Peter R Smith

The "tangle" referred to in my title is a special set of problems that arise in understanding the evolution of mental representation. These are problems over and above those involved in reconstructing evolutionary histories in general, over and above those involved in dealing with human evolution, and even over and above those involved in tackling the evolution of other human psychological traits. I am talking about a peculiar and troublesome set of interactions and possibilities, linked to long-standing debates about the status of folk psychology and the nature of semantic properties

Why these notes? After all, I’ve written An Introduction to Gödel’s Theorems. Surely that’s more than enough to be going on with? Ah, but there’s the snag. It is more than enough. In the writing, as is the way with these things, the book grew far beyond the scope of the lecture notes from which it started. And while I hope the result is still pretty accessible to someone prepared to put in the time and effort, there’s a lot more in the book than is really needed by philosophers meeting the incompleteness theorems for the first time. After all, you might want to get your heads around only those technical basics which are actually needed for understanding philosophical discussions about incompleteness. So you need a cut-down version of the book – an introduction to the Introduction! Well, isn’t that what lectures are for? Indeed. But there’s another snag. I haven’t got many lectures to play with. So either I crack on at quite a fast pace, cover those basics, but perhaps leave too many people puzzled and alarmed. Or I do relaxed talk’n’chalk, highlighting the really Big Ideas, making sure everyone is grasping them as we go along, but inevitably omit important stuff and leave quite a gap between what happens in the lectures and what happens in the book. What to do? I’m going for plan. But then I still need to do something to fill that gap between lectures and book. Hence these notes. The idea, then, is to give relaxed lectures, highlighting Big Ideas, not worrying too much about depth or fine-detail. Then after the lecture, I’ll write up notes that expand things just enough, and then give pointers to relevant chunks of IGT. The idea, however, is for the notes to be more or less stand-alone, and to tell a brief but coherent story read by themselves. So occasionally I’ll copy a paragraph or two from the book, rather than just refer to them. Warning: just occasionally in these notes, I’ll no doubt apply that good maxim ‘Where it doesn’t itch, don’t scratch’.

odel’s Theorems (CUP, heavily corrected fourth printing 2009: henceforth IGT ). Surely that’s more than enough to be going on with? Ah, but there’s the snag. It is more than enough. In the writing, as is the way with these things, the book grew far beyond the scope of the lecture notes from which it started. And while I hope the result is still pretty accessible to someone prepared to put in the time and effort, there is – to be frank – a lot more in the book than is really needed by philosophers meeting the incompleteness theorems for the first time, or indeed by mathematicians wanting a brisk introduction. You might reasonably want to get your heads around only those technical basics which are actually necessary for understanding how the theorems are proved and for appreciating philosophical discussions about incompleteness. So you need a cut-down version of the book – an introduction to the Introduction! Well, isn’t that what lectures are for? Indeed. But there’s another snag. I haven’t got many lectures to play with. So either (A) I crack on at a very fast pace (hard-core mathmo style), cover those basics, but perhaps leave too many people puzzled and alarmed. Or (B) I do relaxed talk’n’chalk, highlighting the really Big Ideas, making sure everyone is grasping them as we go along, but inevitably omit important stuff and leave quite a gap between what happens in the lectures and what happens in the book. What to do? I’m going for plan (B). But then I ought to do something to fill that gap between lectures and book. Hence these notes. The idea, then, is to give relaxed lectures, highlighting Big Ideas, not worrying too much about depth or fine-detail (nor even about getting through all of the day’s intended menu of topics). These notes then expand things just enough, and give pointers to relevant chunks of IGT. Though I hope these notes will be to a fair extent be stand-alone, and tell a brief but coherent story read by themselves: so occasionally I’ll copy a paragraph or two from the book, rather than just refer to them..

In Episode 1, we introduced the very idea of a negation-incomplete formalized theory T . We noted that if we aim to construct a theory of basic arithmetic, we’ll ideally like the theory to be able to prove all the truths expressible in the language of basic arithmetic, and hence to be negation complete. But Gödel’s First Incompleteness Theorem says, very roughly, that a nice theory T containing enough arithmetic will always be negation incomplete. Now, the Theorem comes in two flavours, depending on whether we cash out the idea of being ‘nice enough’ in terms of (i) the semantic idea of T ’s being a sound theory, or (ii) the idea of odel’s own T ’s being a consistent theory which proves enough arithmetic. And we noted that G¨.

My title is intended to echo Hans Reichenbach's The Rise of Scientific Philosophy (1951), and the phrase "scientific epistemology" is intended in two Reichenbachian senses. One involves the epistemology of science; the other involves epistemology undertaken with a scientific orientation. Talk of "progress and procedures" is intended in a similar dual sense. I start by looking back over the last century, at how a family of problems was tackled by scientifically oriented philosophers. These are problems with the nature of evidence and testing – with how, given our limited access to the world and the ambitious reach of our theories, we can have good reason to believe one such theory over another. These discussions were informed especially by skeptical treatments of the problem in Hume. We see in this period a number of different theoretical strands. These are characterized by different raw materials, and by different organizing or paradigm cases – different bets regarding the parts of scientific practice that should function as exemplars.

"Additive variance in fitness" is an important concept in the formal apparatus of population genetics. Wimsatt and Lloyd have argued that this concept can also be used to decide the "unit of selection" in an evolutionary process. The paper argues that the proposed criteria of Wimsatt and Lloyd are ambiguous, and several interpretations of their views are presented. It is argued that none of these interpretations provide acceptable criteria for deciding units of selection. The reason is that additive variance in fitness can be both a cause of evolution, but also a byproduct of selection at another level.

