point of being
  detrimental to the organisms.  However, a {\em general\/}
  concept of ``trends'' in organism lineages can also be called
  orthogenesis---see, for example,
  \cciteAD{Popper:TreeOfKnowledge}. Such a weaker form
  of orthogenesis is certainly not inherently incompatible with
  \th{hs}; indeed Popper himself goes on to suggest a very
  general interpretation of the phenomenon which would be
  completely compatible with \th{hs} (provided always that the
  trend does not proceed to the point of being detrimental to the
  organism). I will not, therefore, refer further to this weaker
  concept.}

Gould graphically describes the problem as follows:
\begin{quote}

The theory of orthogenesis became a touchstone for anti-Darwinian
paleontologists, for it claimed that evolution proceeded in
straight lines that natural selection could not regulate.
Certain trends, once started, could not be stopped even if they
led to extinction.  Thus certain oysters, it was said, coiled
their valves upon each other until they sealed the animal
permanently within; saber-toothed ``tigers'' could not stop
growing their teeth or mammoths their tusks.

But by far the most famous example of orthogenesis was the Irish
Elk itself.  The giant deer had evolved from small forms with
even smaller antlers.  Although the antlers were useful at first,
their growth could not be contained and, like the sorceror's
apprentice, the giant deer discovered only too late that even
good things have their limits.  Bowed by the weight of their
cranial excrescences, caught in the trees or mired in the ponds,
they died.  What wiped out the Irish Elk?  They themselves or,
rather, their own antlers did.

\citeAD[Essay~9, pp.~84--85]{Gould:EverSinceDarwin}

\end{quote}

Gould is, of course, here acting as a Devil's advocate on behalf
of orthogenesis.  In the essay quoted above, he goes on to
discuss two quite plausible alternatives to orthogenesis as a
explanation of the undeniably enormous antlers of the Irish Elk.

Firstly, it may be an artefact of a correlation between body size
and antler size: Gould established that antler size seems to
increase as a superlinear function of body size---so that if
selection favoured increased body size (which is not {\em
im\/}plausible) then exaggerated antler size could result by
conventional selection, as long as the (presumed) disadvantage of
extreme antler size was outweighed by the advantage (whatever it
may be) of increased body size.  Such a correlation is known as
{\em allometry}. Although (as discussed by Gould) this solution
to the problem of orthogenesis (a problem in the context of
\th{hs}) was formulated in the 1930s by Julian Huxley, Gould
states that it had not actually been quantitatively tested---in
the case of the Irish Elk at least---until he himself came to do
so; but, in any case, the measurements he carried out did prove
consistent with the allometric explanation.

Secondly, Gould goes on to question the very claim that the large
antler size of the Elk was necessarily selectively
disadvantageous.  He points out that the antlers could have
played a \role\ in ritualised combat, where extremely large
sizes could quite plausibly have been favoured by selection (the
allometry argument {\em could\/} then run in reverse: there was
not necessarily any selective advantage in large body size {\it
per se\/} but increases in body size were correlated with the
increases in antler size which {\em were\/} selectively favored).
Gould is able to adduce some limited evidence in favour of this
hypothesis from detailed anatomical features of the antlers.

In any case, a definitive decision between these two explanations
is not necessary (and probably not even possible).  The point is
that the claim for an orthogenetic trend (not effectively
controlled by selection) has clearly not been established, and
\th{hs} emerges more or less unscathed.  Gould has elsewhere
similarly debunked the case of the coiled oysters
\cciteAD[Essay~30]{Gould:HensTeeth}.

However, while this deals with cases where evolution seems
positively to have run counter to selection, there is another
class of cases which demonstrate a quite different kind of
difficulty. These are organismic attributes which seem to demand
an explanation in terms of \th{hs} (due, for example, to their
complexity), but for which no consensus has yet emerged as to the
nature of such an explanation.

The primary example of this is, perhaps, the existence of sex (in
the sense of meiosis---not the existence of distinctive male and
female forms). This is evidently a very complex process, which
appears to have evolved over time; the {\em assumption\/} is that
it has done so through natural selection; but a definitive
explanation of why sex should have been thus favoured by natural
selection is lacking. In 1975 Williams went as far as to claim,
in this regard, that ``there is a sort of crisis at hand in
evolutionary biology'' \cciteAD[p.~v]{Williams:SexAndEvolution}.
More recently, Dawkins has stated that: ``The problem of what
sex is good for is as tantalizing as ever''
\cciteAD[p.~274]{Dawkins:NewSelfishGene}.

This does not, of course, represent a refutation of \th{hs}---but
it does perhaps indicate some degree of vulnerability.

A more subtle problem with the supposed corroboration of \th{hs}
arises due to the ease with which more or less {\em arbitrary\/}
organismic attributes can be argued to be positively correlated
with S-value. Thus while I stated above that no {\em
definitive\/} explanation of sex, in terms of correlation with
S-value, has yet been forthcoming, there is no shortage of more
or less plausible {\em hypotheses\/} (indeed, I shall comment
further on one in particular, in section \ref{unjustified}
below). Gould and Lewontin have discussed this general problem in
the form of what they call the {\em adaptationist programme\/}:
\begin{quote}

  We wish to question a deeply ingrained habit of thinking among
  students of evolution.  We call it the adaptationist programme,
  or the Panglossian paradigm \ldots\ This programme regards
  natural selection as so powerful and the constraints upon it so
  few that direct production of adaptation through its operation
  becomes the primary cause of nearly all organic form, function,
  and behaviour.

  \citeAD[pp.~584--585]{Gould:SpandrelsOfSanMarco}

  \bigskip
  \ldots\ if it [the invocation of natural selection] could be
  dismissed after failing some explicit test, then alternatives
  would get their chance.  Unfortunately, a common procedure
  among evolutionists does not allow such definable rejection for
  two reasons.  First, the rejection of one adaptive story
  usually leads to its replacement by another, rather than to a
  suspicion that a different kind of explanation may be required.
  Since the range of adaptive stories is as wide as our minds are
  fertile, new stories can always be postulated.  And if a story
  is not immediately available, one can always plead temporary
  ignorance and trust that it will be forthcoming \ldots\
  Secondly, the criteria for acceptance of a story are so loose
  that many pass without proper confirmation. Often,
  evolutionists use {\em consistency\/} with natural selection as
  the sole criterion and consider their work done when they
  concoct a plausible story. But plausible stories can always be
  told.

  \citeAD[pp.~587--588]{Gould:SpandrelsOfSanMarco}

\end{quote}

Following the adaptationist programme then, one could even,
conceivably, immunise \th{hs} against the discovery of Maynard
Smith's peculiar deep-sea fishes, whose luminous dots echoed
stellar constellations. We might, for example, speculate on the
existence of an ancestor which lived close to the surface, and
camouflaged itself by imitating the night sky. This seems
outrageous, but paleontological evidence would generally be far
too fragmentary to definitively refute it; or, in the unlikely
event that this {\em particular\/} story could actually be
refuted, another modified version could then be generated which
was immunised against the particular refutation. And so on.

Now it should be emphasized that Gould and Lewontin are not
attacking \th{hs} as such. Indeed they explicitly accept the
occurrence and importance of Darwinian selection (``\ldots\
Darwin regarded selection as the most important of evolutionary
mechanisms {\em (as do we)} \ldots''---\ociteAD[p.~589, emphasis
added]{Gould:SpandrelsOfSanMarco}). Their primary objective is to
deprecate a certain {\em style\/} of Darwinian theorizing---i.e.\
that which takes selection to be the necessary explanation of all
attributes of all organisms. Nonetheless, whatever their
motivation, their argument also serves to demonstrate that the
corroboration of \th{hs} (separately from \th{cs}) is, at best,
a somewhat fragile achievement.

I must repeat that I still consider \th{hs} to be definitely
testable, or refutable, {\em in principle}.  For example, we
could conceive of conducting a controlled experiment in which the
characteristics and life histories of all organisms within some
delimited environment are recorded, so that the all episodes of
S-lineage selection (if any) can be definitively established and
recorded. It would then be possible that examples of the
sustained, cumulative, growth of some inate organismic attributes
could be observed which were {\em not\/} attributable to the
(known) cumulative episodes of S-lineage selection.  This would
then represent a refutation of \th{hs}.  Of course, to represent
a severe test of \th{hs}, this experiment may have to be allowed
run in an environment comparable to the entire planet Earth, and
over a comparable (geological) timescale. Thus, although this is
a ``possible'', severe, test in principle, it is entirely
impractical.

The central difficulty in all of this is, of course, that the
empirical phenomena with which \th{hs} deals are of such a scale in
both time and space that they cannot generally be put into the
form of practically repeatable experiments. As Popper incisively
put it:
\begin{quote}

\ldots\ we have to add that the phrase {\it in principle\/} is a
very important restriction.  Neither Darwin nor any Darwinian has
so far given an actual causal explanation of the adaptive
evolution of any single organism or any single organ.  All that
has been shown---and this is very much---is that such
explanations might exist (that is to say, that they are logically
possible).

\citeAD[p.~267]{Popper:TreeOfKnowledge}

\end{quote}

In conclusion, \th{hs} has not been definitively refuted; but
equally, it should not be considered to be highly corroborated
(beyond what it inherits from the corroboration of \th{cs})
either.  Nonetheless it seems to be better corroborated that
any currently competing theory, and should be preferred (at least
for the time being).

\subsection{Organismic Darwinism (\th{d})}

\label{unjustified}

Consider (finally) the following theory:
\begin{description}

\item[\th{d} (Organismic Darwinism):]  The biological world is,
and has always been, a {\em D-system}
\cciteAD[Section~7]{McMullin:DarwinianOntology}, with organisms
functioning as D-actors. More particularly, S-creation in the
biological world is a form of {\em unjustified\/} variation (does
not involve anticipatory models predictive of the S-values of the
resulting S-lineages).

\end{description}

\th{d} is, in effect, a still stronger form of \th{hs}. It adds
the requirement that S-creation be unjustified, or unbiased, with
respect to S-value.  \th{d} claims not just that the biological
world involves (and has always involved) the operation of
S-lineage selection (with biological organisms as actors), but
that it is a D-system proper. \th{d} thus entails \th{hs} but not
{\it vice versa}.

It remains to consider the extent to which \th{d} can be tested,
over and above the testing of \th{cs} and \th{hs}.
The testing of \th{d} turns out to be rather difficult. We can
certainly say that no counter example has been definitively
demonstrated; but, as in the case of \th{hs}, given the
infinitesimal scale of practical experiments compared to the
reality of natural evolution, this cannot be ranked as especially
strong corroboration.

We can do somewhat better by considering the {\em mechanisms\/}
underlying the realisation of heritable characters (in modern
organisms at least). It seems that the origin of new characters
relies, in an essential way, on modification of certain more or
less isolable biochemical components---generally DNA molecules.
I shall term such modifications {\em mutations}, though my usage
will be somewhat more generalised than is conventional.

The claim that S-creation is a form of unjustified variation is a
version of the standard Darwinian hypothesis that the occurrence
of new, heritable, characters is ``random'' (it must be stressed
here that this is a very special usage of the word ``random''
which has little, if anything, to do with conventional
probability theory or stochastic processes). It has been generally
supposed that our modern understanding of the chemical basis of
heredity definitively rules out any involvement of anticipatory
models in the occurrence of mutations. Thus, we have, for
example, Maynard Smith:
\begin{quote}

It is sometimes said---usually by critics of Darwinism---that
mutation is random.  Now `random' is a notoriously difficult word
to define.  I think that most scientists, when they speak of an
event being random, mean that it would not be efficient to
enquire into its causes, either because they think that the cause
is in principle unknowable, as in quantum theory, or because it
would be too much trouble to discover.  In this sense, mutation
is certainly not random.  A lot is known about the causes of
mutation---that is of changes in DNA.  However, most geneticists
do hold two things to be true of mutation.  First, there is no
restriction on the kinds of changes in sequence of DNA molecules
that can arise by mutation, any more than there is a restriction
on the sequence of letters that can be produced by a typewriter.
Second, if a mutation is caused by a particular agent---for
example X-rays---it is not in general true that the effect of the
mutation will be to make the organism more resistant to the
causative agent: in brief, mutations are not adaptive.

\citeAD[p.~40]{MaynardSmith:Structuralism}
\end{quote}

Similarly, and explicitly citing the notion of anticipation,
Dawkins has expressed this idea as follows:
\begin{quote}
There is randomness and randomness, and many people confuse
different meanings of the word.  There are, in truth, many
respects in which mutation is not random.  All I would insist on
is that these respects do {\em not\/} include anything equivalent
to anticipation of what would make life better for the
animal.\footnote{Of course, I would say ``S-lineage''
  rather than ``animal'' here.}

\citeAD[p.~306]{Dawkins:BlindWatchmaker}
\end{quote}

However, this straightforward view has recently been challenged.
To explain this I must first elaborate slightly on the mechanisms
whereby mutations can take place.  It seems that these can be
classified as follows:
\begin{enumerate}

\item Spontaneous, and accidental, modification arising from
uncontrolled effects.  This could include accidental
errors during replication.

\item Natural, systematic, modification of the genetic material,
typically, but not exclusively, in the course of sexual
reproduction. This particularly refers to recombination (during
meiosis) and the union of gametes in fertilisation (syngamy).
However, various other systematic modifications can occur, even
in organisms which do not exhibit a sexual cycle as such
\cciteAD[Chapter~10]{MaynardSmith:EvolutionaryGenetics}.

\item Artificial, systematic, modification of the genetic
material. By this I essentially mean the modern practise of {\em
genetic engineering}.

\end{enumerate}

The first of these, by its (hypothesized) unsystematic nature,
precludes any dependence on anticipatory models.  The third is
included for completeness, but is evidently irrelevant to the
corroboration (or otherwise) of \th{d}: (human) genetic engineers
have not been operative over the requisite geological time
scales.

The second case is much more difficult.

Firstly, it has been suggested that, in a certain sense, the
genetic material of biological organisms may constitute a complex
ecology {\em in its own right}. This is the implication, for
example, of recent theorizing in relation to so-called {\em
selfish DNA\/} (\ociteAD{Doolittle:SelfishGenes};
\ociteAD{Orgel:SelfishDNA}).\footnote{Selfish DNA should not be
  confused with Dawkins' \cciteD{Dawkins:SelfishGene} ``selfish
  genes''; see the discussion by Gould, where he argues {\it
  inter alia\/} that ``the theories of selfish genes and selfish
  DNA could not be more different in the structures of
  explanation that nurture them'' \cciteAD[Essay~13,
  p.~174]{Gould:HensTeeth}.}

If this viewpoint is taken seriously then it seems to at least
open up the possibility that fragments of DNA may incorporate, or
have associated with them, ``inate knowledge'' (anticipatory
models) of the effects of certain genetic processes, and that
this would then affect the participation of the DNA fragments in
such processes.  This sounds like an acceptance that ``mutation''
could be informed by anticipatory models and would therefore not
be random or unbiased in the sense required by \th{d}.

However, such an interpretation would be premature.

While I admit the possibility that some such DNA level
anticipatory models might conceivably exist, the scope of such
models may be limited to the effects on the DNA fragments
themselves---and {\em not\/} on the organisms they may happen to
be embedded within. If this were the case then the genetic
modifications which occur, be they ever so systematic, would
still be ``unjustified'' in the sense required by \th{d}; thus we
must concentrate only on the latter question, of the anticipatory
relationship (if any) between mechanisms for genetic modification
and the S-value of the resulting (organismic) S-lineages.

