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Blanchette, Patricia, , . Frege’s Conception of Logic
2012, New York: Oxford University Press.
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Added by: Clotilde Torregrossa, Contributed by: Alex Yates

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.

Comment: This book would be a suitable resource for independent study, or for a historically oriented course on philosophy of logic, of math, or on early analytic philosophy, especially one which looks at philosophical approaches to axiomatic systems.

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Cardona, Carlos Alberto, , . Kepler: Analogies in the search for the law of refraction
2016, Studies in History and Philosophy of Science Part A 59:22-35.
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Added by: Clotilde Torregrossa, Contributed by: Juan R. Loaiza

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.

Comment: [This is a stub entry. Please add your comments to help us expand it]

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Chatti, Saloua, , . Avicenna on Possibility and Necessity
2014, History and Philosophy of Logic 35(4): 332-353.
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Added by: Sara Peppe, Contributed by:

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.

Comment: This article is useful for eastern philosophy courses and logic courses. Even if in the first part it provides an introductory section on Avicenna’s perspective, it would be better to have some pre-esxisting background on this latter one.

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Chatti, Saloua, , . Extensionalism and Scientific Theory in Quine’s Philosophy
2011, International Studies in the Philosophy of Science 25(1):1-21.
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Added by: Sara Peppe, Contributed by:

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.

Comment: This text provide an in-depth overview and critique on Quine’s perspective on modality and it would be crucial in postgraduate courses of philosophy of science and logic. Previous knowledge on Quine, modality and quantum mechanics is needed.

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Dutilh Novaes, Catarina, , . Formal Languages in Logic: A Philosophical and Cognitive Analysis
2012, Cambridge: Cambridge University Press
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Added by: Jie Gao, Contributed by:

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.

Comment: This book addresses important questions about formal languages: why formalization works and the limitations of formalization. The questions are answered from cognitive, historical and logical points of view. It is a good introductory material for teaching on formal language and psychology of reasoning.

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Fisher, Jennifer, , . On the Philosophy of Logic
2007, Cengage Learning.
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Added by: Berta Grimau, Contributed by: Matt Clemens

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.

Comment: This book provides an introduction to some traditional questions within philosophy of logic. Moreover, it presents some non-classical logics. It includes an introduction to formal classical logic, so no previous technical knowledge is required. Adequate for a first course on philosophy of logic, either as main or further reading.

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Grover, Dorothy, Joseph Kamp, Nuel Belnap. A Prosentential Theory of Truth
1975, Philosophical Studies 27(1): 73-125.
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Added by: Jamie Collin, Contributed by:

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).

Comment: Good as a primary reading on a course on truth, philosophy of language, or on deflationism more generally. Any course that treats deflationary accounts of truth in any detail would deal with the prosentential theory of truth, and this is one of the most historically important presentations of that theory. Would be best used in advanced undergraduate or graduate courses.

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Grover, Dorothy, , . How Significant is the Liar?
2008, In J. C. Beall & Bradley Armour-Garb (eds.), Deflationism and Paradox. OUP Oxford.
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Added by: Jamie Collin, Contributed by:

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’.

Comment: This would be useful in a course on truth, the philosophy of language or paradoxes. It provides a very up to date account of the prosentential theory of truth and how it may be able to deal with semantic paradoxes. Not as technical as some literature on the topic.

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Grover, Dorothy, , . Inheritors and Paradox
1977, Journal of Philosophy 74(10): 590-604
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Added by: Jamie Collin, Contributed by:

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.

Comment: Good as a primary reading on a course on truth, paradox, philosophy of language, or on deflationism more generally. Any course that treats deflationary accounts of truth in any detail would deal with the prosentential theory of truth, and this is one of the most historically important presentations of that theory. This is particularly useful in courses on paradox, as it is a rare articulation of the idea that the liar paradox is not “deep” and does not require large revisions to classical logic. Would be best used in advanced undergraduate or graduate courses.

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Haack, Susan, , . Philosophy of Logics
1978, Cambridge: Cambridge University Press.
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Added by: Jie Gao, Contributed by:

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.

