Alberto Coffa used the phrase "the Copernican turn in semantics" to denote a revolutionary transformation of philosophical views about the connection between the meanings of words and the acceptability of sentences and arguments containing those words. According to the new conception resulting from the Copernican turn, here called "the Copernican view", rules of use are constitutive of the meanings of words. This view has been linked with two doctrines: (A) the instances of meaning-constitutive rules are analytically and a priori true (...) or valid; (B) to grasp a meaning is to accept its rules. The pros and cons of different versions of the Copernican view, ascribable to Wittgenstein, Carnap, Gentzen, Dummett, Prawitz, Boghossian and other authors, will be weighed. A new version will be proposed, which implies neither (A) nor (B). (shrink)

Intuitionism’s disagreement with classical logic is standardly based on its specific understanding of truth. But different intuitionists have actually explicated the notion of truth in fundamentally different ways. These are considered systematically and separately, and evaluated critically. It is argued that each account faces difficult problems. They all either have implausible consequences or are viciously circular.

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

The paper challenges the inferentialist account of concept possession that Paul Boghossian takes as a premise in his account of the transmission of justification by deductive reasoning in his paper 'Blind Reasoning'. Unorthodox speakers who reject the inferences in an alleged possession condition can still have the concept by understanding a word for it. In that sense, the inferences are not analytic. Inferentialist accounts of logical constants, theoretical terms (using the Ramsey-Carnap-Lewis method) and pejorative expressions such as 'Boche' are examined (...) and rejected. It is suggested that epistemological questions cannot be reduced to questions in the theory of thought and meaning. (shrink)

According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of (...) this notion. Another main part of the paper is concerned with a modification of this notion as it occurs in Michael Dummett’s book The Logical Basis of Metaphysics. The two notions are compared and there is a discussion of how they fare as a foundation for a theory of meaning. It is noted that Dummett’s notion has a simpler structure, but it is argued that it is less appropriate for the foundation of a theory of meaning, because the possession of a valid argument for a sentence in Dummett’s sense is not enough to be warranted to assert the sentence. (shrink)

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

The present volume is intended as an all-round introduction to constructivism. Here constructivism is to be understood in the wide sense, and covers in particular Brouwer's intuitionism, Bishop's constructivism and A.A. Markov's constructive recursive mathematics. The ending "-ism" has ideological overtones: "constructive mathematics is the (only) right mathematics"; we hasten, however, to declare that we do not subscribe to this ideology, and that we do not intend to present our material on such a basis.

[Paul Boghossian] The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of ’blind but blameless’ reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is possible. (...) /// [Timothy Williamson] The paper challenges the inferentialist account of concept possession that Paul Boghossian takes as a premise in his account of the transmission of justification by deductive reasoning in his paper ’Blind Reasoning’. Unorthodox speakers who reject the inferences in an alleged possession condition can still have the concept by understanding a word for it. In that sense, the inferences are not analytic. Inferentialist accounts of logical constants, theoretical terms (using the Ramsey-Carnap-Lewis method) and pejorative expressions such as ’Boche’ are examined and rejected. It is suggested that epistemological questions cannot be reduced to questions in the theory of thought and meaning. (shrink)

The traditional picture of logic takes it for granted that "valid arguments have a fundamental epistemic significance", but neither model theory nor traditional proof theory dealing with formal system has been able to give an account of this significance. Since valid arguments as usually understood do not in general have any epistemic significance, the problem is to explain how and why we can nevertheless use them sometimes to acquire knowledge. It is suggested that we should distinguish between arguments and acts (...) of inferences and that we have to reconsider the latter notion to arrive at the desired explanation. More precisely, the notions should be developed so that the following relationship holds: one gets in possession of a ground for a conclusion by inferring it from premisses for which one already has grounds, provided that the inference in question is valid. The paper proposes explications of the concepts of ground and deductively valid inference so that this relationship holds as a conceptual truth. Logical validity of inference is seen as a special case of deductive validity, but does not add anything as far as epistemic significance is concerned—it resides already in the deductively valid inferences. (shrink)

The principle of semantic compositionality, as Jerry Fodor and Ernie Lepore have emphasized, imposes constraints on theories of meaning that it is hard to meet with psychological or epistemic accounts. Here, I argue that this general tendency is exemplified in Michael Dummett's account of meaning. On that account, the so-called manifestability requirement has the effect that the speaker who understands a sentence s must be able to tell whether or not s satisfies central semantic conditions. This requirement is not met (...) by truth-conditional accounts of meaning. On Dummett's view, it is met by a proof conditional account: understanding amounts to knowledge of what counts as a proof of a sentence. A speaker is supposed always to be capable of deciding whether or not a given object is a proof of a given sentence she understands. This requirement comes into conflict with compositionality. If meaning is compositionally determined, then all you need for understanding a sentence is what you get from combining your understanding of the parts according to the mode of composition. But that knowledge is not always sufficient for recognizing any proof at all of a given sentence. Dummett's proof-theoretic argument to the contrary is mistaken. (shrink)