Now the general notion that only certain evolutionary changes, or
mutations, are {\em possible\/} (relative to a given starting
point), and that this strongly constrains the overall path of
evolution, is a fairly common theme.  For example, consider the
following, from Waddington, introducing what he calls
evolutionary ``archetypes'':
\begin{quote}

  You don't just get a ``horse archetype,'' a ``dipteran
  archetype,'' but you get a ``horse family archetype,'' {\em
  with inbuilt characteristics of directions in which
  evolutionary change can easily go.}

  Waddington\\
  \cciteD[p.~115, emphasis added]{Waddington:Archetypes}
\end{quote}

Maynard Smith has more recently considered somewhat similar ideas
under the name ``structuralism''---the view that ``only certain
kinds of structural change are possible to particular organisms''
\cciteAD[p.~40]{MaynardSmith:Structuralism}.

But the gist of these ideas is that, relative to some given
starting point, only certain other points will be mutationally
accessible.  It is true that, on such a view, depending {\em
only\/} on the distribution and characteristics of these, and
their relative accessibility, it may well happen that, relative
to certain points, mutations leading to higher S-value may be
more ``likely'' to occur than those leading to lower S-value.  But
this would not, in itself, indicate the operation of any
anticipatory model in the mutational process, and would not
impact on \th{d} as stated.

However, various workers have taken the {\em further\/} step
of suggesting, more or less explicitly, that organismic evolution
is informed by anticipatory models. Thus we have the following
from D.T.~Campbell:
\begin{quote}
  Bisexuality, heterozygosity, and meiotic cell division
  represent a secondary invention increasing the efficiency of
  the process [of organismic evolution] through increasing the
  range of variation and the rate of readjustment to novel
  environments.

  Campbell\\
  \cciteD[pp.~381--382,
  emphasis added]{Campbell:BlindVariationInCreativeThought}
\end{quote}

In the terms I have used here, this amounts to the suggestion
that sex (the machinery of genetic recombination etc.)
incorporates anticipation of environmental {\em variability\/}
(on a time scale significantly longer than that of any single
organism). This idea has been more recently independently
formulated and elaborated by \citeAD{Stanley:WhyWeHaveSex}.

However, recombination is not conventionally recognised as a form
of ``mutation'' as such, so it might be considered to represent a
case for special pleading.  It would be more significant if
anticipatory models were more generally implicated in genetic
processes.

\citeAD{Lenat:TheRoleOfHeuristics} has explicitly argued, on very
general grounds, for just such a position, when he claims that
the genetic machinery may incorporate evolutionary ``heuristics''
(which I take to be equivalent to my anticipatory models) which
facilitate the subsequent progress of evolution . Furthermore
Boden has also repeated this
suggestion, in particularly clearcut terms:
\begin{quote}
  \ldots\ some strategy of ``Plausible-Generate-and-Test'' is
  needed, {\em whereby mutations of a type likely to be adaptive
  become increasingly probable}\ldots

  \citeAD[p.~312, emphasis added]{Boden:FailureIsNotTheSpur}
\end{quote}

Most recently, this concept has been independently advocated by
two separate biologists, Dawkins and Wills.  The case of Dawkins
is, perhaps, especially significant because, as already noted
above, he explicitly rejected the notion of anticipation, as a
factor in mutation, as recently as 1986. Since that however, he
has speculated as follows: \begin{quote} Is the world filled with
animal groups which not only are successful, as individuals, at
the business of living, but which are also successful in throwing
up new lines for future evolution?

  \citeAD[p.~219]{Dawkins:Evolvability}
\end{quote}

I should say however that Dawkins is still not completely clear
as to what he is proposing, and my interpretation (that he is
now advocating the possibility of a significant anticipatory
component in mutation) may not be correct.

Wills, in discussing what he describes as ``The Wisdom of the
Genes'', is somewhat more explicit:
\begin{quote}
  The theme of this book is that there is an accumulated wisdom
  of the genes that actually makes them better at evolving (and
  sometimes makes them better at not evolving) than were the
  genes of our distant ancestors.

  \nopagebreak
  \citeAD[p.~6]{Wills:WisdomOfGenes}
\end{quote}

To repeat, what I consider important in these various proposals,
from a variety of workers, is not the idea that the range of
accessible mutations may be merely ``limited'' or
``constrained'', {\em but that mutations leading to increased S-value
should be preferentially and systematically generated.}  There is
a subtle difference between these two concepts, but I suggest
that this difference amounts to the idea that anticipatory
models(s) (predicting something about the relative S-value of
organismic S-lineages) are implicated in (at least some) genetic
processes.

There is no contemporary consensus on this issue, and I cannot
offer any definitive conclusion.  However, for my specific
purposes, I think the following observations are salient.

Firstly, all of the workers identified above, who have suggested
some \role\ for anticipatory models in genetic processes, do so on
the assumption that such anticipatory models, if they exist, are
{\em themselves\/} products of a previous process of organismic
S-lineage selection.  That is, while it is argued that S-value is
sometimes increased by a directed process (rather than ``random''
or ``unjustified'' variation), it is accepted that there is
always a {\em residue\/} of cases in which a strictly Darwinian
(``unjustified'') variation must be recognised as acting.  Thus,
there is no fundamental disagreement with \th{d}, but there is a
critical question mark over its {\em scope\/}: roughly speaking,
we must ask what are the relative contributions of
``unjustified'' and ``anticipatory'' variations to the
phylogenetic growth of any particular attribute of interest?

As regards this question of the scope of \th{d} I note that the
\roles\ suggested for anticipatory models in mutation are limited
to extremely generalised predictions---such as that the
environment will be ``variable'' (on a long timescale compared to
single organisms) and therefore there should be a more or less
continuous, but controlled, probing of new genetic variations
(via recombination for example).  There is no suggestion that
there is any detailed modelling of the implications of specific
genetic modifications for the phenotypic properties of the
resulting organism.  Indeed, given our current understanding of
the extreme complexity of this relationship (i.e.\ of epigenetic
development, or embryology), it seems that if anticipatory models
capable of such predictions existed within organisms then they
would be rather prominent, and could hardly escape detection. On
the contrary, there is no indication of any subsystems, {\em
anywhere\/} accessible to contemporary organisms, capable of
predicting the specific effects of particular genetic
modifications {\em for the organism\/} (or its
offspring).\footnote{I am, of course, continuing to discount the
  exceptional case currently presented by the genetic engineers
  of species {\it homo sapiens.}}

On this basis then, I conclude that while the scope of \th{d} may
no longer include {\em all\/} growth in S-value of organismic
S-lineages, it is still the preferred theory for very many cases
of great interest; and that even for those cases where it may not
be {\em directly\/} applicable, it is still indirectly applicable
as a theory of the formation of anticipatory models of mutation.
In one form or the other then, \th{d} still stands as the
``ultimate'' theory of {\em all\/} sustained, cumulative,
phylogenetic growth in organismic attributes.

\subsection{Darwin's Solution}

I have still not explained how \th{d}, or its precursors,
\th{cs} and \th{hs}, actually solve \pr{d}. Indeed, it is not
even clear how they can {\em contribute\/} to a solution---for
they contain no explicit mention of adaptive complexity.

The solution to this lies in the fact that \pr{d} itself states
that there has, in fact, been a sustained, cumulative, growth of
{\em adaptive complexity\/} of biological organisms; given this,
{\em and\/} given \th{hs}, we can say that this growth of
adaptive complexity must have occurred by virtue of its being
positively correlated with S-value. This goes at least some way
to solving \pr{d}; but it is still not an adequate solution. At
best, \th{hs} yields only an explanation for the {\em
retention\/} of (some) increases in adaptive complexity, once
given that they occur---it does not offer any explanation for how
such increases may come about in the first place;\footnote{This,
  precisely, is the sense of the following remark, originally
  attributed to Samuel Butler: `To me it seems that the ``Origin
  of Variation'', whatever it is, is the only true ``Origin of
  Species''.' (quoted by
  \ociteAD[p.~1]{Fisher:GeneticalTheory}).}
but, with the additional claim, embodied in \th{d}, that S-creation is
a process of {\em unjustified\/} variation, we now achieve
something which, if accepted, might be considered a more or less
{\em adequate\/} solution of \pr{d}, for it finally addresses the
source of increased adaptive complexity.  Of course, it still does not
answer this question completely for it does not describe the
process of the origination of variation in any detail; but by
stipulating that the process is unbiased or unjustified, it
removes the need for any sentient or conscious ``designer''.  To
the extent that the objective is to provide an alternative to
Paley's theistic solution to the problem, \th{d} is now adequate.

It is crucial to note here that \th{d} does {\em not\/} entail
that adaptive complexity be {\em always\/} correlated with
S-value, or (therefore) that adaptive complexity should {\em
necessarily\/} grow. Maynard Smith makes the point thus:
\begin{quote}

  There is nothing in neo-Darwinism which enables us to predict a
  long-term increase in complexity.  All one can say is that
  since the first living organisms were presumably very simple,
  then if any large change in complexity has occurred in any
  evolutionary lineage, it must have been in the direction of
  increasing complexity; as Thomas Hood might have said, `Nowhere
  to go but up'.  But why should there have been any striking
  change in complexity?  It is conceivable that the first living
  thing, although simple, was more complex than was strictly
  necessary to survive in the primitive soup, and that evolution
  of greater fitness meant the evolution of still simpler forms.

  \citeAD[pp.~88--89]{MaynardSmith:StatusOfNeoDarwinism}
\end{quote}

That is, \th{d} solves \pr{d} only in the special sense that it
{\em permits\/} a spontaneous growth of adaptive complexity; it
does not compel or predict such growth.  As discussed
previously \cciteAD[Section~9]{McMullin:DarwinianOntology}, I
adopt the position that this is the best that can be achieved.

Finally, I should add that an attempt to realise the growth of
adaptive complexity, via (genuinely) Darwinian processes, in
{\em artificial\/} systems, could, in itself, represent a further kind of
test of \th{d}.  While such tests could not provide a strong {\em
refutation\/} of \th{d} (due to the necessarily limited scale of
artificial systems compared to biological evolution) the {\em
successful\/} demonstration of significant, spontaneous, growth
in adaptive complexity in artificial \mbox{(D-)systems,} were it to be
achieved, would still represent a significant {\em corroboration\/} for
\th{d}.

\section{Competitors}
\begin{quote}

  \ldots\ I do not think that Darwinian natural selection is the
  only thing we need to understand to understand evolution.
  However, I do think that Darwin's theory is correct, and that
  it is the only adequate explanation for what is for me the most
  characteristic feature of living organisms.  This feature is
  the way in which their structure and behaviour adapts them to
  survive and reproduce in a specific environment.

  \nopagebreak
  \citeAD[p.~40]{MaynardSmith:Structuralism}

\end{quote}

I agree with the sentiments expressed here by Maynard Smith. The
application of Darwinism to the biological world, embodied
specifically by \th{d}, is surely not a complete or final
solution to \pr{d}---in fact, I propose to consider some detailed,
technical, difficulties with it in a future work
\cite{McMullin:GenicAndOrganismic}. Nonetheless,
I consider that there is currently no significant {\em
competitor\/} to it. To establish this, I must consider a number
of supposed competitors, and identify their deficiencies relative
to \th{d}.

In general, any competitor of \th{d} must hold that the
biological world {\em fails\/} to be a D-system (or has so failed
in the past) in some significant, specified, respects.  The
comparison between \th{d} and each competitor must therefore
focus on the particular respects in which this failure is
claimed.

\subsection{Saltationism (Revisited)}

\label{saltation2}

I consider first (because I think it a very special case) the
idea of {\em saltationism}.  As already introduced in
section~\ref{saltation1}, saltation (properly so-called) involves
``large'' evolutionary changes (up to and including the
establishment of new species), which may involve ``large''
increases in adaptive complexity, occurring in a single
generation (which is to say, a single episode of S-creation).

In section~\ref{saltation1} I argued only that saltationism is
not an alternative or competitor to \th{t}.  The question which I
now wish to address is whether, {\em within\/} \th{t}, it might
be a competitor or alternative to \th{d}.

The point of saltationism (relative to \pr{d}) is, roughly
speaking, that if such ``large'' increases in adaptive complexity
occur in a single generation, then the ``truly'' creative aspect
of evolution {\em must\/} lie in these changes, with selection playing,
at best, a secondary \role\ of weeding out grossly deformed
organisms.

Darwin was adamant that the existence of saltations would be
utterly incompatible with his theory: ``If it could be
demonstrated that any complex organ existed which could not
possibly have been formed by numerous, successive, slight
modifications, my theory would absolutely break down''
\cciteAD[Chapter~VI, p.~219]{Darwin:TheOriginOfSpecies}. Darwin
here presents, in opposition to saltationism, what I have termed
{\em gradualism\/}: the doctrine that ``large'' evolutionary
changes (or, at least, ``large'' increases in adaptive
complexity) can only occur by accumulation of a ``large'' number
of individually ``small'' changes, each being retained via
natural selection (which requires some significant number of
generations for each such episode).

In some sense then, Darwin considered gradualism to be an
inherent part of \th{d}, and saltationism to therefore represent
a significant competitor to \th{d}. Popper seems (at one time at
least) to have shared this view of Darwin's: ``Gradualness is
thus, from a logical point of view, the central prediction of the
theory. (It seems to me that it is its only prediction.)''
\cciteAD[pp.~137--138]{Popper:Autobiography}.

However, this view was opposed by Thomas Henry Huxley even on the
very eve of publication of {\em The Origin}, when he
wrote to Darwin that: ``You have loaded yourself with an
unnecessary difficulty in adopting {\it Natura non facit
saltum\/} so unreservedly'' (quoted by
\ociteAD[Essay~17]{Gould:PandasThumb}).

I shall here adopt Huxley's position precisely.  Saltationism is
not a competitor of Darwinism---or, at least, not necessarily so;
rather, saltationism and gradualism are competing
{\em elaborations\/} of \th{d}.  \th{d} says nothing about the
``size'' of the variations which have been the subject of
S-lineage selection; and, {\it pace\/} Popper, I do not see that
any ``prediction'' relating to this can be wrung from
it.\footnote{I should note however that Popper's formulation of
  Darwinian theory, on which he bases his prediction of
  gradualness \cciteAD[pp.~135--136]{Popper:Autobiography}, is not
  quite identical with my \th{d}.}
In fact, as noted in section~\ref{dprob}, I do not accept that
adaptive complexity (whatever about S-value) admits of a metric
which would allow ``size'' to be meaningfully introduced (at the
level of \th{d}) at all.

I hold that this is a strictly correct statement of the logical
status of saltationism (and gradualism) relative to Darwinism.
However, lest there be any confusion, I should stress that I am
not commenting ({\em either\/} way) on the relative merits of
saltationism versus gradualism {\it qua\/} elaborations (rather
than competitors) of \th{d}.  In fact, any conclusion on this
requires a definite commitment to some particular interpretation
of ``large'' versus ``small'' variations. A comprehensive
discussion would take me too far afield here, but I should like
to consider, in detail, just one particular approach to this
question; this may allow me to isolate just what Darwin was
``really'' concerned with, in his stipulation of gradualist
evolution.

\citeAD[pp.~41--44]{Fisher:GeneticalTheory} has formulated a
detailed, in principle, argument {\em against\/} a particular
version of saltationism (though Fisher himself does not use this
word).  I shall first paraphrase and elaborate his argument,
though using my own terminology.

Suppose that S-class can be identified with a point in some
Euclidean $n$-space, where $n$ is ``large''.  Roughly speaking,
we suppose that some set of potential organisms (or, more
properly, potential S-lineages) of interest (i.e.\ which can
potentially compete with, or selectively eliminate, each other)
can ``match'' their environment more or less well in each of $n$
distinct traits or characters.  Any given S-lineage can be
represented by a point in this space.  A D-lineage (``species''
in Fisher's terms) would be represented by a set of such
points---a somewhat amorphous ``cloud'' in the S-class space.
With each S-creation event a new point appears; every time an
S-lineage is selectively eliminated (or dies for any other
reason) a point disappears. Thus, over time, the set of points
making up the D-lineage could ``move'' through the
space.

