Peter Smith

Needless to say, Charles Parsons’s long awaited book1 is a must-read for anyone with an interest in the philosophy of mathematics. But as Parsons himself says, this has been a very long time in the writing. Its chapters extensively “draw on”, “incorporate material from”, “overlap considerably with”, or “are expanded versions of” papers published over the last twenty-five or so years. What we are reading is thus a multi-layered text with different passages added at different times. And this makes for a rather bumpy read. There is another route Parsons could have taken: he could have reprinted the relevant papers with postscripts, and then top-and-tailed the collection with a preface and added concluding reflections. It must sound very ungrateful, but I rather suspect that that might have worked better. Much of the book is about arithmetic. But Parsons has woven into the discussion claims about mathematics more generally and about set theory in particular. We might well have a basic worry about this structure: for do defensible claims about the ontology and epistemology of arithmetic have to be generalizable to apply to more infinitary mathematics? For example, suppose you are attracted to a Hellman-like modal structuralist account of arithmetic: then should you think it a problem if you suspect that such an account can’t readily be extended to cope e.g. with set theory (since you boggle at the idea of possible worlds free of abstracta but with enough structure to somehow model ZFC)? Parsons himself seems to waver over such questions. So for present purposes, I’ll focus just on arithmetic, and in what follows I’ll revisit two of the most familiar Parsonian themes, his views on structuralism as an account of the ontology of arithmetic, and his exploration of the role of intuition in grounding arithmetical knowledge.

Needless to say, Charles Parsons’s long awaited book1 is a must-read for anyone with an interest in the philosophy of mathematics. But as Parsons himself says, this has been a very long time in the writing. Its chapters extensively “draw on”, “incorporate material from”, “overlap considerably with”, or “are expanded versions of” papers published over the last twenty-five or so years. What we are reading is thus a multi-layered text with different passages added at different times. And this makes for a rather bumpy read. There is another route Parsons could have taken: he could have reprinted the relevant papers with postscripts, and then top-and-tailed the collection with a preface and added concluding reflections. It must sound very ungrateful, but I rather suspect that that might have worked better. Much of the book is about arithmetic. But Parsons has woven into the discussion claims about mathematics more generally and about set theory in particular. We might well have a basic worry about this structure: for do defensible claims about the ontology and epistemology of arithmetic have to be generalizable to apply to more infinitary mathematics? For example, suppose you are attracted to a Hellman-like modal structuralist account of arithmetic: then should you think it a problem if you suspect that such an account can’t readily be extended to cope e.g. with set theory (since you boggle at the idea of possible worlds free of abstracta but with enough structure to somehow model ZFC)? Parsons himself seems to waver over such questions. So for present purposes, I’ll focus just on arithmetic, and in what follows I’ll revisit two of the most familiar Parsonian themes, his views on structuralism as an account of the ontology of arithmetic, and his exploration of the role of intuition in grounding arithmetical knowledge

Our understanding of communication and its evolution has advanced significantly through the study of simple models involving interacting senders and receivers of signals. Many theorists have thought that the resources of mathematical information theory are all that are needed to capture the meaning or content that is being communicated in these systems. However, the way theorists routinely talk about the models implicitly draws on a conception of content that is richer than bare informational content, especially in contexts where false content is important. This article shows that this concept can be made precise by defining a notion of functional content that captures the degree to which different states of the world are involved in stabilizing senders’ and receivers’ use of a signal at equilibrium. A series of case studies is used to contrast functional content with informational content, and to illustrate the explanatory role and limitations of this definition of functional content. _1_ Introduction _2_ Modelling Framework _3_ Two Kinds of Content _3.1_ Informational content _3.2_ Functional content _4_ Cases _4.1_ Case 1: Simplest case _4.2_ Case 2: Partial pooling _4.3_ Case 3: Bottleneck _4.4_ Case 4: Partial common interest _4.5_ Case 5: Deception _4.6_ Case 6: A further problem arising from divergent interests _5_ Discussion Appendix

Modeling work by Brian Skyrms and others in recent years has transformed the theoretical role of David Lewis's 1969 model of signaling. The latter can now be understood as a minimal model of communication in all its forms. In this article, we explain how the Lewis model has been generalized, and consider how it and its variants contribute to ongoing debates in several areas. Specifically, we consider connections between the models and four topics: The role of common interest in communication, signaling within the organism, meaning, and the evolution of human communication and language.

