Paul Cohen’s method of forcing, together with Saul Kripke’s related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the aspects (...) of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments. (shrink)

This is a collection of twenty-five papers and reviews by the leading analytic philosopher of our time. It adds to the papers on metaphysics and epistemology to be found in his previous two-volume collection published by Oxford University Press. One previously unpublished paper—“Why Conditionalize?”—is included. Australasian philosophers may note with some pride that eleven of the pieces were first published in the Australasian Journal of Philosophy.

Possible-worlds talk obscures, rather than clarifies, the debate about haecceitism. In this paper I distinguish haecceitism and anti-haecceitism from other doctrines that sometimes go under those names. Then I defend the claim that there are no non-tendentious definitions of ‘haecceitism’ and ‘anti-haecceitism’ using possible-worlds talk. That is, any definition of ‘haecceitism’ using possible-worlds talk depends, for its correctness, on a substantive theory of the nature of possible worlds. This explains why using possible-worlds talk when discussing haecceitism causes confusion: if the (...) parties to the discussion presuppose different theories of the nature of possible worlds, then they will mean different things by ‘haecceitism’. (shrink)

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

Turing computation over a non-linguistic domain presupposes a notation for the domain. Accordingly, computability theory studies notations for various non-linguistic domains. It illuminates how different ways of representing a domain support different finite mechanical procedures over that domain. Formal definitions and theorems yield a principled classification of notations based upon their computational properties. To understand computability theory, we must recognize that representation is a key target of mathematical inquiry. We must also recognize that computability theory is an intensional enterprise: it (...) studies entities as represented in certain ways, rather than entities detached from any means of representing them. (shrink)

I propose that the meanings of vague expressions render the truth conditions of utterances of sentences containing them sensitive to our interests. For example, 'expensive' is analyzed as meaning 'costs a lot', which in turn is analyzed as meaning 'costs significantly greater than the norm'. Whether a difference is a significant difference depends on what our interests are. Appeal to the proposal is shown to provide an attractive resolution of the sorites paradox that is compatible with classical logic and semantics.

Over recent years, the psychology of concepts has been rejuvenated by new work on prototypes, inventive ideas on causal cognition, the development of neo-empiricist theories of concepts, and the inputs of the budding neuropsychology of concepts. But our empirical knowledge about concepts has yet to be organized in a coherent framework. -/- In Doing without Concepts, Edouard Machery argues that the dominant psychological theories of concepts fail to provide such a framework and that drastic conceptual changes are required to make (...) sense of the research on concepts in psychology and neuropsychology. Machery shows that the class of concepts divides into several distinct kinds that have little in common with one another and that for this very reason, it is a mistake to attempt to encompass all known phenomena within a single theory of concepts. In brief, concepts are not a natural kind. Machery concludes that the theoretical notion of concept should be eliminated from the theoretical apparatus of contemporary psychology and should be replaced with theoretical notions that are more appropriate for fulfilling psychologists' goals. The notion of concept has encouraged psychologists to believe that a single theory of concepts could be developed, leading to useless theoretical controversies between the dominant paradigms of concepts. Keeping this notion would slow down, and maybe prevent, the development of a more adequate classification and would overshadow the theoretical and empirical issues that are raised by this more adequate classification. Anyone interested in cognitive science's emerging view of the mind will find Machery's provocative ideas of interest. (shrink)

In recent years, the integration of philosophical with scientific theorizing has started to yield new insights. This chapter surveys some recent philosophical and empirical work on the nature and structure of action, on conscious agency, and on our knowledge of actions.

Ichikawa and Jarvis offer a new rationalist theory of mental content and defend a traditional epistemology of philosophy. They argue that philosophical inquiry is continuous with non-philosophical inquiry, and can be genuinely a priori, and that intuitions do not play an important role in mental content or the a priori.

considered an objection that he says he thought was first put to him by Max Black. He says.

Gaining information can be modelled as a narrowing of epistemic space . Intuitively, becoming informed that such-and-such is the case rules out certain scenarios or would-be possibilities. Chalmers’s account of epistemic space treats it as a space of a priori possibility and so has trouble in dealing with the information which we intuitively feel can be gained from logical inference. I propose a more inclusive notion of epistemic space, based on Priest’s notion of open worlds yet which contains only those (...) epistemic scenarios which are not obviously impossible. Whether something is obvious is not always a determinate matter and so the resulting picture is of an epistemic space with fuzzy boundaries. (shrink)

Aboutness has been studied from any number of angles. Brentano made it the defining feature of the mental. Phenomenologists try to pin down the aboutness-features of particular mental states. Materialists sometimes claim to have grounded aboutness in natural regularities. Attempts have even been made, in library science and information theory, to operationalize the notion. But it has played no real role in philosophical semantics. This is surprising; sentences have aboutness-properties if anything does. Aboutness is the first book to examine through (...) a philosophical lens the role of subject matter in meaning. A long-standing tradition sees meaning as truth-conditions, to be specified by listing the scenarios in which a sentence is true. Nothing is said about the principle of selection--about what in a scenario gets it onto the list. Subject matter is the missing link here. A sentence is true because of how matters stand where its subject matter is concerned. Stephen Yablo maintains that this is not just a feature of subject matter, but its essence. One indicates what a sentence is about by mapping out logical space according to its changing ways of being true or false. The notion of content that results--directed content--is brought to bear on a range of philosophical topics, including ontology, verisimilitude, knowledge, loose talk, assertive content, and philosophical methodology. Written by one of today's leading philosophers, Aboutness represents a major advance in semantics and the philosophy of language. (shrink)

When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: it is about something, towards which one’s mind is directed. What is the logic of thought, so understood? This book begins to explore the idea that, to answer the question, we should take topics seriously. It proposes a hyperintensional account of the propositional contents of thought, arguing that these are individuated not only by the set of possible worlds at which they are true, but also by (...) their topic: what they are about. The book then builds epistemic, doxastic, probabilistic, and conditional logics based on this view. It applies them to issues ranging from dogmatism, scepticism, and epistemic fallibilism, to imagination and suppositional reasoning, belief revision, framing effects, and the acceptability of indicative conditionals. (shrink)

Examines the nature of cognitive penetrability hypothesis, which holds that our beliefs, desires, and possibly our emotions literally affect how we see the world. Assesses both cognitive penetrability and impenetrability and explores their philosophical consequences.