Now, the environment itself will also be represented by a point
in this space---in the sense that some particular S-lineage, or
some particular set of characteristics, would be ``best matched''
to the environment.  Fisher identifies the distance between any
other point in the space, and this ``optimal'' point as a measure
of the ``degree of adaptation'' (strictly one should say the
reciprocal of this distance is a measure  of degree of
adaptation).  Thus, to the extent that the points making up a
D-lineage lie ``close'' to this optimal point, then the D-lineage
is said to be ``well adapted''.

While Fisher does not expressly say so (as far as I can see) it
seems that we must assume that, to the extent that ``adaptation'' in
this sense occurs by Darwinian selection, the degree of
adaptation must be well correlated with S-value. That is, if we
imagine adding another dimension to the space to represent
S-value, and thus establish a ``surface'' of S-value, it follows
that the optimum point will be at the (global) peak of this
surface.  Again, it seems implicit in Fisher's discussion that
this must be the {\em only\/} peak in the surface, in general
(though I shall return to critique this idea below).  That being the
case, the evolution of a D-lineage can be envisaged as a process
of {\em hill-climbing}; S-creation events result in new points
being tested; where any of these are ``uphill'' relative to the
existing points they will selectively displace old points etc.
Evolution would be represented by a trajectory whereby a point
(or set of points) representing the S-lineage(s) of a D-lineage
approaches more or less closely to this peak (and, indeed, could
track it if it moves slowly enough---which is to say the
environment changes slowly enough).\footnote{It seems clear from
  Fisher's description of his space in terms of a {\em match\/}
  along each dimension to the organism's (or better, S-lineage's)
  environment, that it is, in effect, a space of {\em
  phenotypic\/} characteristics. The qualitative characteristics
  of this space are also just those described by
  \citeAD{Lewontin:Adaptation}; but Lewontin identifies his space
  as being one of {\em gene frequencies,} rather than phenotypic
  characteristics, which would be a different kind of thing
  entirely. \citeAD[Chapter~9]{Provine:SewallWright} provides a
  much more detailed discussion of these issues.}

Fisher supposes that S-creation (mutation) might be modelled, at
least approximately,  in this space by the appearance of a new
point (S-lineage) which is displaced from some existing point
(corresponding to the parent(s)) in a random direction. The word
``random'' {\em is\/} used here in its technical, stochastic,
sense: i.e.\ the direction of displacement is a random variable
uniformly distributed over all possible directions. The
interpretation of ``possible directions'' depends, of course, on
the dimensionality of the space ($n$).  The size of the
displacement may also vary, of course, presumably in some
``random'' manner.  For our purposes we need not worry about the
details of this. For the moment, we can consider just the set of
all possible displacements of a ``fixed'' size $r$; subsequently,
we shall go on to consider the expected effects of different such
sets (i.e.\ having different values of $r$).

Let $d$ denote the diameter of the circle centered on the
adaptive peak, and passing through the ``parental'' point
(S-lineage); that is, $d/2$ is the distance from this point to
the peak (and $d^{-1}$ is a formal measure of ``degree of
adaptation'').  $r$ denotes the (fixed) size of a randomly directed
displacement from this point, identifying a new point (S-lineage)
resulting from an S-creation event.

It is now (trivially?) clear that, $\forall \; r > d$, and
regardless of the dimensionality of the space ($n$), the
probability of the new point being closer to the peak must be
zero (even if it were in the ``perfect'' direction---pointed
straight at the peak---it would still overshoot by more that the
original distance, $d/2$, on the other side).  To put this
another way, evolutionary improvements in adaptation can occur
{\em only\/} through displacements $r < d$.  If we define a
``saltation'' as any displacement for which $r > d$ (and
acknowledging that this definition will quantitatively vary with
the ``instantaneous'' degree of adaptation) then Fisher's result
(at least in a first version) is that, in this particular sense,
Darwinian evolution cannot proceed by saltations.

In fact, Fisher's result is significantly stronger than this.
While it is true that, regardless of $n$, the probability of
improvement (in Fisher's model) is zero $\forall \; r > d$, this
does not, in itself, say what happens for $r < d$.  It turns out
that this is moderately complicated, and depends crucially on the
dimensionality of the space.  Informally, the greater the
dimensionality, the more extra ways there are of getting a
displacement in the ``wrong'' direction, and therefore the lower
the probability of getting an improvement.  Fisher's quantitative
version of this is that, for ``large'' $n$, the probability of
improvement approaches zero for all $r$ much greater than
$d/\sqrt{n}$.  So we can now refine and strengthen the overall
result by defining a ``saltation'' as any displacement for which
$r \stackrel{>}{\sim} d/\sqrt{n}$. In other words, improvements
in adaptation can feasibly come about {\em only\/} through
displacements $r \stackrel{<}{\sim} d/\sqrt{n}$, which, for
``large'' $n$, means $r \ll d$.  And the greater the number of
dimensions, the stronger this result becomes.\footnote{I note
  that Dawkins has also recently presented an alternative version
  of this argument of Fisher's
  \cciteAD[pp.~230--236]{Dawkins:BlindWatchmaker}; however,
  Dawkins' discussion is limited to the weaker version of
  Fisher's result (he does not mention the effect or significance
  of the dimensionality of the space), and also harbours a minor
  technical error which is potentially confusing (at least, it
  confused {\em me\/}).  This is not a substantive point, but, for
  completeness, I include a more detailed review in
  Appendix~\ref{Microscope}.}

This argument seems quite convincing---{\em in its own terms\/};
but the question is whether the situation envisaged by Fisher is
a good model of S-creation.

A first problem is the (implicit) assumption that, in the
relevant space, the S-value surface has a single peak or optimum.
This seems to be quite unjustified; and of course, if there are
multiple peaks then ``large'' displacements in the space
(``saltation'') may well allow a D-lineage to move to a separate
(and ``better'') peak.  Indeed, this may be actually {\em
necessary\/} for continued evolution (to ``escape'' from local
optima). This point seems to have been a central aspect of the
disagreement between Wright and Fisher about the general nature
of evolutionary change; Wright has long argued, in his {\em
shifting balance\/} theory, that what we might call ``peak
jumping'' of some sort (albeit not necessarily by single
mutational events) is, at the very least, an important
evolutionary process \cciteAD{Wright:ShiftingBalanceTheory}.
\citeAD[pp.~172--173]{Turner:FishersFaith} has also considered
this issue of multiple adaptive peaks, including a
reconsideration of an analogy cited by both Fisher and Dawkins
(see Appendix~\ref{Microscope} below), and concludes that
Fisher's analysis, as an argument against the {\em possibility\/}
of saltationism, simply does not work (although he does hold that
saltations cannot suffice to explain {\em all\/} increases in
adaptive complexity).

But quite aside from this question as to the existence of
multiple ``adaptive peaks'', there is an even deeper problem
here.  We must ask whether S-class should be modelled by a point
in a ``fixed'' Euclidean $n$-space (discrete or continuous) {\em
at all}. It might seem that, in modern terms, this could surely
be achieved by defining S-class directly on the basis of DNA
sequence (compare, in particular, the ``genetic
\mbox{(hyper-)space''} of
\ociteAD[p.~73]{Dawkins:BlindWatchmaker}). There are various
possible problems with this---for example there is no way to
represent the evolution of the ``genetic system'' itself in such
a scheme.  Furthermore, as noted in section~\ref{unjustified}, it
is now considered that there may be significant systematic
aspects to the modification of DNA sequence in mutation.  But
more seriously, it is clear that no {\em single\/} notion of
S-value would be applicable throughout such a space (see also the
more detailed discussion in
\ociteAD[Section~8]{McMullin:DarwinianOntology}).

In any case, to conclude this discussion of saltationism: I take
the view that, as long as S-creation (saltationary or otherwise)
is {\em not\/} taken to be informed by anticipatory models (and
this is certainly the case for the version considered by Fisher)
then the question of what ``size'' of variations will be
evolutionarily significant may be an interesting one---but it
lies entirely {\em within\/} the scope of \th{d}. Saltationism,
in this sense, is not a competitor to \th{d}.  If, on the other
hand, one means to {\em define\/} ``saltations'' as variations
whose ``size'' is such that they could not ``plausibly'' arise by
unjustified variation (i.e.\ without the involvement of some kind
of anticipatory model or knowledge) then saltationism does indeed
become a competitor to \th{d}.  This {\em seems\/} to be the
essence (though not the detail) of Fisher's argument.  But, in
that case, saltationism becomes equivalent to what I call {\em
mutationism\/}---and I will discuss {\em that}, its own right, in
section~\ref{mutationism} below.

\subsection{Theism {\it et al.\/}}

A valid competitor of \th{d} is, of course, Paley's own
theory---that the growth of adaptive complexity is due to the
intervention of some supernatural agent, of more or less
unspecified nature. While Paley probably thought in terms of
special creation, the exact nature of the intervention is not
important here---it could be by way of creation, biasing of
selection, or biasing of variation, or any combination of these.

Paley's argument, briefly, was that the mere existence of
adaptive complexity {\em demanded\/} the existence of a
``creator'' in some sense.  Further, since this argument can be
applied recursively, it demands an {\em immortal\/} creator,
which is to say {\em God} (by any other name).

The crux of the argument (and the point of the ``watchmaker''
analogy) is the claim that, in effect, adaptive complexity {\em
cannot\/} spontaneously grow, except by the intervention of an
intelligent and/or conscious agent. The crux of \th{d} is, of
course, the converse claim, precisely that adaptive complexity
{\em can\/} grow spontaneously.

Now it has been admitted that there are serious limits to the
extent that \th{d} can be severely tested.  Nonetheless, it is
the case that \th{d} has effectively withstood such tests as
have been attempted.  Furthermore, the {\em corroborability\/} of
\th{d} is, of course, greater than Paley's theism; in fact, it
is greater than {\em any\/} competitor which fails to stipulate a
definite mechanism for the growth of adaptive complexity---i.e.\
which fails to make testable predictions. No matter what
evolutionary, or even non-evolutionary, pattern were observed in
the biological world, it could not refute a generalised theistic,
or metaphysical, explanation.  Thus, \th{d} can and should be
rationally preferred to such theories.

I may say that clinging to a more or less theistic solution of
\pr{d}, merely on the basis that \th{d} is too ``difficult'' to
believe (or perhaps I should say simply too {\em unpalatable\/})
is no substitute for a serious attempt to formulate and carry out
severe tests of \th{d}.  Dawkins has rather caustically
characterised the former approach as mere ``argument from personal
incredulity'' \cciteAD[p.~38]{Dawkins:BlindWatchmaker}.

Finally, I should stress that, while the (hypothesized) existence
of God cannot seriously compete with \th{d} (in the current
state of testing) as a solution of \pr{d}, the acceptance of
\th{d} in its turn does not, in any way, preclude a general
belief in the existence of some God; it merely, tentatively,
precludes Her involvement in the growth of adaptive
complexity\ldots

\subsection{Mutationism}
\label{mutationism}
\begin{quote}
  It is hard for us to comprehend now but, in the early years of
  this century when the phenomenon of mutation was first named,
  it was regarded not as a necessary part of Darwinian theory but as
  an {\em alternative\/} theory of evolution!

  \citeAD[p.~305]{Dawkins:BlindWatchmaker}
\end{quote}

Saltationism, as I have described it, was concerned only with the
``sizes'' of mutation which are significant in the evolutionary
process---it accepts or presupposes that these changes are
unjustified or unbiased with respect to S-value.
{\em Mutationism}, on the other hand, is not particularly, or
necessarily, concerned with the relative sizes of mutations, but
rather holds that mutations are significantly {\em biased\/}
in some sense.  While the nature of this bias need not be fixed,
or universal, if mutationism is to address \pr{d} we must
suppose that, in some evolutionary lineages at least, there has
been a persistent bias toward increased adaptive complexity.
Given that such biases exist, we may conclude that major
features of evolution, particularly including growth in adaptive
complexity, are primarily (if not exclusively) due to the
directional bias of mutation, and not to natural
selection.\footnote{Assuming that the {\em operation\/} of
  selection is still accepted (\th{hs}), then, to make this
  argument fully coherent, we must further suppose that, among
  the spectrum of mutants of increased adaptive complexity, there
  are consistently some which {\em also\/} represent increased
  S-value.}

Unlike saltationism, mutationism is a genuine competitor to
\th{d}---it offers a different, rather than a more detailed,
solution to \pr{d}.  Unlike theism, it is not metaphysical; while
it may be vague about the mechanisms for mutational biases, it
stipulates that such biases exist---especially a bias toward
increased adaptive complexity.  Such biases should therefore
manifest themselves if we look for them under natural and/or
experimental conditions. Indeed, a significant factor in the
original impetus of the mutationist theory may be traced to
de~Vries' interpretation of certain spontaneous, inheritable,
variations he observed in wild plants; de~Vries interpreted these
events (wrongly as it subsequently transpired) as the spontaneous
formation of new species (\ociteAD[p.~82]{Hardy:LivingStream};
\ociteAD[pp.~112--113]{Wills:WisdomOfGenes}).  Indeed, it was
de~Vries who coined the term {\em mutations\/} for such
phenomena.  Similarly, the (supposed) phenomenon of orthogenesis,
discussed in section~\ref{hstry} above, appeared to support a
mutationist view of evolution.

The original mutationist school did not address the question of
how the required mutational biases could come about.  Dawkins
describes the situation as follows:
\begin{quote}
  The problem with mutation as the sole evolutionary force is
  simply stated: how on earth is mutation supposed to {\em
  `know'} what will be good for the animal and what will not?  Of
  all possible changes that might occur to an existing complex
  mechanism like an organ, the vast majority will make it worse.
  Only a tiny minority of changes will make it better.  Anybody
  who wants to argue that mutation, without selection, is the
  driving force of evolution, must explain how it comes about
  that mutations tend to be for the better.  By what mysterious,
  built-in wisdom does the body choose to mutate in the direction
  of getting better, rather than worse? \ldots\ The mutationists,
  needless to say, never answered it.  The odd thing is that the
  question hardly seems to have occurred to them.

  \citeAD[pp.~305--306]{Dawkins:BlindWatchmaker}
\end{quote}

However, Dawkins is perhaps benefiting somewhat from hindsight
here: as long as there seemed to exist empirical phenomena
(spontaneous speciation in a single generation, orthogenetic
trends) which supported mutationism against \th{d}, it was not
necessary to stipulate a mechanism for directed mutation;
obviously the elucidation of such mechanisms would be a
significant element of any mutationist research programme---but
it would not be {\em un\/}reasonable to defer this until, say,
mutationism was accepted over \th{d}.

In any case, this original mutationist school withered away, as
the empirical basis for it was found to be flawed, and it became
clear that the particulate view of inheritance (implied by
mutationism), which had initially been supposed to be
incompatible with \th{d}, was, in fact, complementary (or even
essential) to it.  In the terms I am using here, tests which were
thought to be decisive between mutationism and \th{d} were not,
in fact, decisive at all, for the evidence was actually
compatible with both theories; and since the information content,
or corroborability, of \th{d} was greater (since it does not
postulate any particular biases, of unspecified origin, in the
mutational process) it was clearly preferable.

Subsequently, our increased knowledge of genetic processes
at the level of molecular biology seemed to decisively rule out
the existence of any mechanism for the persistently biased
mutations required by mutationism, and the theory was considered
to be more or less definitively refuted.