We present a dynamic model of the evolution of communication in a Lewis signaling game while systematically varying the degree of common interest between sender and receiver. We show that the level of common interest between sender and receiver is strongly predictive of the amount of information transferred between them. We also discuss a set of rare but interesting cases in which common interest is almost entirely absent, yet substantial information transfer persists in a *cheap talk* regime, and offer a diagnosis of how this may arise.

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?

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

How did our capacities mentally to represent the world evolve? Here is one kind of answer: To represent the world is to have a special kind of wiring inside your head, and special physical connections between that wiring and the world. How do organisms come to have that kind of wiring? Both evolution and individual learning are involved, but there has at least to be an evolutionary explanation of how some organisms acquired the capacity to wire themselves up as representers. This evolutionary story probably will be one about the usefulness of that special kind of inner wiring for dealing with environmental problems; we owe this special wiring to a long history of mutation and natural selection. Asking about the evolution of mental representation is no different form asking about the evolution of the immune system or warm-bloodedness. We might hear this first answer from people like Fred Dretske, Ruth Millikan, David Papineau, and Kim Sterelny.

How did our capacities mentally to represent the world evolve? Here is one kind of answer: To represent the world is to have a special kind of wiring inside your head, and special physical connections between that wiring and the world. How do organisms come to have that kind of wiring? Both evolution and individual learning are involved, but there has at least to be an evolutionary explanation of how some organisms acquired the capacity to wire themselves up as representers. This evolutionary story probably will be one about the usefulness of that special kind of inner wiring for dealing with environmental problems; we owe this special wiring to a long history of mutation and natural selection. Asking about the evolution of mental representation is no different form asking about the evolution of the immune system or warm-bloodedness. We might hear this first answer from people like Fred Dretske, Ruth Millikan, David Papineau, and Kim Sterelny.

I discuss the bearing on the mind-body problem of some general characteristics of living systems, including the physical basis of metabolism and the relation between living activity and cognitive capacities in simple organisms. I then attempt to describe stages in the history of animal life important to the evolution of subjective experience. Features of the biological basis of cognition are used to criticize arguments against materialism that draw on the conceivability of a separation between mental and physical. I also argue against commonly held views about the "multiple realizability" of mental states of the kind seen in humans. The aim of the paper is to reconfigure and narrow the "explanatory gap" between mental and physical.

Methods and goals in philosophy are discussed by first describing an ideal, and then looking at how the ideal might be approached. David Lewis’s work in metaphysics is critically examined and compared to analogous work by Mackie and Carnap. Some large-scale philosophical systematic work, especially in metaphysics, is best treated as model-building, in a sense of that term that draws on the philosophy of science. Models are constructed in a way that involves deliberate simplification, or other imaginative modification of reality, in order to make relationships visible or problems tractable

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.

John Dewey’s Experience and Nature has the potential to transform several areas of philosophy. The book is lengthy and difficult, but it has great importance for a knot of issues in epistemology, metaphysics, and philosophy of mind. It bears also on metaphilosophy, devoting many pages to the discipline’s characteristic pathologies, and advancing a view of what sort of guidance “naturalism” provides. Later chapters move on to discuss art, morality, and value. So this is a major statement by Dewey. It may one day transform moral philosophy as he hopes, but this review will focus on the central ideas of the first two-thirds of the book. Here Dewey does succeed, I think, in motivating us to look at his core topics—experience and nature—in a new way. And though Dewey’s language is often obscure and unhelpful, some of the main ideas are simpler than they look.Earlier “pragmatist” philosophical work was novel in its focus on the relation between thought and action. This work had a broadly emp