Diversity Reading List

Introduction: The decade from the mid-twenties to the mid-thirties was undoubtedly the most crucial for the twentieth Century notion of subjective probability. It was in 1926 that Frank Ramsey wrote his essay 'Truth and probability', presented at the Moral Science Club in Cambridge and published posthumously in 1931. There he put forward for the first time a definition of probability as degree of belief, that had been anticipated only by E. Borel in 1924, in a review of J. M. Keynes' Treatise on Ten years after Ramsey's paper, namely in 1935, Bruno de Finetti gave a series of lectures at the Institut Poincare in Paris, published in 1937 under the title 'La prévision: ses lois logiques, ses sources subjectives'. In this paper subjective probability, defined in a way analogous to that adopted by Ramsey, was implemented with the notion of exchangeability, that de Finetti had already worked out in 1928- 1930. Exchangeability confers applicability to the notion of subjective probability, and fills the gap between frequency and probability as degree of belief. It was only when these two were tied together that subjectivism could become a full-fledged interpretation of probability and gain credibility among probabilists and statisticians. One can then say that with the publication of 'La prévision' the formation process of a subjective notion of probability was completed.

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The paper discusses two problems with Graham Priest's version of dialetheism: the thesis that one cannot be rationally obliged to both accept and reject something, and the use of a Contraction-less conditional in dealing with Curry paradoxes. Some solutions are suggested.

Summary: Classic presentation of the prosentential theory of truth: an important, though minority, deflationist account of truth. Prosententialists take 'It is true that' to be a prosentence forming operator that anaphorically picks out content from claims made further back in the anaphoric chain (in the same way that pronouns such as 'he', 'she' and 'it' anaphorically pick out referents from nouns further back in the anaphoric chain).

Summary: Classic account of the way in which the prosentential theory of truth handles the liar paradox. Prosententialists take 'It is true that' to be a prosentence forming operator that anaphorically picks out content from claims made further back in the anaphoric chain (in the same way that pronouns such as 'he', 'she' and 'it' anaphorically pick out referents from nouns further back in the anaphoric chain). Liar sentences have no proposition-stating antecedents in the anaphoric chain. As a result, the problem of the liar does not arise.

Summary: Grover argues that one should be unconcerned about the liar paradox. In formal languages there are uniform ties between syntax and semantics: a term, in all its occurrences, carries a fixed meaning; and sequences of sentences that are (syntactically) proofs are always (semantically) inferences. These two features do not hold of natural languages. Grover makes use of this claim to argue that there are no arguments to contradictions from liar sentences in natural languages, as the relevant syntactic 'moves' do not come with relevant semantic 'moves'.

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While contemporary feminist philosophical discussions focus on the oppressiveness of universality which obliterates “difference,” the complete demise of universality might hamper feminist philosophy in its political project of furthering the well-being of all women. Dewey's thoroughly functionalized, relativized, and fallibilized understanding of universality may help us cut universality down to size while also appreciating its limited contribution. Deweyan universality may signify the ongoing search for a genuinely common language in the midst of difference.

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This chapter gives a survey of the field of philosophy where the philosophical foundations of modern logic were discussed and where such themes of logic were discussed that were on the borderline between logic and other branches of the philosophical enterprise, such as metaphysics and epistemology. The contributions made by Gottlob Frege and Charles Peirce are included since their work in logic is closely related to and also strongly motivated by their philosophical views and interests. In addition, the chapter pays attention to a few philosophers to whom logic amounted to traditional Aristotelian logic and to those who commented on the nature of logic from a philosophical perspective without making any significant contribution to the development of formal logic.

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In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice. In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics including the distinction between formal and informal proofs, visualization and artefacts, mathematical explanation and understanding, value judgments, and mathematical design. We conclude with some remarks on the potential connections between the philosophy of mathematical practice and mathematics education.

Abstract: Many have argued that unified theories ought to be pursued wherever possible. We deny this on the basis of social-epistemological and game-theoretic considerations. Consequently, those seeking a more ubiquitous role for unification must either attend to the scientific community's social structure in greater detail than has been the case, and/or radically revise their conception of unification.

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Can there be a feminist logic? By most accounts the answer would be no. What l find remarkable is the great difference in the justifications provided for this conclusion. The impossibility of feminist logic is defended, on the one hand, on the grounds that logic itself is most fundamentally a form of domination and so is inimical to feminist aims. Other philosophers, while also defending the impossibility of feminist logic, do so from the conviction that it is feminist theory rather than logic that is the problem. For these thinkers, feminism cannot make any interesting or important contribution to logic because feminist theory is fundamentally shallow or misguided. In this paper I will argue that both positions are mistaken: Logic is neither as totalizing as the one side believes nor is feminist theory as inconsequential for logic as the other pole would have it. In the course of these arguments, I describe the work of several feminist logicians, showing the possibility and value of feminist approaches to logic.