However, as discussed in section \ref{unjustified}, the notion of
directed mutation has recently been resurrected, in the
form of Wills' ``wisdom of the genes'' or Dawkins' ``evolution of
evolvability''.  While these recent authors do not refer to
themselves as mutationists (perhaps wisely) the logical structure
of their theories is at least similar to the original
mutationists.  Nonetheless, there are two decisive differences in
this {\em neo\/}-mutationism:
\begin{itemize}

\item Directed mutation is {\em not\/} considered to be
responsible for detailed evolutionary changes, typical of
increased adaptive complexity---because that would require the
existence of an anticipatory model capable of predicting the
detailed phenotypic effects of given genetic modifications, and
there is no evidence for the existence of such models.

\item In any case, insofar as mutation is considered to be
directed at all, the mechanism for this direction is itself
considered to be the outcome of earlier Darwinian selection, in
the sense of \th{d}.

\end{itemize}

In conclusion: mutationism, in its original form, as a competitor
of \th{d} (in solving \pr{d}) has been effectively refuted; and
in its modern form it is no longer a competitor to \th{d}, but
more like a possible elaboration (and even then having strictly
limited scope).

\subsection{Lamarckism}
\label{lamarck}
\begin{quote}
  The Lamarckian theory seems to have great emotional appeal, for
  certain types of intellectual as well as for laymen.  I was
  once approached by a colleague, a celebrated Marxist historian
  and a most cultivated and well-read man.  He understood, he
  said, that the facts all seemed to be against the Lamarckian
  theory, but was there really no hope that it might be true?  I
  told him that in my opinion there was none, and he accepted
  this with sincere regret, saying that for ideological reasons
  he had wanted Lamarckism to be true.  It seemed to offer such
  positive hopes for the betterment of humanity.

  \citeAD[p.~291]{Dawkins:BlindWatchmaker}
\end{quote}

The term {\em Lamarckism\/} has been used to denote a wide
variety of evolutionary theories, not all of which are fairly
attributable to the original Chevalier de
Lamarck. Lamarck\footnote{According to
  \citeAD[pp.~65--66]{Wills:WisdomOfGenes}, the title {\em
  Chevalier de Lamarck\/} was a somewhat dubious affectation
  (Lamarck's ``real'' name being Jean-Baptiste Antoine de Monet).
  However, convention now decrees that he is known simply as
  Lamarck, and I shall conform to this.}
appears to have accepted evolutionary descent or transmutation of
species (\th{t}---see, for example,
\ociteAD[p.~289]{Dawkins:BlindWatchmaker}), and thus was
attempting to confront more or less the same problem as Darwin,
the growth of adaptive complexity (\pr{d}).  However, his attempt
long predated Darwin's work, and as a result is not easily
compared to it.

Lamarck's central idea, to explain the evolution of adaptive
complexity, seems to have involved ascribing evolutionary force
to the wishes, or perceived needs, of organisms themselves
(\ociteAD[p.~67]{Wills:WisdomOfGenes};
\ociteAD[p.~289]{Dawkins:BlindWatchmaker}).  Roughly speaking the
theory goes like this:
\begin{enumerate}

\item Organisms have ``desires'', or ``aims'', or ``objectives''
(these need not be conscious).

\item Among these is a generalised desire for ``improvement'' or
``perfection''.

\item In response to these desires, organisms are, in fact,
successful (to a greater or lesser extent) in improving
themselves during their lifetimes.  The effect of ``use and
disuse'' on morphological characters is commonly cited; examples
include the development of muscles through exercise, darkening of
skin exposed to sunlight etc. However, the theory does not hinge
on use and disuse as a {\em sole\/} mechanism for improvement; it
suffices that improvement is possible, howsoever it occurs.

\item {\em The improvements which organisms actually achieve during
their lifetimes are (preferentially) transmitted to their
offspring\/}---i.e.\ organisms can somehow control which of their
characteristics are inherited and which are not. This is the
celebrated ``inheritance of acquired characteristics''---though
the latter phrase is potentially misleading, as I shall discuss
below.

\item In this way, an evolutionary lineage can show progressive
improvement of its members as a cumulative result of their
individual, incremental, success in improving themselves.

\end{enumerate}

I may say that, in this form, Lamarckism seems eminently
reasonable.  In particular, the truth of points 1, 2, and~3 seems
quite clear; 4~requires support, but is not {\em inherently\/}
implausible; and~5 (which is to say the solution of \pr{d}) is
then simply the logical consequence of what has gone before.
Furthermore, in ascribing a central \role\ to the efforts of
organisms themselves toward their self-improvement, it seems
positively attractive (as compared to \th{d}) in restoring some
kind of purpose to (human) life. It is perhaps not surprising,
therefore, that Lamarckism continues to be a kind of holy grail
of evolutionary theorizing, pursued despite the continuing
privations of the quest, as reflected in Dawkins' earlier
anecdote.

The modern genetic theory of inheritance was not, of course,
available to Lamarck.  But his theory can be described in modern
terms as a particular elaboration of mutationism.  What
Lamarckism adds to mutationism is a specific mechanism for
distinguishing between ``good'' mutations and ``bad'' mutations:
good mutations are precisely those which transmit characters that
an organism has tried and found beneficial in its own lifetime.
This is, at first sight at least, rather a good proposal, and, if
mutationism were successful as a {\em general\/} theory, then this
specific elaboration would certainly bear careful consideration.

Unfortunately, as previously discussed, mutationism itself, as a
general theory of evolution, has been found severely wanting.
This is primarily because it seems to rely on the existence of
anticipatory models of the (phenotypic) effects of specific
genetic transformations.  Such models do not seem to exist (except in
the most rudimentary and limited sense); and given the complexity
of the mapping from genotype to phenotype, it seems unlikely that
any detailed models of this sort could feasibly be constructed.

This argument is equally, if not more effective against
Lamarckism; for Lamarckism demands not only {\em some\/}
anticipatory model (of embryology), but a model that operates in
the direction from phenotype to genotype.  This relationship is,
if anything, vastly more complex that the mapping from genotype
to phenotype.  Dawkins has dubbed the virtual impossibility of
carrying out a mapping from phenotype back to genotype the
{\em Central Dogma of Embryology\/}
\cciteAD[p.~174]{Dawkins:ExtendedPhenotype}. This was apparently
inspired by the Central Dogma of {\em Molecular Genetics}.  The
latter states that DNA sequence may be translated into protein
sequence, but not {\it vice versa.}  While this seems to hold in
practise, there is no deep reason why it should not be
contravened: the coding from DNA to protein is relatively
straightforward and easily reversible in principle.  The Central
Dogma of Embryology, on the other hand, is much stronger---for
the mapping in question is, to say the least, extremely complex.
These two ``Central Dogmas'' should therefore be kept clearly
distinct, and not confused with each other.  The significance of
the distinction is the following: the Central Dogma of Molecular
Genetics precludes Lamarckian inheritance---but only very weakly
so.  If this were the only barrier, then we could easily envisage
that Lamarckian inheritance, even if it now no longer occurs,
could well have played a significant \role\ in the past. But the
Central Dogma of Embryology seems to rule out any \role\ for
Lamarckian inheritance for as long as life has employed an
embryology remotely as complex as now exists on Earth.  This is a
much stronger refutation.

It should be noted that while Lamarckian evolution entails the
existence of Lamarckian inheritance---the inheritance of
``acquired'' characteristics---the converse does not hold.
Lamarckian {\em inheritance\/} is not synonymous with Lamarckian
{\em evolution\/} (or Lamarck{\em -ism}, as I am using the term).
That is, even if it should one day be discovered that at least
some ``acquired'' characteristics could be translated back into
genetic modifications which would preserve them indefinitely,
this would still not {\em entail\/} Lamarckian evolution.  For
the latter, we require that ``favourable'' (acquired)
characteristics be {\em preferentially\/} transmitted.  This is a
more important distinction than may at first appear, as we shall
see.

The refutation of Lamarckism, based on the Central Dogma of
Embryology, is logically compelling---but it is still vaguely
unsatisfactory.  One is still left with the feeling that, even if
\th{d} is the only effective solution to the growth of
adaptive complexity in the (terrestrial) biological world,
Lamarckism still offers a better solution ``in principle''. Thus,
we might suppose that Lamarckian evolution may well occur on some
other planet---or {\em could be stimulated in an artificial
evolutionary system.}  The attraction of this is that it seems
inherently much more ``efficient'' than Darwinian evolution---the
experiences gained by an organism in its lifetime need not
be disgarded when the organism dies, but can be retained,
accumulated, and capitalised on.  If this reasoning is correct,
then it would seem that, despite the failure of Lamarckism as a
{\em biological\/} theory, it might still offer a short cut to
success in artificial evolution.  This possibility needs,
therefore, to be carefully analysed.

The proposal then is as follows. We assume that we have some
natural or artificial system, which exhibits sustained growth
in adaptive complexity. We suppose (for the sake of argument) that
Lamarckian evolution, in the terms described above, {\em does\/}
occur in this system.  We then ask whether this could be a
satisfactory explanation of the observed growth in adaptive
complexity.

Lamarckian evolution implies two things---an organism must
develop new or modified characteristics (not possessed by its
parent(s)), in somatic time, and it must selectively transmit
those found to be ``favourable'' to its offspring. Two distinct,
but closely related problems arise:
\begin{enumerate}

\item How {\em can\/} an organism develop ``favourable'', ``new''
characteristics relative to its parent(s)?

\item How can an organism (consciously or otherwise) distinguish
``favourable'' from ``unfavourable'' acquired characteristics?

\end{enumerate}

In many ways we have just recast the original problem, but
now localised in the lifetime of a single organism.  That is, we
must either assume that there is a bias in the generation of new
characteristics (so that ``favourable'' ones are preferentially
generated), or we must assume some mechanism for ``selecting''
favourable from unfavourable ones (or some combination of these
two).

Let us suppose there {\em is\/} a favourable bias in the
generation of new characteristics.  This is just the original
mutationism dressed up slightly.  It is made possible, or
plausible, by the assumption that Lamarckian {\em inheritance\/}
is possible.  But it begs the question of the source of the bias.
The only possible answer seems to be the use of effective
anticipatory models, to anticipate that certain modifications
will be advantageous before they are actually carried out.  It is
Boden's ``Plausible-Generate-and-Test'' again
(section~\ref{unjustified} above---see
\ociteAD{Boden:FailureIsNotTheSpur}).  It could well be a
significant evolutionary process: but we should then have to ask
where the anticipatory models which support it came from in the
first place. Ultimately {\em (if Popper's position on induction
is accepted)\/} this must lead back to a reliance on {\em
unjustified\/} variation again.

Well then, let us restrict attention to unjustified variations
generated in the lifetime of the organism.  We can still eschew
\th{d} provided that the organism itself can select or
distinguish between favourable and unfavourable variations (i.e.\
the organism(s) carry out the selection of variations which are
transmitted and retained, rather than ``natural'' selection).
But this then begs the question of the origin for the selection
{\em criteria\/} used by an organism. Related questions are, for
example, how does an organism (or perhaps we should say
``lineage'' in this Lamarckian context) come to classify certain
stimuli as ``painful'', or other stimuli as ``rewarding'' etc.? This
line of argument seems to lead inevitably back to natural,
S-lineage, selection as the {\em ultimate\/} evolutionary force.

The conclusion from all this is that Lamarckian evolution, if it
were practical (i.e.\ if the Central Dogma of Embryology could be
somehow rescinded), might well be a very significant and important
evolutionary process; but it could never, {\em in principle\/} be
a complete solution to the problem of the growth of adaptive
complexity.  The most we can say seems to be that Lamarckism
might be a useful extension or enhancement of \th{d}: but it
could never compete with or replace it---it simply does not solve
the problem at hand.  Dawkins has previously made much the same
arguments, concluding that:
\begin{quote}
  \ldots\ the Lamarckian theory can explain adaptive improvement
  in evolution only by, as it were, riding on the back of the
  Darwinian theory.  Given that Darwinian selection is there in
  the background, to ensure that some acquired characteristics
  are advantageous, and to provide a mechanism for discriminating
  the advantageous from the disadvantageous acquisitions, the
  inheritance of acquired characteristics might, conceivably,
  lead to some evolutionary improvement.  But the {\em
  improvement}, such as it is, is all due to the Darwinian
  underpinning.  We are forced back to Darwinism to explain the
  adaptive aspect of evolution.

  \citeAD[p.~300]{Dawkins:BlindWatchmaker}
\end{quote}

While I consider that these arguments do, finally and decisively,
eliminate Lamarckism as a {\em competitor\/} of Darwinism, there
is yet an epilogue. I have perhaps been slightly disingenuous in this
discussion.  Roughly, the argument was that Lamarckian evolution
is not {\em practical}, and even if it were it would be {\em
inadequate}. I hold to this conclusion; but it can easily be read
as ``Lamarckian evolution is not {\em possible,} and even if it
were it would be {\em insignificant}''.  I do not intend these
much stronger claims.

In fact, it can be argued that a form of Lamarckian evolution is
not only possible, but well known, and has been crucially
significant in the evolution of at least one species.  This is
so-called {\em cultural\/} evolution, particularly in the human
species.  Humans acquire cultural characteristics (``knowledge'')
selected by their parents (among others) from their own
accumulated wisdom. Humans, in turn, generate new characteristics
(``knowledge'') not possessed or transmitted from their parents.
This is Lamarckian evolution {\it par excellence}, and is
undoubtedly a ``significant'' mechanism for the evolution of the
unique characteristics of this extraordinary animal.

I accept this, in a limited sense which I shall detail below; but
emphasize again that it cannot be considered a {\em solution\/}
to the problem of the growth of adaptive complexity in general,
and the growth of human knowledge in particular.  This is worth
clarifying because at least one biologist has implied not only
that Lamarckian evolution is a {\em significant\/} mechanism in
human, cultural, evolution (which I can accept) but that it is in
some sense an {\em explanation\/} of it.  The claim is made by
Gould, and seems worth quoting at length:
\begin{quote}
  {\it Homo sapiens\/} arose at least 50,000 years ago, and we
  have not a shred of evidence for any genetic improvement since
  then. I suspect that the average Cro-Magnon, properly trained,
  could have handled computers with the best of us (for what its
  worth, they had slightly larger brains than we do).  All that
  we have accomplished, for better or for worse, is a result of
  cultural evolution.  And we have done it at rates unmatched by
  orders of magnitude in all the previous history of life.
  Geologists cannot measure a few hundred or a few thousand years
  in the context of our planet's history.  Yet, in this
  millimicrosecond, we have transformed the surface of our planet
  through the influence of one unaltered biological
  invention---self-consciousness.  From perhaps one hundred
  thousand people with axes to more than four billion with bombs,
  rocket ships, cities, televisions, and computers---and all
  without substantial genetic change.

  Cultural evolution has progressed at rates that Darwinian
  processes cannot begin to approach.  Darwinian evolution
  continues in {\it Homo sapiens}, but at rates so slow that it
  no longer has much impact on our history.  {\em This crux in
  the earth's history has been reached because Lamarckian
  processes have finally been unleashed upon it.}  Human cultural
  evolution, in strong opposition to our biological history, is
  Lamarckian in character.  What we learn in one generation, we
  transmit directly by teaching and writing.  Acquired characters
  are inherited in technology and culture.  {\em Lamarckian
  evolution is rapid and accumulative.}  It {\em explains\/} the
  cardinal difference between our past, purely biological mode of
  change, and our current, maddening acceleration toward
  something new and liberating---or toward the abyss.

