Peter R. R. Smith

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..

Chaotic dynamics has been hailed as the third great scientific revolution in physics this century, comparable to relativity and quantum mechanics. In this book, Peter Smith takes a cool, critical look at such claims. He cuts through the hype and rhetoric by explaining some of the basic mathematical ideas in a clear and accessible way, and by carefully discussing the methodological issues which arise. In particular, he explores the new kinds of explanation of empirical phenomena which modern dynamics can deliver. Explaining Chaos will be compulsory reading for philosophers of science and for anyone who has wondered about the conceptual foundations of chaos theory.

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.

How does science work? Does it tell us what the world is "really" like? What makes it different from other ways of understanding the universe? In Theory and Reality , Peter Godfrey-Smith addresses these questions by taking the reader on a grand tour of one hundred years of debate about science. The result is a completely accessible introduction to the main themes of the philosophy of science. Intended for undergraduates and general readers with no prior background in philosophy, Theory and Reality covers logical positivism the problems of induction and confirmation Karl Popper's theory of science Thomas Kuhn and "scientific revolutions" the views of Imre Lakatos, Larry Laudan, and Paul Feyerabend and challenges to the field from sociology of science, feminism, and science studies. The book then looks in more detail at some specific problems and theories, including scientific realism, the theory-ladeness of observation, scientific explanation, and Bayesianism. Finally, Godfrey-Smith defends a form of philosophical naturalism as the best way to solve the main problems in the field. Throughout the text he points out connections between philosophical debates and wider discussions about science in recent decades, such as the infamous "science wars." Examples and asides engage the beginning student a glossary of terms explains key concepts and suggestions for further reading are included at the end of each chapter. However, this is a textbook that doesn't feel like a textbook because it captures the historical drama of changes in how science has been conceived over the last one hundred years. Like no other text in this field, Theory and Reality combines a survey of recent history of the philosophy of science with current key debates in language that any beginning scholar or critical reader can follow.

A “sender–receiver” framework based on models developed in several fields can provide a general treatment of communicative and symbolic phenomena, replacing traditional semiotic theories that have failed to live up to the hopes of their advocates. Sender–receiver models have mostly been applied to linguistic behavior, gestures, and other ephemeral interactions between individuals. I look at the application of this framework to enduring artifacts, including pictures, using indigenous rock art in Australia as a case study.

Neyman-Pearson methods in statistics distinguish between Type I and Type II errors. Through rigid control of Type I error, the "null" hypothesis typically receives the benefit of the doubt. I compare philosophers' interpretations of this feature of Neyman-Pearson tests with interpretations given in statistics textbooks. The pragmatic view of the tests advocated by Neyman, largely rejected by philosophers, lives on in many textbooks. Birnbaum thought the pragmatic view has a useful "heuristic" role in understanding testing. I suggest that it may have the opposite effect.

It is well known that informational theories of representation have trouble accounting for error. Informational semantics is a family of theories attempting a naturalistic, unashamedly reductive explanation of the semantic and intentional properties of thought and language. Most simply, the informational approach explains truth-conditional content in terms of causal, nomic, or simply regular correlation between a representation and a state of affairs. The central work is Dretske (1981), and the theory was largely developed at the University of Wisconsin by Fred Dretske, Dennis Stampe, and Berent Enc. Recently, informational semantics has roamed far beyond its Wisconsin home, and built a sizeable collection of followers. Converts include Jerry Fodor (1987), Robert Stalnaker (1984) and, less faithfully, Paul and Patricia Churchland (1983) and Hartry Field (1986). But for some years informational semantics has been hounded by a problem with error – the classic presentation is Fodor (1984) – and no other problem has hounded the theory so persistently.

The paper links discussions of two topics: biological individuality and the simplest forms of mentality. I discuss several attempts to locate the boundary between metabolic activity and ‘minimal cognition.’ I then look at differences between the kinds of individuality present in unicellular life, multicellular life in general, and animals of several kinds. Nervous systems, which are clearly relevant to cognition and subjectivity, also play an important role in the form of individuality seen in animals. The last part of the paper links these biological transitions to the evolutionary history of subjective experience.