Diversity Reading List

Publisher’s Note:

This book is a consideration of Hegel’s view on logic and basic logical concepts such as truth, form, validity, and contradiction, and aims to assess this view’s relevance for contemporary philosophical logic. The literature on Hegel’s logic is fairly rich. The attention to contemporary philosophical logic places the present research closer to those works interested in the link between Hegel’s thought and analytical philosophy, Koch 2014, Brandom 2014, 1-15, Pippin 2016, Moyar 2017, Quante & Mooren 2018 among others). In this context, one particularity of this book consists in focusing on something that has been generally underrated in the literature: the idea that, for Hegel as well as for Aristotle and many other authors, logic is the study of the forms of truth, i.e. the forms that our thought can assume in searching for truth. In this light, Hegel’s thinking about logic is a fundamental reference point for anyone interested in a philosophical foundation of logic.

Publisher's Note: Jennifer Fisher's On the Philosophy of Logic explores questions about logic often overlooked by philosophers. Which of the many different logics available to us is right? How would we know? What makes a logic right in the first place? Is logic really a good guide to human reasoning? An ideal companion text for any course in symbolic logic, this lively and accessible book explains important logical concepts, introduces classical logic and its problems and alternatives, and reveals the rich and interesting philosophical issues that arise in exploring the fundamentals of logic.

Abstract: In this paper we first explore how Wittgenstein’s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein’s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics (Wittgenstein 1973). We will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics. The central philosophical investigation concerns Wittgenstein’s shift to abandoning the essentialist concept of language and therefore denying the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—are immersed in a form of life, in a cultural or social formation and are embedded in the totality of communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure-making and sand drawing, to illustrate Wittgenstein’s ideas. Based on an ethnomathematical comparative analysis, we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality, as expressed in both string figure-making and sand drawing practices, from one society to another. Finally, we suggest that a philosophical-anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cultures. Philosophical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better characterize mathematical practices in both sociological and epistemological terms.

Publisher's Note: What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

Publisher's Note: Not limited to merely mathematics, probability has a rich and controversial philosophical aspect. 'A Philosophical Introduction to Probability' showcases lesser-known philosophical notions of probability and explores the debate over their interpretations. Galavotti traces the history of probability and its mathematical properties and then discusses various philosophical positions on probability, from the Pierre Simon de Laplace's 'classical' interpretation of probability to the logical interpretation proposed by John Maynard Keynes. This book is a valuable resource for students in philosophy and mathematics and all readers interested in notions of probability

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.

Abstract:

This paper starts out from two feminist criticisms of classical logic, namely Andrea Nye’s general rejection of logic and Val Plumwood’s criticism of the standard notion of negation in classical logic. I then look at some of Gottlob Frege’s reflections on negation in one of his later Logical Investigations. It will appear clear that Frege’s notion of negation is not easily pegged in the general category of ‘Otherness’ that Plumwood uses to characterize negation in classical logic. In the second half of the paper, I discuss the claim that the adversarial method of argumentation in philosophy is hostile to feminist goals and perhaps responsible for the low numbers of women engaged in academic philosophy. Against this hypothesis, I claim that a more naturalistic perspective on logic can avoid essentialism and provide a feminist friendly and pluralist view of logic, human reasoning, and philosophical argumentation.

Abstract:

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.

Content: Govier distinguishes four kinds of slippery slope arguments - conceptual, precedential, causal and mixed - and argues that only the last kind are likely to ever be sound.

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: 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'.

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.

Abstract:

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.

Summary: Argues against deflationary conceptions of truth. Deflationism provides a descriptive account of the term 'true', but these claims, argues Gupta, are both very strong and problematic.

Summary: The Liar and other semantic paradoxes pose a difficult problem for all theories of truth. Any theory that aims to improve our understanding of the concept of truth must, when fully stated, include an account of the paradoxes. Not only deflationism but also its competitors - for instance, correspondence and coherence - must ultimately address the paradoxes. The question that concerns me in this essay is whether it is especially urgent for deflationism to do so. Are the paradoxes a special threat, a special problem, for deflationism? I will argue that they are not.1 Deflationists can leave the paradoxes to the specialists to puzzle over. It is the specialists who will be well served if they keep some insights of deflationism firmly in view.