  \citeAD[pp.~70--71, emphasis added]{Gould:PandasThumb}
\end{quote}

There is certainly an underlying terminological difference here
between myself and Gould.  In this context he is restricting
``Darwinism'' to mean what I have called ``Organismic
Darwinism''. So part of his point is, presumably, that cultural
evolution is different because it does not rely on the
(organismic) actors of (organismic) Darwinism.   I quite agree
with this---I freely admit that cultural evolution involves the
emergence of a new kind of {\em Darwinian\/} actor (the
linguistically formulated hypothesis) and new selective forces or
environments (preeminently, the environment of {\em science\/}
which seeks to select ``true'' theories---or, at least, to reject
``false'' ones).  But it does seem that
Gould intends something much stronger than this---not just a
change in the actors, but a change in the evolutionary process or
mechanism. A change, in fact, away from anything that might be
called Darwinism, even by analogy. I reject entirely this
implication that {\em Lamarckian\/} processes impart to cultural
evolution its crucial distinguishing features.  Rather I argue
that the crucial processes, which {\em might\/} constitute an
explanation of how cultural evolution can show a growth of
adaptive complexity (human knowledge), are still essentially
Darwinian rather than Lamarckian.

In more detail, this Darwinian underpinning to cultural evolution
is manifested in two distinct ways:
\begin{itemize}

\item The organismic pre-requisites (whatever they are) to
support cultural evolution must first have evolved by
conventional organismic Darwinism (though there may have been
some interaction between these two processes at a late
stage).

\item Cultural evolution itself relies, ultimately, on
unjustified variation and selection.  The variations are not
recorded in organismic genetic material, but rather in books,
pictures, computer files etc.  Selection is (typically) carried
out by argument and/or testing rather than via relative S-value
of competing organismic S-lineages.  But the {\em process\/} is
still an essentially Darwinian one, even if the actors are no
longer sensibly regarded as organisms.

\end{itemize}

This kind of view has been advocated (though in more
circumscribed form) by Dawkins in his theory of the (Darwinian)
evolution of {\em memes\/}
\cciteAD[Chapter~11]{Dawkins:NewSelfishGene}. In its strongest
form, the picture I have presented here is just the evolutionary
epistemology of \citeAD{Campbell:EvolutionaryEpistemology} or the
Popperian growth of knowledge by {\em conjectures and
refutations\/} \cciteAD{Popper:Conjectures}.

\section{On the Scientific Status of Organismic Darwinism}

I have presented and analysed Organismic Darwinism as an
essentially straightforward theory---whose scientific status is
not problematic.  Indeed, this was a crucial, if implicit,
assumption in my comparison between \th{d} and metaphysical
competitors such as Paley's theism.  I stand over this claim for
the scientific status of \th{d}, but must admit that this has not
been a universally accepted position.

In fact, the status of Organismic Darwinism is a very vexing
question, which has received considerable attention in both the
biological and philosophical literature; the debate has
been positively acrimonious on occasion. The issue is clearly a
matter of some importance for my stated purposes here---for if
the status of Darwinism is unclear even within biology, its
extension into other fields must necessarily be suspect.

I shall not presume to offer any definitive ``resolution'' to
this question, but will simply attempt to make my own position as
clear as possible.

I consider two general questions: whether Darwinism may be a mere
{\em tautology}, or, failing that, whether it may be {\em
irrefutable\/} (and thus {\em metaphysical\/}).  These two issues
are commonly conflated---for example by
\citeAD{MaynardSmith:StatusOfNeoDarwinism}. It is of course true
that all tautologies are untestable and therefore (in a trivial
sense) metaphysical, but the converse does not hold---theories
may well be metaphysical yet not tautologous. Thus, given that
Darwinism is {\em not\/} actually tautological then its
testability becomes entirely moot, and must be considered in its
own right.

\subsection{Tautology\ldots}
\begin{quote}
  My dear Darwin,---I have been so repeatedly struck by the utter
  inability of numbers of intelligent persons to see clearly, or
  at all, the self-acting and necessary effects of Natural
  Selection, that I am led to conclude that the term itself, and
  your mode of illustrating it, however clear and beautiful to
  many of us, are yet not the best adapted to impress it on the
  general naturalist public \ldots\ I wish, therefore, to suggest
  to you the possibility of entirely avoiding this source of
  misconception in your great work (if not now too late), and
  also in any future editions of the `Origin', and I think it may
  be done without difficulty and very effectually by adopting
  Spencer's term (which he generally uses in preference to
  Natural Selection), viz. `Survival of the Fittest'.

  \citeAD{Wallace:Letter1866}\\
  (Quoted by \ociteAD[pp.~179--180]{Dawkins:ExtendedPhenotype})
\end{quote}

I believe that the charge of tautology levelled against
Organismic Darwinism is quite mistaken.  However, contrary to,
for example,
\citeAD[pp.~180--181]{Dawkins:ExtendedPhenotype}, I also consider
that the confusion is deep seated and subtle.  In particular, I
believe that there are (at least) three quite different {\em
kinds\/} of misconception involved.

There are a number of more or less authoritative replies to the
tautology charge already available in the literature (some of
which I shall comment upon below); but these have, in general,
only recognised one or another of the various possible
misconceptions. I am not aware of any previous discussion which
has clearly distinguished all three kinds of misconception which
I identify here.  I suggest that this may explain why this debate
has sometimes appeared interminable: the participants have
frequently been talking at cross purposes. In itself, this would
justify the somewhat lengthy discussion given here; but the
discussion is also justifiable in its own terms for it
illuminates some quite important aspects of Darwinian theory
which might not otherwise be explicitly dealt with.

The discussion will (not surprisingly) be quite complex and
potentially confusing.  Therefore let me outline the general
structure in advance.

The arguments all revolve around Spencer's unfortunate phrase
``the survival of the fittest''. I shall initially show how the
phrase can be interpreted as an (approximately)
correct, non-tautologous, statement of \th{cs} (or, more
generally, \th{hs})---which is, presumably, the interpretation
Spencer intended. The first misconception which I consider is such
that the phrase is still ``correctly'' interpreted (i.e.\
as a statement of \th{cs}), but, in a certain peculiar and
austere sense, is labelled as tautologous {\em anyway}. Under the second
misconception, there are two distinct ways in which the phrase
can more or less correctly be interpreted as a {\em definition\/} of
``fitness''; both of these interpretations are, of course,
tautologous, but they are not statements of \th{cs} and do not
impinge upon its status. Under the third (and final)
misconception, there is an interpretation of the phrase which is
not strictly tautologous, but is not equivalent to \th{cs} (or
\th{hs}) either (and is, in fact, mistaken). This last error does
involve an element of circular reasoning, and might therefore be
still said to ``smack'' of tautology; in many ways it is the most
pernicious misconception of all.

In presenting this analysis I do not claim that my taxonomy is
complete or unique.  In practice, various combinations and
permutations of the errors identified below may well be
simultaneously present in any single author's treatment; and, of
course, there may be new errors which I am
unwittingly originating, in carrying out this very analysis.

\subsubsection{On ``survival''}

To analyse the arguments effectively, it is first necessary to
distinguish two quite separate notions of ``survival'':

\begin{quote}
{\bf Survival$_1$:} The survival of individual organisms (or
D-actors).
\end{quote}
Survival$_1$ obviously does not refer to survival in any absolute
sense: individual organisms are essentially mortal, and have
a finite lifetime---it is hardly meaningful to speak of individual
organisms ``surviving'' without qualification.  However, some
organisms do survive {\em longer\/} relative to others.  More
generally, there is potentially a valid notion of ``mean
survival$_1$''---i.e.\ that a certain ``kind'' (S-class?) of
organism may, in given environmental conditions, show a
consistent distribution of values for survival$_1$. Furthermore,
if (and only if) there exist {\em heritable\/} characteristic(s)
distinguishing such different ``kinds'' then they can serve to
differentiate S-classes (and, thus, S-lineages). In that case
coherent S-lineages, exhibiting distinctive (statistical)
distributions of survival$_1$, can be formed.  This distribution
of survival$_1$ would be a characteristic of an S-lineage, and
its mean value would be essentially equivalent to the reciprocal
of what has previously been called S-mortality. In fact, (mean)
survival$_1$ can be thought of as a crude measure of S-value
(crude because the latter depends, at least, on S-fecundity as
well as S-mortality); in particular it will generally be true
that the greater the value of (mean) survival$_1$ then the
greater the S-value of the corresponding S-lineage.

I emphasize that (mean) survival$_1$ (as with S-value proper) is
defined as an objective characteristic of an S-lineage in given
environmental conditions, which can (in principle) be evaluated
independently of any knowledge of the success or otherwise of the
S-lineage in competition with other S-lineages.

\begin{quote}
{\bf Survival$_2$:} The survival of organism lineages (in
particular, S-lineages).
\end{quote}
Survival$_2$ {\em does\/} (potentially) refer to ``absolute''
survival---in the sense that organism lineages can (apparently)
survive indefinitely long.

Survival$_2$ may also be related to S-value, but not in the
relatively direct way which holds for survival$_1$.
Let us suppose that, for {\em independent\/} reasons, we believe
that two competing S-lineages have significantly different
S-values.  Then we can infer that whichever S-lineage is the
eventual survivor$_2$ must have the greater value of S-value.  Note
carefully that this inference is valid if and only if we {\em
already\/} know that we are dealing with a case of S-lineage
selection.

It should be clear that survival$_1$ and survival$_2$ are not the
same thing.  While they {\em may\/} be related (ultimately via
\th{cs} as we shall see), this relationship is a contingent one;
it would not hold if, for example, there were no inheritable
characteristics which were well correlated with survival$_1$; or
if the S-lineages distinguished by different values of (mean)
survival$_1$ were not actually in competition with each other
etc.

\subsubsection{What Spencer Meant To Say?}

I suggest that the only correct interpretation of Spencer's phrase
(which is not {\em necessarily\/} the interpretation Spencer himself
intended) is the following: we interpret ``survival'' as
survival$_2$ (i.e.\ survival of \mbox{(S-)lineages);} we interpret
``fitness'' as {\em S-value}; ``the survival of the fittest'' is
then at once the assertion that:
\begin{itemize}

\item There exist at least some lineages which are fitter than
others (which implicitly requires fitness to be hereditary to
some extent).  Lineages so distinguished are, precisely,
S-lineages.

\item At least some of these S-lineages, of differing fitness,
are in competition with each other.

\item As a result, S-lineage selection occurs and, in any such
episode, the surviving S-lineage will be the fitter (i.e.\ having
the greater S-value).

\end{itemize}

As it stands this is simply \th{cs}. Assuming (by default) the
extension of this process indefinitely back in evolutionary time,
we get \th{hs}. It is not tautological---any more than \th{cs} or
\th{hs} is.

Again, it must be emphasized that this non-tautologous
formulation relies on the fact that S-value (fitness) is not {\em
defined\/} by lineage ``survival''---it is, in principle,
something that can be assessed of an S-lineage isolated from
competition (it is, in fact, a prerequisite for the operation of
selection). However, confusion might arise in cases where, for
{\em independent\/} reasons, one {\em already\/} believes that the
displacement of one S-lineage by another is, in fact, a case of
selection: in that scenario one can validly, and
non-tautologically, infer that the surviving S-lineage must have
had the greater S-value.

Essentially this (correct) interpretation has been commonly
identified in the literature---for example by Medawar
(see \ociteAD[p.~12]{Moorhead:WistarSymposium}), and
\citeAD[p.~58]{Hodge:DarwinsTheorizing}.

\subsubsection{Misconception 1: Logic}

As detailed in the previous section, once the premises for
natural selection are granted (and this is an empirical question)
then the outcome---``the survival of the fittest''---is assured.
That is, if we adopt these premises as {\em axioms}, in the sense
of a formal logical system (i.e.\ they are taken to be ``true'' by
definition), then ``the survival of the fittest'' becomes a
theorem of the system, which is to say, in the strict terminology
of formal logic, a {\em tautology}.

This is, of course, a technically valid point; but it can hardly
be called a {\em criticism}. It amounts to interpreting Spencer's
phrase {\em only\/} as the (necessarily ``tautological'') conclusion
of a certain deduction---rather than as an implicit assertion of
the truth of the premises which lead to that conclusion. This is
at best pedantic, at worst misleading. It is equivalent to saying
that $E=mc^2$ (say) is a tautology---given the relevant properties
of $E$, $m$ and $c$. As Maynard Smith has put it,
\begin{quote}
  Of course Darwinism contains tautological features: any
  scientific theory containing two lines of algebra does so\ldots

  \cciteAD[p.~85]{MaynardSmith:StatusOfNeoDarwinism}
\end{quote}

This is such a peculiar misconception that it seems difficult to
believe that it should genuinely arise. In practise I suggest
that it does not normally arise in isolation, but may be
combined with one of the other distinct misconceptions yet to be
described.  Having said that, there {\em is\/} at least one case
where this misconception seems to have been uniquely involved:
\begin{quote}
  The notion of natural selection depends on the empirically
  verifiable observation that offspring on the average resemble
  their parents more closely than they do the other members of
  the population, that individuals are not all the same; that all
  environments are not the same.  Concepts such as natural
  selection by the survival of the fittest are tautologous; that
  is, they simply restate the fact that only the properties of
  organisms which survive to produce offspring, or to produce
  more offspring than their cohorts, will appear in succeeding
  generations.

  \citeAD[p.~5]{Eden:Inadequacies}
\end{quote}

Eden does seem to use the correct interpretation of Spencer's
phrase (notwithstanding the fact that he immediately goes on to
use ``survive'' in the sense of survival$_1$ rather than
survival$_2$); but insofar as he describes it as a tautology he
merely seems to mean that {\em any\/} valid deduction
(``restatement'') from true premises is a ``tautology''.  While
formally correct, the observation does not add anything except,
possibly, confusion.

Consider also, the following comment from Dawkins:
\begin{quote}
  Biologists thought they needed a word for that hypothetical
  quantity that tends to be maximized as a result of natural
  selection.  They could have chosen `selective potential', or
  `survivability', or `W' but in fact they lit upon `fitness'.
  They did the equivalent of recognizing that the definition they
  were seeking must be `whatever it takes to make the survival of
  the fittest into a tautology'.  They redefined fitness
  accordingly.

  \citeAD[pp.~181--182]{Dawkins:ExtendedPhenotype}
\end{quote}

I suggest that what Dawkins means here is that fitness can be
(indeed has been) defined as whatever it takes to make ``the
survival$_2$ of the fittest'' into a logical consequence of the
existence of heritable fitness variations and competition. I
should emphasize that, in context, Dawkins is {\em not\/}
suggesting that this ``tautology'' can be translated into any
{\em criticism\/} of Darwinism; but, as with Eden's version, I
still find the reference to ``tautology'' to be confusing
and gratuitous.

\subsubsection{Misconception 2: Words}
\label{misconception2}
Spencer's phrase does reduce strictly to a tautology if
``fitness'' is equated with ``survival''; that is, the phrase is
read as a {\em definition\/} of fitness (and definitions are, of
course, a paradigmatic case of tautology). This formulation of the
tautology argument is the most common; a good example would be
that of \citeAD[pp.~241--242]{Popper:CloudsAndClocks}.\footnote{However note
  that Popper has since repudiated this analysis, as I
  shall discuss in section~\ref{metaphysics} below.}
As Dawkins puts it, this kind of argument is ``a remarkable
example of the elevation of words above their station''
\cciteAD[p.~181]{Dawkins:ExtendedPhenotype}.