The Conscious Brain brings neuroscientific evidence to bear on enduring philosophical questions. Major philosophical and scientific theories of consciousness are surveyed, challenged, and extended.

Introduction, Contributions to the founding of the theory of transfinite numbers, Article I, Article II.

We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. I explicate the challenge (...) both in general and for the particular case of logic. I also argue that two seemingly attractive responses – appealing to a faculty of rational insight or to the nature of concept possession – are incapable of answering the challenge. (shrink)

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.... The chief virtue of the book is its systematic character. From Frege to Quine most philosophical logicians have restricted themselves by piecemeal and local assaults on the problems involved. The book is marked by a genial tolerance. Carnap sees himself as proposing conventions rather than asserting truths. However he provides plenty of matter (...) for argument."-Anthony Quinton, Hibbert Journal. (shrink)

I propose to consider the question, "Can machines think?" This should begin with definitions of the meaning of the terms "machine" and "think." The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous, If the meaning of the words "machine" and "think" are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to (...) the question, "Can machines think?" is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words. The new form of the problem can be described in terms of a game which we call the 'imitation game." It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart front the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A." The interrogator is allowed to put questions to A and B. We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?". (shrink)

This is a welcome reprint of a book that continues to grow in importance.

In the philosophical literature on mental states, the paradigmatic examples of mental states are beliefs, desires, intentions, and phenomenal states such as being in pain. The corresponding list in the psychological literature on mental state attribution includes one further member: the state of knowledge. This article examines the reasons why developmental, comparative and social psychologists have classified knowledge as a mental state, while most recent philosophers--with the notable exception of Timothy Williamson-- have not. The disagreement is traced back to a (...) difference in how each side understands the relationship between the concepts of knowledge and belief, concepts which are understood in both disciplines to be closely linked. Psychologists and philosophers other than Williamson have generally have disagreed about which of the pair is prior and which is derivative. The rival claims of priority are examined both in the light of philosophical arguments by Williamson and others, and in the light of empirical work on mental state attribution. (shrink)

In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends (...) her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences. (shrink)

What do we see? We are visually conscious of colors and shapes, but are we also visually conscious of complex properties such as being John Malkovich? In this book, Susanna Siegel develops a framework for understanding the contents of visual experience, and argues that these contents involve all sorts of complex properties. Siegel starts by analyzing the notion of the contents of experience, and by arguing that theorists of all stripes should accept that experiences have contents. She then introduces a (...) method for discovering the contents of experience: the method of phenomenal contrast. This method relies only minimally on introspection, and allows rigorous support for claims about experience. She then applies the method to make the case that we are conscious of many kinds of properties, of all sorts of causal properties, and of many other complex properties. She goes on to use the method to help analyze difficult questions about our consciousness of objects and their role in the contents of experience, and to reconceptualize the distinction between perception and sensation. Siegel's results are important for many areas of philosophy, including the philosophy of mind, epistemology, and the philosophy of science. They are also important for the psychology and cognitive neuroscience of vision. (shrink)

Elijah Chudnoff elaborates and defends a view of intuition according to which intuition purports to, and reveals, how matters stand in abstract reality by making us aware of that reality through the intellect. He explores the experience of having an intuition; justification for beliefs that derives from intuition; and contact with abstract reality.

The paper explores the distinction between two doctrines, both of which inform theory construction in much of modern cognitive psychology: the representational theory of mind and the computational theory of mind. According to the former, propositional attitudes are to be construed as relations that organisms bear to mental representations. According to the latter, mental processes have access only to formal (nonsemantic) properties of the mental representations over which they are defined.The following claims are defended: (1) That the traditional dispute between (...) “rational” and “naturalistic” psychology is plausibly viewed as an argument about the status of the computational theory of mind. Rational psychologists accept a formality condition on the specification of mental processes; naturalists do not. (2) That to accept the formality condition is to endorse a version of methodological solipsism. (3) That the acceptance of some such condition is warranted, at least for that part of psychology which concerns itself with theories of the mental causation of behavior. This is because: (4) such theories require nontransparent taxonomies of mental states; and (5) nontransparent taxonomies individuate mental states without reference to their semantic properties. Equivalently, (6) nontransparent taxonomies respect the way that the organism represents the object of its propositional attitudes toitself, and it is this representation which functions in the causation of behavior.The final section of the paper considers the prospect for a naturalistic psychology: one which defines its generalizations over relations between mental representations and their environmental causes, thus seeking to account for the semantic properties of propositional attitudes. Two related arguments are proposed, both leading to the conclusion that no such research strategy is likely to prove fruitful. (shrink)

I call the activity of assessing and developing improvements of our representational devices ‘conceptual engineering’.¹ The aim of this chapter is to present an argument for why conceptual engineering is important for all parts of philosophy (and, more generally, all inquiry). Section I of the chapter provides some background and defines key terms. Section II presents the argument. Section III responds to seven objections. The replies also serve to develop the argument and clarify what conceptual engineering is.