Comment: This textbook is intended particularly for philosophy students who have completed a first course in elementary logic. But, though the book is clearly written, such students still may find the content difficult, as it addresses difficult topics in the foundations of logic the primary literature for which is very technical. That said, it has been a widely used textbook for courses on philosophy of logic. Chapters of it can be used individually in accordance with the arrangements of the course.

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Haack, Susan, , . The Justification of Deduction
1976, Mind 85 (337): 112-119.
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Added by: Jie Gao, Contributed by:

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.

Comment: This paper argues that justification for deduction, like justification for induction, also has the problem of circularity. It is suitable for teachings on topic of justification for inference in a course on philosophy of logic.

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Hendricks, Vincent, , John Symons. Epistemic Logic
2006, Stanford Encyclopedia of Philosophy.
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Added by: Jamie Collin, Contributed by:

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.

Comment: This would be useful in a course on epistemology, formal epistemology, philosophical logic or formal methods in philosophy. This is quite a compact entry for the Stanford Enclyclopedia of Philosophy. It is not hugely technical, but symbol-phobes will find it logic-heavy.

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Keefe, Rosanna, , . Theories of Vagueness
2000, Cambridge University Press.
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Added by: Berta Grimau, Contributed by:

Publisher’s Note: Most expressions in natural language are vague. But what is the best semantic treatment of terms like ‘heap’, ‘red’ and ‘child’? And what is the logic of arguments involving this kind of vague expression? These questions are receiving increasing philosophical attention, and in this timely book Rosanna Keefe explores the questions of what we should want from an account of vagueness and how we should assess rival theories. Her discussion ranges widely and comprehensively over the main theories of vagueness and their supporting arguments, and she offers a powerful and original defence of a form of supervaluationism, a theory that requires almost no deviation from standard logic yet can accommodate the lack of sharp boundaries to vague predicates and deal with the paradoxes of vagueness in a methodologically satisfying way. Her study will be of particular interest to readers in philosophy of language and of mind, philosophical logic, epistemology and metaphysics.

Comment: This book could be used in a philosophy of logic or a philosophy of language course which had a section on vagueness (either at undergraduate or postgraduate level). The first chapter provides a good main reading for such purpose. The book can also be used in a course focused on vagueness exclusively. The technical discussion is minimized throughout and presupposes only some familiarity with elementary logic.

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Kukla, Rebecca, , . Myth, Memory and Misrecognition in Sellars’ ‘Empiricism and the Philosophy of Mind’
2000, Philosophical Studies (101) 2-3 161-211.
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Added by: Andrea Blomqvist, Contributed by: Rory Wilson

Introduction: In increasing numbers, philosophers are coming to read Sellars’ “Empiricism and the Philosophy of Mind” (1997, hereafter EPM) as having dealt the definitive death blow to the idea that inner states with epistemic authority could have this authority immediately. EPM purportedly proves that instead, such states necessarily show up already embedded within a web of inferentially articulated conceptual knowledge, and that in order for this to be possible,  the epistemic subject must be a negotiator of a normative space in which standards of justification and correctness are already recognized. […] In this paper I will attempt to show that Sellars’ mythical explanations in EPM employ a very specific and rhetorically complex methodology, and likewise that we will not be in a position to critically assess the paper’s arguments unless we give careful attention to its overall textual structure and to the nature of the mythical explanations it employs.

Comment: A companion to Sellars’ ‘Empiricism and the Philosophy of Mind’ for students more inclined to social philosophy.

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Negri, Sara, Jan von Plato, Aarne Ranta. Structural Proof Theory
2001, Cambridge University Press.
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Added by: Berta Grimau, Contributed by:

Publisher’s Note: Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory – natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.

Comment: This book can be used both in a general course on proof theory for advanced Undergraduates or for Masters students, and for specialized courses – for example, a course on natural deduction. Chapters 1-4 can be used as background reading of a general course. Chapter 1, 5 and 8 could be used in a course on natural deduction. The presentation is self-contained and the book should be readable without any previous knowledge of logic.

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