This misconception leads to tautology regardless of whether we
take ``survival'' to mean survival$_1$ or survival$_2$.
Both cases are conceptually possible, although they have quite
different flavours.  In general, writers suffering from this
misconception are not clear about which sense they intend. In
fact, the most likely scenario may be a failure to distinguish
that there {\em are\/} two possible, but distinct, strictly
tautologous interpretations---for if that fact is once
recognised, the possibility of a non-tautologous (and correct)
interpretation more or less immediately presents
itself.\footnote{There may be a lingering misconception that all
  tautologies are equivalent, so that the
  possibility of ``distinct'' tautologies cannot arise; this is
  not the case. All tautologies have the same {\em truth\/} value
  (namely, unconditionally ``true''), so that they are {\em
  logically\/} equivalent---but this is not at all the same
  thing. ``Cats are a kind of domesticated feline'' and ``$\pi$
  is the ratio of the circumference to the diameter of a circle''
  are ({\it qua\/} definitions) two {\em different\/}
  tautologies.}

The two distinct cases of this misconception are as follows:
\begin{description}

\item[Case 1: ] {\em the survival$_1$ of the survivors$_1$}

This amounts to defining fitness as (mean) survival$_1$.

Now this interpretation is not ``incorrect''. As already
discussed above, survival$_1$ is indeed a possible, though
extremely crude, measure of S-value; and ``fitness'' can be (and
commonly is) interpreted as synonymous with S-value.  So it is
not entirely unreasonable to define fitness as (mean)
survival$_1$ (other things, particularly S-fecundity, being
equal).

But of course, under this interpretation, the phrase is no longer
an expression of (the theory of) natural selection---it
is merely a preliminary definition.  Pointing out its
tautologous nature cannot impinge at all on the status of
\th{cs} or \th{hs}.

\item[Case 2: ] {\em the survival$_2$ of the survivors$_2$}

This amounts to defining fitness as survival$_2$.

Unlike case~1, this is hardly even a coherent definition.
Since survival$_2$ is (at any given time) a binary valued
quantity, it is at least peculiar to equate it with ``fitness''
which, on any common sense interpretation, should be continuous valued.

But let us stretch this point, for the time being. We {\em
could\/} consider the phrase as equating fitness with
survival$_2$, {\em regardless of whether natural selection is
known to be operational}. But, as far as I am aware, this would
be a usage of ``fitness'' which has never been seriously
proposed, is counterintuitive, and would be of no apparent
utility.

This leaves only the possibility that we consider the phrase as a
definition of fitness {\em only in cases where we have prior,
independent, knowledge of the operation of natural selection.}

Well, in this case we cannot say it is positively incorrect---the
operation of selection guarantees precisely that survival$_2$
{\em will\/} be related to S-value (the ``normal'' meaning of
fitness), as already discussed for the correct, non-tautologous,
interpretation of Spencer's phrase.  At this point we are back to
a similar situation to that obtaining with Case~1: the
interpretation can ``reasonably'' be adopted, but it is no longer
an expression of (the theory of) natural selection---it is merely
a preliminary definition (and a rather confusing one at that).
Adopting this definition, we would then have to introduce some
additional term other than fitness (S-value perhaps?), whose
definition would {\em not\/} be already contingent on the
operation of selection, before we could even formulate \th{cs}
properly.  But, in any case, we again conclude that pointing out
the tautologous nature of this interpretation cannot impinge at
all on the status of \th{cs}, or \th{hs}.

\end{description}

\subsubsection{Misconception 3: Adaptation}

\label{misconception3}

The final misconception which arises does not strictly involve a
tautology, and is only incidentally inspired or supported by
Spencer's phrase.  However, it does involve a degree of ``circular''
reasoning, is sometimes {\em said\/} to be tautologous, and is commonly
associated with the strictly tautologous misconception(s) of the
previous section.  It is therefore appropriate to consider it
here.

I shall present the ``argument'' in what I consider to be its
plainest form, but caution that it is rarely if ever expressed
in such explicit terms:
\begin{enumerate}

\item \th{d} is proposed as a solution of \pr{d}---i.e.\ as an
explanation for the growth of adaptive complexity in the
phylogenetic tree.

\item For \th{d} to successfully solve \pr{d} would require
that it {\em predict\/} (statistically or otherwise) the growth
of adaptive complexity.

\item At best, the only thing that \th{d} actually predicts is a
growth of S-value in certain lineages.

\item Thus \th{d} can be said to solve \pr{d} only by
\mbox{(re-)defining}
adaptive complexity to be the same as S-value (fitness).  This
effectively uses a circular definition, which is just such that
the problem to be solved (originally \pr{d}) becomes simply
``whatever problem {\em can\/} be solved (by \th{d})''.

\end{enumerate}

Arguments of this sort are tacitly involved whenever there is a
debate about the relationship between ``fitness'' and
``adaptation''.  Darwinism is first taken to be a theory of the
growth of ``adaptation'' (informally conceived of in terms of
adaptive {\em complexity\/}); but it is then noticed that
Darwinism {\it per se\/} can actually only explain the growth of
``fitness'' (in the sense of S-value); so it seems that it can
work as an explanation only if adaptation is {\em defined\/} as
equivalent to fitness (and we forget our original informal notion
of adaptive complexity, or adaptation to an environment).  This
does not turn Darwinism into a tautology in any strict sense
(though it does involve a kind of circularity); but if this step
is taken then Darwinism loses its ability to solve the kind of
problem we were originally interested in---for the terms of the
problem no longer appear in the theory. It is thus greatly
diminished in scope and significance.

Popper raised essentially this problem in what was (as far as I
am aware) his earliest consideration of the status of Organismic
Darwinism---his Herbert Spencer lecture, {\em Evolution and the
Tree of Knowledge\/}:
\begin{quote}
  \ldots\ survival, or success in the sense of an increase in
  numbers, may be due to either of two distinguishable
  circumstances.  A species may succeed or prosper because it has
  managed, say, to improve its speed, or its teeth, or its skill,
  or its intelligence; or it may succeed or prosper merely
  because it has managed to increase its fecundity.  It is clear
  that a sufficient increase in fecundity depending fundamentally
  on genetical factors, or a shortening of the period of
  immaturity, may have the same survival value as, or even a
  greater survival value than, say, an increase in skill or in
  intelligence.

  \ldots\ But be this as it may, it should be possible, I think,
  to [measure] the {\it success in the adaptation of the
  individual organisms\/} of a species \ldots

  Without some distinction such as this \ldots\ we are liable to
  lose sight of the original problems of Lamarck and Darwin, and
  especially of the explanatory power of Darwin's theory \ldots

  \citeAD[pp.~271--272]{Popper:TreeOfKnowledge}
\end{quote}

Popper is essentially pointing out that the temptation to equate
adaptation (or adaptive complexity) with fitness (or S-value)
must be resisted at all costs, for otherwise we lose contact with
the problems we wish to solve. \citeAD{Lewontin:Adaptation} has
discussed this problem in very similar terms. Hull
has also recently made much the same point, concluding that the
requirement to identify adaptive complexity (which he actually
calls ``fitness'') independently of S-value (which he terms
``differential perpetuation'') cannot be circumvented ``without
evolutionary theory degenerating into an empirically empty
formalism'' \cciteAD[pp.~318--319]{Hull:IndividualityAndSelection}.

Now I have, indeed, been careful not to define adaptive
complexity in terms of S-value (or fitness).  Granted, I have not
attempted any formal or detailed definition of adaptive
complexity; and I have particularly eschewed any attempt to
establish a metric for it. But, as already discussed in
section~\ref{dprob}, this vagueness is not untypical in the
field; and I would argue that my general formulation in terms of
{\em inborn knowledge\/}
\cciteAD[pp.~258--259]{Popper:TreeOfKnowledge}
or {\em anticipatory systems\/} \cciteAD{Rosen:AnticipatorySystems}
is still a more definite ontological commitment that is usual.

It must be repeated that misconception~3 does not strictly
involve a tautology.  It is in this light that we must read
Hodge's \cciteD[p.~58]{Hodge:DarwinsTheorizing} claim that it is
``a mistake to defend natural selection against the tautology
objection by proposing criteria of fitness independent of
reproductive success''.  I suggest that Hodge is here referring
only to the {\em strictly\/} tautologous arguments already
discussed (particularly the two cases of misconception~2), and
{\em not\/} to misconception~3, which has quite a separate
character. Dunbar \cciteD[p.~10]{Dunbar:Tautology}, on the other
hand, {\em rejects\/} the argument that \th{cs} cannot be
tautological because it is empirically testable (i.e.\ the kind
of argument offered by Hodge), saying that ``this claim misses
the point entirely''. I contend that Dunbar is effectively taking
up a position precisely complementary to that of Hodge, confining
his attention exclusively to misconception~3 and ignoring or
dismissing misconceptions~1 and/or~2. My position is that,
despite the apparent contradiction between Hodge and Dunbar, they
are actually both correct, so far as they go---but they are
discussing different problems (I shall consider Dunbar's analysis
in more detail below).

At this point my argument is that misconception~3 is mistaken in
concluding that adaptation or adaptive complexity should, or
must, be defined in terms of S-value (fitness). I therefore
insist on retaining essentially independent definitions of
adaptive complexity and fitness (and thus retain \pr{d} in its
interesting form). What then are we to make of the original
criticism---that \th{d} cannot actually solve this problem, for
it does not predict the growth of adaptive complexity
(so-defined)?

This brings us to the nub of the problem, which is to ask how
much we can sensibly ask of a proposed solution of \pr{d}.  The
error is in supposing that a solution must (or even can) take the
form of some general theory which predicts a growth in adaptive
complexity. This derives in part from a fundamental
misunderstanding of what \pr{d} actually says.  \pr{d}
recognises that there has been a sustained, and progressive,
growth in adaptive complexity, in at least some evolutionary
lineages, and asks for an explanation of how this could be
(preferably one which does not assume the pre-existence of an
even more complex creator). It does {\em not\/} say that growth
in adaptive complexity {\em must\/} occur (in general or in
particular lineages); or that it had to occur in the particular
way which it did; or that it must continue occurring.  {\em But
only the latter kinds of problem would call for a solution which
incorporates a general prediction of growth of adaptive
complexity.}

We might characterise the general difficulty here as a
supposition that \pr{d} entails some kind of guaranteed,
monotonic, ``progress'' (in adaptive complexity). It is a harking
back to the ``great chain of being''.  As Gould puts it: ``The
familiar iconographies of evolution are all directed---sometimes
crudely, sometimes subtly---toward reinforcing a comfortable view
of human inevitability and superiority''
\cciteAD[p.~28]{Gould:WonderfulLife}. The idea of necessary progress
in evolution is so deeply entrenched that it is very difficult to
free oneself of it. Not even Darwin himself was completely
immune.  Although, as discussed in section~\ref{hstry} above, he
explicitly emphasized that the {\em absence\/} of ``perfection''
in biological organisms should be interpreted as positive
evidence in favour of the operation of natural selection (at
least as compared with a theistic theory), we still find him
remarking, in the concluding pages of {\em The Origin}, that
``\ldots\ as natural selection works solely by and for the good
of each being, {\em all corporeal and mental endowments will tend
to progress towards perfection\/}'' \cciteAD[Chapter~XIV,
emphasis added]{Darwin:TheOriginOfSpecies}.\footnote{See
  \cciteAD[Essay~4]{Gould:EverSinceDarwin} for a more detailed
  discussion of whether Darwin ``really'' endorsed the idea of
  necessary progress in evolution.}

Once, however, we free ourselves from the preconception that
organismic evolution is a story of necessary or inevitable
``progress''---and excise this idea from \pr{d}---then the way is
open to consider \th{d} as offering at least a partial solution;
indeed, as I have already argued (section~\ref{lamarck}), it may
offer as good a (general) solution as it is possible to give {\em
in principle}.

Briefly, as has been commented upon several times, \th{d} cannot
and does not predict the growth of adaptive complexity.  However,
given that adaptive complexity {\em has\/} grown, \th{d} can
retrospectively offer a generalised explanation for it---namely
that the growth of adaptive complexity ``happens'' to have been
correlated with the growth of S-value---and, crucially, \th{d}
can do this without postulating the existence of any ``designer''
(anticipatory system) directing the overall course of evolution.

\th{d} in itself, does not explain why adaptive complexity
should be correlated with S-value either in general, or in any
particular case; not does it explain how (heritable) adaptive
complexity can increase at all, in general or in any particular
case. In addressing \pr{d} it {\em does\/} entail that some
(heritable) increases in adaptive complexity have occurred, and
that, of these, at least some have been correlated with S-value;
but it does not require increases in adaptive complexity to
have been ``designed'' or ``anticipated'' (i.e.\ preferentially
generated), or that they should have been {\em universally\/}
correlated with S-value.

Now, of course, \th{d} {\em does\/} predict more or less
monotonic ``progress'' in one very specialised sense: increase in
S-value (within some lineages).  But that much is true of all
D-systems, and does not impinge at all on the central problem of
the growth of adaptive complexity.  No doubt we could conduct a
certain amount of evolutionary theorizing without ever referring
to adaptive complexity: but we can certainly never solve \pr{d}.
The crucial extra step, which is rarely made explicit is to say
that, given \th{d}, adaptive complexity can grow in evolutionary
lineages if and only if at least some increases in adaptive
complexity occur, and, of these, at least some are correlated
with a net increase in S-value (i.e.\ are selectively retained).

Of course, the reasoning given here only works at all if it is
accepted that an increase in adaptive complexity {\em might\/} be
correlated with greater S-value.  If I had defined adaptive
complexity in some (strange) way which was intrinsically opposed
to S-value (say, necessarily involving unconditional altruism on
the part of the S-lineage) then the argument could not go
through.  But my actual definition---which corresponds to
something like ``inate knowledge''---does precisely have the
characteristic that, {\it ceteris paribus}, it may be expected to
be correlated with higher S-values.  But the explicit inclusion
of the {\it ceteris paribus\/} clause is crucial here; to ignore
or omit it would effectively mean a reversion to equating
adaptive complexity with S-value, and thus defining away the real
problem.

None of this is to say that the growth of adaptive complexity
cannot be explained (or even predicted); it simply claims that
there cannot be any {\em general\/} theory of it (as always, this
is just another way of denying the existence of a logic of
induction).  \th{d} asserts precisely that, for all {\em
particular\/} historical cases of an increase in adaptive
complexity, there is a {\em particular\/} explanation, involving
an undirected or unbiased variation in adaptive complexity (which
happened to be an increase) which was selectively favoured. It
may or may not be possible to organise these particular,
historical, explanations into a smaller number of more general
cases: but I take the view that it will not be possible to
translate these particular explanations, nor generalisations
of them, into predictions for continuing growth of
adaptive complexity into the future. The aggregation of all the
particular cases (if such could be individually established)
would then be the complete (historical) ``explanation'' of all
growth of adaptive complexity in the biological world. But
\th{d} does not assert that such growth had to occur, nor that
it will continue into the future, nor even that it would
necessarily recur on another ``similar'' planet.

The confusions and misconceptions discussed here have centred on
the distinction between ``adaptation'' and ``fitness''.  For this
reason I have tried to avoid these terms in my own
general presentation of Darwinism: the only lingering remnant is
the ``adaptive'' in ``adaptive complexity''. I have retained this
in deference to the existing biological literature, but I suggest
that it might actually be better to eliminate even this
concession.  In speaking of the ``adaptation'' of biological
organisms it seems almost impossible not to think in terms
specifically relating to their success in living and
procreating---which is to positively invite a reversion to the
relatively sterile concept of S-value.

