Diversity Reading List

Publisher's Note: In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic. She argues that the fruitfulness of Frege's conception of logic, and the illuminating differences between that conception and those more modern views that have largely supplanted it, are best understood against the backdrop of a clear account of the role of conceptual analysis in logical investigation. The first part of the book locates the role of conceptual analysis in Frege's logicist project. Blanchette argues that despite a number of difficulties, Frege's use of analysis in the service of logicism is a powerful and coherent tool. As a result of coming to grips with his use of that tool, we can see that there is, despite appearances, no conflict between Frege's intention to demonstrate the grounds of ordinary arithmetic and the fact that the numerals of his derived sentences fail to co-refer with ordinary numerals. In the second part of the book, Blanchette explores the resulting conception of logic itself, and some of the straightforward ways in which Frege's conception differs from its now-familiar descendants. In particular, Blanchette argues that consistency, as Frege understands it, differs significantly from the kind of consistency demonstrable via the construction of models. To appreciate this difference is to appreciate the extent to which Frege was right in his debate with Hilbert over consistency- and independence-proofs in geometry. For similar reasons, modern results such as the completeness of formal systems and the categoricity of theories do not have for Frege the same importance they are commonly taken to have by his post-Tarskian descendants. These differences, together with the coherence of Frege's position, provide reason for caution with respect to the appeal to formal systems and their properties in the treatment of fundamental logical properties and relations.

Publisher's Note: This paper examines the methodology used by Kepler to discover a quantitative law of refraction. The aim is to argue that this methodology follows a heuristic method based on the following two Pythagorean principles: (1) sameness is made known by sameness, and (2) harmony arises from establishing a limit to what is unlimited. We will analyse some of the author's proposed analogies to find the aforementioned law and argue that the investigation's heuristic pursues such principles.

Abstract: In this paper, I raise the following problem: How does Avicenna define modalities? What oppositional relations are there between modal propositions, whether quantified or not? After giving Avicenna's definitions of possibility, necessity and impossibility, I analyze the modal oppositions as they are stated by him. This leads to the following results: 1. The relations between the singular modal propositions may be represented by means of a hexagon. Those between the quantified propositions may be represented by means of two hexagons that one could relate to each other. 2. This is so because the exact negation of the bilateral possible, i.e. 'necessary or impossible' is given and applied to the quantified possible propositions. 3. Avicenna distinguishes between the scopes of modality which can be either external (de dicto) or internal (de re). His formulations are external unlike al-F̄ar̄ab̄;’s ones. However his treatment of modal oppositions remains incomplete because not all the relations between the modal propositions are stated explicitly. A complete analysis is provided in this paper that fills the gaps of the theory and represents the relations by means of a complex figure containing 12 vertices and several squares and hexagons.

Abstract: In this article, I analyze Quine's conception of science, which is a radical defence of extensionalism on the grounds that first?order logic is the most adequate logic for science. I examine some criticisms addressed to it, which show the role of modalities and probabilities in science and argue that Quine's treatment of probability minimizes the intensional character of scientific language and methods by considering that probability is extensionalizable. But this extensionalizing leads to untenable results in some cases and is not consistent with the fact that Quine himself admits confirmation which includes probability. Quine's extensionalism does not account for this fact and then seems unrealistic, even if science ought to be extensional in so far as it is descriptive and mathematically expressible.

Publisher’s Note: Formal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use (and the uses of formalisms more generally elsewhere) actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science.

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.

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.

Publisher's Note: The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack's book has established an international reputation (translated into five languages) for its accessibility, clarity, conciseness, orderliness, and range as well as for its thorough scholarship and careful analyses. Haack discusses the scope and purpose of logic, validity, truth-functions, quantification and ontology, names, descriptions, truth, truth-bearers, the set-theoretical and semantic paradoxes, and modality. She also explores the motivations for a whole range of nonclassical systems of logic, including many-valued logics, fuzzy logic, modal and tense logics, and relevance logics.

Abstract: It is often taken for granted by writers who propose - and, for that matter, by writers who oppose - 'justifications' of inductions, that deduction either does not need, or can readily be provided with, justification. The purpose of this paper is to argue that, contrary to this common opinion, problems analogous to those which, notoriously, arise in the attempt to justify induction, also arise in the attempt to justify deduction.

Introduction: Though it is hardly uncontroversial, the thesis that logic is normative enjoys widespread agreement—probably just about as much agreement as one is ever likely to find in philosophy. There is far less agreement, however, on what exactly this thesis amounts to. To begin with, proponents of the
thesis can’t seem to agree on whether the normative authority of logic is robust or weak. If logic is robustly normative, it has a normative authority that is independent of our attitudes or conventions; if it is weakly normative, it has a normative au- thority that is entirely dependent on our attitudes or conventions. This fundamental disagreement about the normative authority of logic seems to leave little room for any point of agreement among the proponents of the thesis. Furthermore, some opponents of the thesis allow that logic is “entangled” with the normative to the extent that it has normative consequences that are instrumental to the achievement of our wider goals (Russell 2017). This makes it difficult to discern any daylight between the views of those who hold that logic is not normative and those who hold that it is only weakly so. In the next section, I will argue that the thesis that unites the proponents and excludes the opponents is that logical statements and the judgments they can be used to express—such as those concerning logical validity or logical entailment—are normative statements and judgments, in the sense that they analytically, semantically, or conceptually have normative consequences. In section 3, I will critically assess whether logical statements and judgments are indeed normative in this sense. I will consider the prospects of various accounts of what the normative consequences of logical statements or judgments might be, and find them all to be wanting. This, I claim, gives us good reason to deny that logic is normative.

Abstract: This chapter investigates what we disagree about when we disagree about logic, on the assumption that judgments of logical validity are normative. If logic is normative, then the popular anti-realist thesis that there are no normative facts or properties generalizes—it entails that there are no logical facts or properties. When faced with this anti-realism, it is tempting to endorse a pluralist thesis, according to which two people who disagree about the validity of an argument can both say something true. This chapter explores the limitations of three prominent forms of pluralism: contextualism, relativism, and expressivism. It argues that none of these forms of pluralism gives an adequate account of what we disagree about when we disagree about logic.

Abstract: Epistemic logic is the logic of knowledge and belief. It provides insight into the properties of individual knowers, has provided a means to model complicated scenarios involving groups of knowers and has improved our understanding of the dynamics of inquiry.

Abstract: This paper enumerates Irigaray's main arguments and thoughts regarding the gendered nature of language and "the logos".