Group-structured populations, of the kind prominent in discussions of multilevel selection, are contrasted with ‘neighbor-structured’ populations. I argue that it is a necessary condition on multilevel description of a selection process that there should be a nonarbitrary division of the population into equivalence classes (or an approximation to this situation). The discussion is focused via comparisons between two famous problem cases involving group structure (altruism and heterozygote advantage) and two neighbor-structured cases that resemble them. Conclusions are also drawn about the role of correlated interaction in the evolution of altruism. 1 Introduction 2 Two Kinds of Population Structure 3 Objections and Replies 4 Particles on a Line 5 Conclusion Appendix: Neighborhoods and Selection CiteULike    Connotea    Del.icio.us    What's this?

The role played by the concept of genetic coding in biology is discussed. I argue that this concept makes a real contribution to solving a specific problem in cell biology. But attempts to make the idea of genetic coding do theoretical work elsewhere in biology, and in philosophy of biology, are probably mistaken. In particular, the concept of genetic coding should not be used (as it often is) to express a distinction between the traits of whole organisms that are coded for in the genes, and the traits that are not.

Group-structured and neighbor-structured populations are compared, especially in relation to multilevel selection theory and evolutionary transitions. I argue that purely neighborstructured populations, which can feature the evolution of altruism, are not properly described in multilevel terms. The ability to “gestalt switch” between individualist and multilevel frameworks is then linked to the investigation of “major transitions” in evolution. Some explanatory concepts are naturally linked to one framework or the other, but a full understanding is best achieved via the use of both.

Maynard Smith is right that one of the most striking features of contemporary biology is the ever-increasing prominence of the concept of information, along with related concepts like representation, programming, and coding. Maynard Smith is also right that this is surely a phenomenon which philosophers of science should examine closely. We should try to understand exactly what sorts of theoretical commitment are made when biological systems are described in these terms, and what connection there is between semantic descriptions in biology and in other domains.

One of the most striking developments in recent biology has been the proliferation of concepts such as coding, information, representation and programming, especially applied to genes. The idea that genes can be described as having semantic properties, as well as ordinary causal properties, has become so uncontroversial in many quarters that it now appears prominently in biology textbooks. Scott Gilbert's widely used developmental biology text, to pick just one example, tell us that "the inherited information needed for development and metabolism is encoded in the DNA sequences of the chromosomes" (Gilbert 1997 p. 5).

We’ve now proved our key version of the First Theorem, Theorem 42. If T is the right kind of ω-consistent theory including enough arithmetic, then there will be an arithmetic sentence GT such that T GT and T ¬GT. Moreover, GT is constructed so that it is true if and only if unprovable-in T (so it is true). Now recall that, for a p.r. axiomatized theory T , Prf T(m, n) is the relation which holds just if m is the super g.n. of a sequence of wffs that is a T proof of a sentence with g.n. n. This relation is p.r. decidable (see §25.4). Assuming T extends Q, it can capture any p.r. decidable relation, including Prf T (§22). So we can define..

The commentaries by Dennett, Sterelny, and Queller on Darwinian Populations and Natural Selection (DPNS) are so constructive that they make it possible to extend and improve the book’s framework in several ways. My replies will focus on points of disagreement, and I will pick a small number of themes and develop them in detail. The three replies below are mostly self-contained, except that all my comments about genes, discussed by all three critics, are in the reply to Queller. Agential views of evolution, discussed by Queller and Dennett, are addressed in my reply to Dennett

A wide range of ecological and evolutionary models predict variety in phenotype or behavior when a population is at equilibrium. This heterogeneity can be realized in different ways. For example, it can be realized through a complex population of individuals exhibiting different simple behaviors, or through a simple population of individuals exhibiting complex, varying behaviors. In some theoretical frameworks these different realizations are treated as equivalent, but natural selection distinguishes between these two alternatives in subtle ways. By investigating an increasingly complex series of models, from a simple fluctuating selection model up to a finite population hawk/dove game, we explore the selective pressures which discriminate between pure strategists, mixed at the population level, and individual mixed strategists. Our analysis reveals some important limitations to the ESS framework often employed to investigate the evolution of complex behavior.

Our last big theorem – Theorem 6 – tells us that if a theory meets certain conditions, then it must be negation incomplete. And we made some initial arm-waving remarks to the effect that it seems plausible that we should want theories which meet those conditions. Later, we announced that there actually is a consistent weak arithmetic with a first-order logic which meets the conditions (in which case, stronger arithmetics will also meet the conditions); but we didn’t say anything about what such a weak theory really looks like. In fact, we haven’t looked at any detailed theory of arithmetic yet! It is high time, then, that we stop operating at the extreme level of abstraction of Episodes 1 and 2, and start getting our hands dirty. This Episode introduces a couple of weak arithmetics, before we tackle the canonical first-order arithmetic PA in the following instalment. By all means skip fairly lightly over some of the more boring proof details! But it is certainly worth getting just a flavour of how these two simple formal theories work

Research in archaeology and anthropology on the evolution of modern patterns of human behavior often makes use of general theories of signs, usually derived from semiotics. Recent work generalizing David Lewis’ 1969 model of signaling provides a better theory of signs than those currently in use. This approach is based on the coevolution of behaviors of sign production and sign interpretation. I discuss these models and then look at applications to human prehistoric behavior, focusing on body ornamentation, tools, and other artifacts.