A particularly ``good'' example of this is Dunbar's analysis
\cciteAD{Dunbar:Tautology}. He
is very clear about the {\em need\/} to distinguish
``adaptation'' and ``fitness''.  Furthermore, he seems to adopt
much the same kind of distinction as I have suggested above,
interpreting adaptation in terms of ``problem-solving''
\cciteAD[p.~11]{Dunbar:Tautology}
(following \ociteAD{Lewontin:Adaptation}, among others). He
seems to recognise the essential {\em independence\/} of the two
concepts  when he cites Dobzhansky (apparently favourably) as
saying that ``we cannot draw inferences about fitness from a
knowledge of adaptation, nor of adaptation from a knowledge of
fitness'' \cciteAD[p.~14]{Dunbar:Tautology}.
However, he then goes on to explicitly deal
with the alleged circularity of Darwinian explanations, in the
following terms:
\begin{quote}
  The relationship between the concepts of adaptation and fitness
  might seem to confirm the worst fears of the anti-Darwinians.
  Each appears to depend on the other in a way which makes them
  virtually inseparable.  It is, however, crucial to appreciate
  that they are not {\it definitionally\/} interdependent:
  adaptation is not {\it defined\/} in terms of fitness, nor vice
  versa.  Adaptation (and hence reproductive success) is defined
  with reference to {\it individuals}, whereas fitness is defined
  with reference to genes and is thus a characteristic of
  populations.

  \cciteAD[p.~16--17]{Dunbar:Tautology}
\end{quote}

Dunbar here seems to suggest that the distinction between
adaptation and fitness is (merely?) a distinction between
properties of organisms and (consequent) properties of lineages.
The best interpretation I can offer of this is as a somewhat
tortuous reference to what I have called misconception~2
above---effectively a failure to distinguish survival$_1$ and
survival$_2$. Having thus retreated from the real
issue---misconception~3---Dunbar finds that he must admit that a
significant circularity may still remain in Darwinian theory. It
is perhaps not surprising that he then resorts to the
philosophical relativism of Kuhn and Feyerabend as his final
defence of Darwinism against circularity.
I, of course, take the view that such a conclusion is
unsatisfactory and unnecessary---that the conceptual independence
of fitness and adaptation (S-value and adaptive complexity)
can and should be recognised, and this
can be done without depriving Darwinism of its power as an
explanatory schema.  However, it does underline the point that
the terminology of ``fitness'' and ``adaptation'' may be
critically flawed.  Thus, if one confines oneself to discussion
in terms of (inate) knowledge, or (inate) anticipatory models,
instead of adaptation or adaptive complexity, it may be easier to
remember that there is no {\em necessary\/} connection between
these things and their retention or growth under natural
selection.  It should then be clear that any connection which may
exist will have to be individually argued for in each particular
case.

\subsection{\ldots\ or Metaphysics?}
\label{metaphysics}
As with the idea that Darwinism may be tautological, the
assertion that it is essentially metaphysical has been more or
less independently suggested (and criticised) by a number of
different authors.

The criticism of the so-called {\em adaptationist programme\/}
by Gould and Lewontin is an
example of this kind of argument
\cciteAD[p.~589]{Gould:SpandrelsOfSanMarco}. Indeed, Lewontin
has explicitly claimed that ``the adaptationist programme makes
of adaptation a metaphysical postulate, not only incapable of
refutation, but necessarily confirmed by every observation''
(\ociteAD{Lewontin:EncyclopediaEinaudi}, as quoted by
\ociteAD[p.~38]{MaynardSmith:Optimization}).

However, as already discussed at length in section~\ref{hstry}
above, the claim put forward by Gould and Lewontin is not
strictly that Darwinism {\it per se\/} is metaphysical.  Indeed,
they accept the reality of natural selection (i.e.\ \th{hs});
their argument is about which evolutionary phenomena are
explicable in terms of selection.  The adaptationist programme,
which they criticise, presumes that {\em all\/} evolutionary
phenomena (or organismic attributes) are the direct outcome of
selection.\footnote{In this respect, the term ``adaptationist''
  is unfortunate, as it invites a form of the tautology
  misconception~3; ``selectionist'' might be less prejudicial.}
Conversely, it seems clear that Gould and Lewontin accept that
what I have called complex adaptation, where it exists, does
demand an explanation in terms of selection; and, while such
explanations may, individually, be almost impossible to test in
practise, they are testable in principle, and are not therefore
metaphysical. Thus, {\em in terms of the problem of complex
adaptation (\pr{d}),\/} Gould and Lewontin appear to accept that
\th{d} is not metaphysical, and, indeed, that it is the best
theory currently available.

Concerns of a similar sort to those raised by Gould and Lewontin
have been independently discussed by various other workers.  For
example, they were prominent in the discussions at the {\em
Wistar\/} symposium on ``Mathematical Challenges to the
neo-Darwinian Interpretation of Evolution''
\cciteAD{Moorhead:WistarSymposium}.  Although Popper was not
present at this symposium, he was repeatedly cited (directly or
indirectly) as the source for such concerns.  Thus, for example,
Medawar makes the following comment in introducing the symposium:
\begin{quote}
  Then there are philosophical or methodological objections to
  evolutionary theory.  They have been very well voiced by
  Professor Karl Popper---that the current neo-Darwinian Theory
  has the methodological defect of explaining too much.  It is
  too difficult to imagine or envisage an evolutionary episode
  which could {\em not\/} be explained by the formulae of
  neo-Darwinism.
\end{quote}

Unfortunately, there are no detailed citations to original
sources, and I am not aware of Popper ever having
published {\em exactly\/} this criticism of Darwinism.  In any case,
my response to this argument is essentially as already discussed
in the case of Gould and Lewontin: while \th{d} is, undoubtedly,
difficult to test in respect of the evolution of specific complex
adaptations, it is still testable in principle (i.e.\ is not
metaphysical) and is the best theory currently available.

However, Popper {\em has\/} published a slightly different
argument for regarding Darwinism as metaphysical---or, more
precisely, as a {\em metaphysical research programme}
\cciteAD[Section~37]{Popper:Autobiography}. This arose (at least
partly) because, as already noted in
section~\ref{misconception2}, Popper's earliest considerations of
the status of Darwinian theory suffered from a form of
misconception~2, and he felt that the theory was therefore
``almost tautological''; yet he also felt that, {\em despite
this,} the theory had considerable explanatory power. Popper
seems to have thought that this apparent contradiction might be
resolved by regarding Darwinism as a metaphysical research
programme.  While I think his interpretation of Darwinism as
tautologous was mistaken, I actually agree that, in a certain
limited sense, it {\em can\/} usefully be regarded as
metaphysical.

Firstly, as discussed in \cciteAD{McMullin:DarwinianOntology}, I
consider that it is not unreasonable to describe the {\em
abstract\/} form of Darwinian theory, presented in that essay,
as a metaphysical research programme in Popper's sense. It is not a
scientific theory until the primitive entities (especially
D-actors) are given some specific empirical interpretation.  It must be
emphasized that to view this admission (of the metaphysical
nature of the abstract theory) as a {\em criticism\/} of any
particular interpretation of the theory (such as Organismic
Darwinism) would be to indulge again in a form of the tautology
misconception~1.  This, for example, is the only way in which I
can understand one of Peters' purported criticisms of Organismic
Darwinism \cciteAD[p.~4]{Peters:Tautology}, which is apparently
based on its being a specific interpretation of the axiomatic
Darwinism of \citeAD{Williams:ConsequencesOfEvolution}.

Having said that, it must be recognised that the abstract or
axiomatic form of Darwinism is metaphysical in a deeper or more
profound sense than the conventional abstract theories underlying
all science.  The general kind of problem which abstract
Darwinism seeks to solve is the growth of knowledge; and its
mechanism of solution entails a refusal to make predictions---it
``works'' (in the face of the impossibility of a logic of
induction) precisely by {\em declining\/} to predict the growth
of knowledge.  This is a quite unique kind of abstract theory.
It follows that, {\em even\/} when the abstract theory is
interpreted in specific empirical terms (such as in the form of
Organismic Darwinism) it can never predict the {\em future\/}
growth of knowledge.  We must say that, as long as such a
particular interpretation of Darwinism is viewed as an {\em
historical\/} theory of the {\em past\/} growth of knowledge it
is perfectly testable (in terms of ``retrodictions'') and
scientific; but if it is mistaken for a ``universal law'' of the
growth of knowledge, then, since it cannot predict such growth,
it must be treated as metaphysical. The (metaphysical) position
adopted here is, of course, that no ``universal law''
of the growth of knowledge exists.

It can be seen that this argument for viewing even Organismic
Darwinism (as opposed to Darwinism in the abstract) as metaphysical
hinges on its (in)ability to predict the future growth of
knowledge, or adaptive complexity; thus it is closely related to
what I have labelled tautology misconception~3.  This is brought
out clearly by considering Popper's most substantive
presentation of this viewpoint:
\begin{quote}
  \ldots assume that we find life on Mars consisting of exactly
  three species of bacteria with a genetic outfit similar to that
  of three terrestrial species.  Is [organismic] Darwinism
  refuted?  By no means.  We shall say that these three species
  were the only forms among the many mutants which were
  sufficiently well adjusted to survive.  And we shall say the
  same if there is only one species (or none).  Thus Darwinism
  does not really {\em predict\/} the evolution of variety.  It
  therefore cannot really {\em explain\/} it.  At best, it can
  predict the evolution of variety under ``favourable
  conditions''.  But it is hardly possible to describe in general
  terms what favourable conditions are---except that, in their
  presence, a variety of forms will emerge.

  And yet I believe I have taken the theory almost at its
  best---almost in its most testable form.  One might say that it
  ``almost predicts'' a great variety of forms of life.  In other
  fields, its predictive or explanatory power is still more
  disappointing.  Take ``adaptation''.  At first sight natural
  selection appears to explain it, and in a way it does; but
  hardly in a scientific way.  To say that a species now living
  is adapted to its environment is, in fact, almost tautological.
  Indeed we use the terms ``adaptation'' and ``selection'' in
  such a way that we can say that, if a species were not adapted,
  it would have been eliminated by natural selection.  Similarly,
  if a species has been eliminated it must have been ill adapted
  to the conditions.  Adaptation or fitness is {\em defined\/} by
  modern evolutionists as survival value, and can be measured by
  actual success in survival: there is hardly any possibility of
  testing a theory as feeble as this.

  \citeAD[pp.~136--137]{Popper:Autobiography}
\end{quote}

As already mentioned, Popper had earlier
\cciteAD{Popper:TreeOfKnowledge} recognised the
danger of misconception~3, and the consequent need to keep
adaptation and fitness (selection) clearly separated; but in this
later consideration of the problem he seems to have decided that
such separation cannot be achieved. Viewed as a putative theory
of the growth of adaptive complexity (i.e.\ of the evolution of a
``rich variety'' of more or less ``well adapted'' forms),
Darwinism then becomes irrefutable (metaphysical), for, no matter
how little the variety or adaptation we observe, it {\em could\/}
still result from Darwinian processes.

Clearly, I agree with the essence of Popper's argument; the
difference is that instead of disgarding Darwinism, I disgard the
idea that adaptation and fitness be defined in terms of one
another.  Granted, Darwinism cannot then ``predict'' the growth
of adaptation or adaptive complexity.  But, once adaptation is
interpreted in terms of {\em knowledge\/} this becomes precisely
consistent with Popper's general evolutionary epistemology, and
is seen as the strongest kind of theory we can expect.  And, as a
theory of the {\em historical\/} growth of adaptive complexity in
the biological world, it is perfectly scientific.

I have expended some effort in considering Popper's criticism of
the scientific status of Darwinism because I think it relates to
some difficult and important issues, which are relevant
objectives of this essay as a whole. However, it must be added
that Popper himself has, in any case, since modified his views
significantly \cciteAD{Popper:EmergenceOfMind}.

In particular, Popper has now recognised and corrected the error
implicit in tautology misconception~2, and accepted that
(Organismic) Darwinism can be so formulated that it is definitely
not tautologous. Unfortunately, he then goes on to say that, in
such a form, it is literally false (has been refuted).  At first
sight this is an even worse accusation than the original
assertion that the theory was (almost) tautologous and/or
metaphysical.  However, Popper's reformulation is the strong one
that {\em all\/} aspects of the phylogenetic tree are the outcome
of cumulative natural selection; such a strong claim, which is
essentially equivalent to the adaptationist programme criticised by
Gould and Lewontin, is, indeed, false. Popper does not explicitly
consider the lesser (but still non-tautologous) claim that all
instances of the growth of adaptive complexity (i.e.\ my \pr{d})
are the outcome of cumulative natural selection (i.e.\ my
\th{d}), and certainly does not argue that {\em this\/}
formulation has been refuted; so there is, in fact, no conflict
with the views I have expressed.

In conclusion, let me reiterate that I consider \th{d}, viewed as
an historical theory of the growth of adaptive, organismic,
complexity, to qualify as a good scientific theory---{\em
despite\/} the fact that actually testing it in specific cases is
enormously difficult. More specifically, \th{d} qualifies as
scientific according to {\em Popper's\/} criteria.  I emphasize
this last point because, even though Popper might be called a
``\naive'' falsificationist with respect to the {\em logic\/} of
(scientific) theories, he has always been a critical
falsificationist with respect to the {\em methodology\/} of
actually carrying out scientific research. This point has,
apparently, been commonly misunderstood or misrepresented
(\ociteAD[pp.~23--24]{Magee:Popper};
\ociteAD[pp.~981--984]{Popper:Replies}). The relevance of the
distinction here is that it can be a perfectly consistent
Popperian position to assert that Darwinism is scientific by
virtue of its (logical) falsifiability, {\em even\/} if such
falsifiability is {\em methodologically\/} almost impossible to
exploit (i.e.\ tests which could falsify the theory may be
perfectly conceivable, yet wholly impractical).

In this section I have given a detailed discussion of Popper's
assertions that Darwinism may be tautological and/or
metaphysical. I have noted that these assertions were, at the
least, confused, and that Popper himself has subsequently
clarified and corrected his position. I believe that this puts
the substantive issues to rest.  In closing, however, I note that
Popper's excursions into evolutionary biology seem, for
whatever reason, to have also occasionally provoked some quite
mistaken and/or irrelevant responses from professional
biologists; by definition, these do not affect the important
issues here, and therefore I relegate even my brief discussion of
them to Appendix~\ref{Herring}.

\section{Conclusion}

This essay has been concerned with the nature and status of
Darwinian theory in its conventional biological setting.  This is
important because there are persistent suggestions that, in some
sense, Organismic Darwinism is significantly or even fatally
flawed.  Clearly, if such doubts were justified, then it would
hardly be appropriate to consider the extension of Darwinism to any
other field.

I have suggested that such misgivings are unfounded: that a
careful analysis of Organismic Darwinism reveals it to be
perfectly scientific, and currently the best available theory to
explain the growth of adaptive organismic complexity. On the
other hand, I also hope to have established that this result is
by no means straightforward.  Darwinian theory is structurally
complex, and is, furthermore, extremely difficult to test {\em in
its entirety}.  While I have argued that it is better corroborated
than its competitors, these competitors do deserve serious
consideration, and the limitations in the {\em practical\/}
corroborability of Darwinism need to be acknowledged.  Similarly,
great care must be taken to avoid a variety of more or less
subtle misconceptions about the nature of Organismic Darwinism.

The most significant single result claimed in this essay is
that Organismic Darwinism is necessarily, and perhaps
irredeemably, incomplete: heritable variation and natural
selection do not and cannot, in themselves, guarantee any growth
in adaptive complexity.

Finally: this essay has been concerned exclusively with
establishing that Darwinism in general, and Organismic Darwinism
in particular, provide a more or less satisfactory {\em
overall\/} framework for the discussion of evolutionary biology;
granting that this has now been established, it must still be
admitted that there is considerable on-going debate, {\em
within\/} the scope of \th{d}, as to its detailed workings and
interpretation. These are inner issues in evolutionary biology,
which do not challenge the {\em essential\/} correctness of
\th{d}; nonetheless they represent substantive disagreements
which would necessarily colour any practical attempt to realise
artificial Darwinism.  I therefore intend, in a separate essay
\cciteAD{McMullin:GenicAndOrganismic}, to at least establish what
these disagreements are, if not to actually resolve them.

This is an internal Technical Report, and I rely on the
informality of that medium to excuse the many rough edges
remaining. In any case, I would greatly appreciate comments and
criticism of any sort.

\section*{Acknowledgements}

This essay is part of an ongoing attack on the problem of
realising the spontaneous growth of Artificial Knowledge by
Darwinian (or any other!) means.  In this pursuit, I have
benefited greatly from discussions with colleagues, particularly
Noel Murphy in DCU, and John Kelly of University College Dublin.
Paul~McKevitt also made useful comments on an earlier draft of
the essay. I am indebted to the School of Electronic Engineering
in DCU (particularly through the agency of its Head, Charles
\mbox{McCorkell}) for continuing encouragement, not to mention material
support. All errors remain, of course, my own responsibility.

\clearpage
\appendix
\section*{Appendices}
\addcontentsline{toc}{section}{Appendices}
\section{Dawkins' Microscope}
\label{Microscope}
Fisher's \cciteD[pp.~41--44]{Fisher:GeneticalTheory} argument
against saltationism (discussed in section~\ref{saltation2}
above) centers on the \mbox{(im-)probability} that a random
movement in a Euclidean $n$-space will bring a given point closer
to a specified target (``optimal'') point; he gives exact results
for the cases $n = 3$ and $n\rightarrow\infty$, and a qualitative
discussion based on these.
\citeAD[pp.~230--236]{Dawkins:BlindWatchmaker}, on the other
hand, in a generally laudable attempt to simplify Fisher's
original argument, chooses to work with a system in which $n =
1$. Now this {\em is\/} actually derived from an hypothetical
analogy given by Fisher: \begin{quote}

  The conformity of these statistical requirements with common
  experience will be perceived by comparison with the mechanical
  adaptation of an instrument such as a microscope, when adjusted
  for distinct vision.  If we imagine a derangement of the system
  by moving a little each of the lenses, either longitudinally or
  transversely, or by twisting through an angle, by altering the
  refractive index and transparency of the different components,
  or the curvature, or the polish of the interfaces, it is
  sufficiently obvious that any large derangement will have a
  very small probability of improving the adjustment, while in
  the case of alterations much less than the smallest of those
  intentionally effected by the maker or operator, the chance of
  improvement should be almost exactly one half.

  \cite[p.~44]{Fisher:GeneticalTheory}
\end{quote}

Note carefully, that, as originally stated by Fisher, this
example involves multiple degrees of freedom ($n$ is certainly
more than~3) and is therefore a perfectly correct illustration of
Fisher's abstract analysis.  However, Dawkins' version of the
example is rather different:
\begin{quote}
  Suppose that the {\it (sic)\/} lens is slightly lower than it
  ought to be for perfect focus, say a tenth of an inch too close
  to the slide. Now if we move it a small amount, say a hundredth
  of an inch, in a random direction, what are the odds that the
  focus will improve?

  \cite[p.~232]{Dawkins:BlindWatchmaker}
\end{quote}

By talking specifically in terms of the alteration of a single
real-valued parameter (the position of ``the'' lens) Dawkins
implicitly shifts from Fisher's multiple degrees of freedom (``by
moving a little {\em each\/} of the lenses'' etc.) to just a
single degree of freedom, which yields a mutational space of just
one dimension ($n = 1$).  This is a case which was not explicitly
analysed by Fisher at all; and as it happens, the behaviour in this
case is rather distinctive. Dawkins seems (at first at least) to
have overlooked this for his qualitative discussion of the
outcome still directly echoes Fisher's discussion of the case
$n\rightarrow\infty$:
\begin{quote}

  I think it really will now be sufficiently obvious [!] that the
  smaller we make the move, the closer we shall approach the
  extreme case in which the odds of an improvement are one-half;
  and the larger we make the move, the closer we shall approach
  the extreme case in which the odds of an improvement are zero.

  \citeAD[p.~232]{Dawkins:BlindWatchmaker}
\end{quote}

The technically correct statement for the $n = 1$ case is
actually as follows (with $r$ and $d$ as defined by Fisher---see
the discussion in section~\ref{saltation2} above). The adjustment
is $\pm r$ with equal probability of each of the two directions.
Then $\forall \; r \geq d$ the probability of improvement is exactly
0 (as already noted, this holds regardless of $n$); and $\forall
\; r < d$ the probability of improvement is exactly $0.5$ (this is
specific to the case $n = 1$).  Note that the probability does
{\em not\/} (in this special case) change continuously with $r$,
approaching 0.5 only in the limit as $r \rightarrow 0$, as
described by Dawkins; rather, it changes discontinuously at
$r = d$, and is otherwise constant. Strangely, Dawkins {\em
does\/} (implicitly) use this correct analysis when he comes to
consider a specific numerical example:
\begin{quote}
  If the microscope starts 2 inches out of focus, then a random
  change of 1 inch has a 50 per cent chance of being an
  improvement, {\em just as a random change of one-hundredth of
  an inch has.}

  \citeAD[p.~232, emphasis added]{Dawkins:BlindWatchmaker}
\end{quote}

Dawkins further confuses matters (for me at least) by stating
that Fisher's argument ``depends on the initial assumption that
the microscope was already pretty close to being in focus before
we even started making random adjustments''
\cciteAD[p.232]{Dawkins:BlindWatchmaker}.  In fact, Fisher makes
no formal or explicit statement of such an assumption (presumably
Dawkins takes it as implicit in the reference, at the start of
the paragraph quoted above, to the microscope being ``adjusted
for distinct vision''); and, more to the point, it is certainly
not {\em necessary\/} to Fisher's argument.  His result is, in
effect, scaled relative to $d$, and therefore holds {\em
regardless of how large $d$ might be}.  To be fair, Dawkins
actually goes on to say this (more or less)---the point he wishes
to make about the ``initial'' distance from the peak ($d/2$)
being ``small'' seems to be quite separate (though I confess I am
still not quite clear what this separate point is); but his
conflation of the two issues seems to me to be another
unnecessary distraction.

But to conclude on this issue, while Dawkins' discussion is
technically slightly inconsistent, and therefore somewhat
confusing, it would not merit discussion for that in itself.  My
real reason for reviewing Dawkins' version of Fisher's argument
is to point out that, as stated, it yields only the {\em weak\/}
form of the result---that adaptation (in this model of evolution
at least) can be improved only by displacements of size $r < d$;
whereas, Fisher's original argument does not even explicitly
mention this weaker result, but emphasizes instead the case of
``large'' $n$ ($n \rightarrow \infty$), which yields the
distinct, and stronger, result that adaptation can be feasibly
improved only by much smaller displacements than this (we must
actually have $r \stackrel{<}{\sim} d / \sqrt{n}$, which is to
say, $r \ll d$).

% [The following discussion is, I think, flawed; but there may be a
% core of something useful in it, so I comment it out instead of
% actually deleting it....]
%
% Dawkins has presented another separate discussion of saltationism
% (\ociteAD[pp.~233--236]{Dawkins:BlindWatchmaker};
% \ociteAD[pp.~414--418]{Dawkins:UniversalDarwinism}).  Briefly, he
% contrasts what he calls a {\em Boeing~747\/} saltation with a
% {\em Stretched~DC-8\/} saltation.  The former envisages a
% complete Boeing~747 being constructed through the chance effects
% of, say, a tornado blowing through a junk yard (Dawkins
% ``credits'' this original idea to Sir Fred Hoyle); the latter
% corresponds to a Stretched~DC-8 being constructed by the same
% process as a normal DC-8 but with a relatively minor change in
% procedures (namely, a section which is already duplicated several
% times along the fuselage is duplicated a few more
% times---complete with seats, services, etc.).  Both of these
% might be called saltations, for they both involve ``large''
% changes in the organisation of a collection of parts; but Dawkins
% argues that only the 747~variety involves a ``large'' increase in
% ``complexity'', and it is only this kind of saltation that is
% ruled out as a significant factor in evolution.
%
% Dawkins appears to view this argument as quite separate from
% Fisher's analysis, but I am not fully satisfied that there is a
% real distinction.  While he now implicitly introduces some notion
% of hierarchical embryological development into the discussion, I
% am not sure how this makes any substantive difference. We have a
% space (of configurations of junk yard materials) of high
% dimensionality, with peaks which are (by Dawkins' hypothesis) few
% and far between.  That being the case, if we take a ``large''
% jump in a ``random'' direction (747~saltation) then (regardless
% of our starting point) it is exceedingly unlikely that we will
% land anywhere near any peak. If, on the other hand, we are
% already half way up a peak, and we take a very ``small'' jump
% then there may be a significant probability (approaching 0.5 for
% arbitrarily small jumps) that we will get a little bit closer
% (Stretched~DC-8) to the local peak.
%
% Given this interpretation, a similar criticism can be made as of
% Fisher's original argument: it must be accepted that there are
% multiple peaks in the space (if you have the materials in your
% junk yard to build a 747 then surely there are many other
% machines, more or less equally ``functional'', potentially
% constructible from the same parts? The assumption of a
% structured, hierarchical, ``embryological'' process, only seems
% to strengthens this claim).   Now, in this case, without a
% comprehensive and quantitative theory of the topology of the
% S-value landscape it is quite impossible to rule out, as
% significant (albeit rare) evolutionary events, jumps that go from
% the neighbourhood of one peak to the neighbourhood of a quite
% separate one, (which, I suggest, is the only sensible
% ``definition'' of saltation in this context).
%
% Granted, ``small'' jumps (and plenty of them) must still be
% called upon to explain an evolutionary trajectory which consists
% in climbing to the top of a local peak; but a purely qualitative
% discussion (such as that provided by Dawkins) is quite incapable
% of establishing the relative contributions of these two cases to
% biological evolution as a whole.  It may well be that one is
% wholly dominant, to the extent that the other can be more or less
% ignored; but Dawkins has surely not demonstrated
% this.
%
% In any case, Dawkins seems to have since modified his views
% somewhat, with his introduction of a concept of the ``evolution
% of evolvability'' \cciteAD{Dawkins:Evolvability}; this is
% discussed at greater length in sections\ref{unjustified}
% and~\ref{mutationism} above.

\section{Three Red Herrings}
\label{Herring}
In the body of the report I detailed my views of the scientific
status of Organismic Darwinism, including an extended
consideration of Karl Popper's various comments on this issue. If
the only response to Popper's analysis had been to criticise and
highlight his error, then that could be the end of this
discussion. Unfortunately, it is the case that, for whatever
reason, Popper's analysis has provoked, {\it inter alia}, some
responses which actually tend to further confuse the issues
rather than clarify them, and these should therefore be
considered here, even if only briefly.

Firstly, consider the following comment by Rose:
\begin{quote}
  \ldots But more than a century ago Darwin pointed out quite
  bluntly that there was no such thing as fact-collecting in a
  vacuum; facts are always collected {\em for\/} or {\em
  against\/} a particular hypothesis.  Popper, of course, has
  made his career as a philosopher of science elaborating
  Darwin's insight (though without, I believe, ever crediting it,
  perhaps because of the reservations he has had, at least over
  a long part of his philosophical career, concerning the
  scientific status of Darwinian evolutionary theory).

  \citeAD[p.~4]{Rose:IntroductionToScienceAndBeyond}
\end{quote}

This really seems a very cheap shot. If Rose had any valid
criticism to offer, either of Popper personally (for failing to
credit his sources appropriately), or of Popper's view of
Darwinism, then he could have expressed these forthrightly and
substantively---rather than confounding the two, in the form of a
purely offhand remark, as he has.  In any case, one would have
thought that, before making such an attack, he would have taken
the elementary precaution of being factually correct.  As it
happens, Popper {\em has\/} explicitly credited Darwin with the
insight that ``all observation must be for or against some
view'', \cciteAD[p.~259]{Popper:TreeOfKnowledge}. In fact,
Popper gives a detailed citation, which is rather more than Rose
does. More pertinently, this acknowledgment appears in the
lecture {\em Evolution and the Tree of Knowledge},
which was discussed in section~\ref{misconception3} above---i.e.\
one of the primary documents which Rose would necessarily be
familiar with {\em if\/} he had ever given any serious
consideration to Popper's ``reservations about the scientific
status of Darwinism''.  In any case, the important point which I
wish to make is that innuendo is hardly a substitute for rational
criticism.

Consider next, the discussion by \citeAD{Halstead:Popper}.
Halstead is described as a paleontologist, and the proximal
target of his criticism seems indeed to be Popper's analysis of
(Organismic) Darwinism.  However, he does not in fact attempt any
direct response to these views of Popper's, but chooses instead
to launch a peculiarly speculative and personalised attack on
Popper's entire philosophy of science. Popper has provided his
own response to this \cciteAD{Popper:HalsteadLetter};
Bondi has also independently made similar criticisms of
Halstead's position \cciteAD{Bondi:HalsteadLetter}.  Halstead's
primary error is to suppose that Popper has denied scientific
status to (Organismic) Darwinism {\em because\/} its phenomena are
essentially historical. Halstead asserted this particular idea
without any definite citation of Popper's work.  I am not aware
of Popper ever having made such a claim,\footnote{Halstead's
  criticism {\em might\/} validly have been leveled at Peters, who
  certainly comes close to denying scientific status to Darwinism
  on the basis of its historical nature
  \cciteAD{Peters:Tautology}.  However,
  Halstead does not cite Peters, and, in any case, Peters
  describes his ``criteria for the acceptance of a scientific
  theory'' as deriving from the logical positivists---which, in
  itself, would automatically redirect any criticism of Peters'
  view away from Popper.}
and, in his own response to Halstead, he stipulates that
historical disciplines may indeed be perfectly scientific
according to his criteria.

Finally, consider \citeAD[p.~347]{Gribbin:DoubleHelix}. He
firstly asserts (possibly working from secondary sources) that
Popper's comments on (Organismic) Darwinism are ``half-baked'';
but he then offers, as his primary refutation of Popper's views,
the work of \citeAD{Penny:TestingTheTheoryOfEvolution} on
establishing the structure of the phylogenetic tree from protein
sequencing data. Gribbin actually describes this as ``\ldots\ the
test I like best, which seems utterly to refute both Popper's
original claim and the spurious arguments of those who invoke
Popper as an ally in their attacks on evolutionary theorizing'';
but, as discussed in section~\ref{origin} above, this work
relates entirely to \th{t} and (therefore) does not bear on
\th{d} at all!

In fact Popper has, so far as I am aware, always accepted the
reality of evolutionary descent. Thus, we have, for example, his
comment:
\begin{quote}
  I have always been extremely interested in the theory of
  evolution, and very ready to accept evolution as a fact.

  \citeAD[p.~133]{Popper:Autobiography}
\end{quote}

There is thus no reasonable sense in which the work of Penny
{\it et al.\/} could be interpreted as being contrary to (much
less as ``utterly refuting'') anything proposed by Popper.

In conclusion, the interesting point in all of this is that, even
though Popper was, in fact, mistaken in his analysis of
Darwinism, and even though there are good arguments against his
views, all three of these writers have chosen instead to
attribute to Popper views which he has never actually expressed
or defended! It seems to me that such stratagems, whether
conscious or otherwise, have only served to further confuse the
issues at hand.

\clearpage
\bibliography{phd}
\bibliographystyle{citeAD}

\end{document}
