Cauman, Leigh S., and . First Order Logic: An Introduction

1998, Walter de Gruyter & Co.

Publisher’s Note: This teaching book is designed to help its readers to reason systematically, reliably, and to some extent self-consciously, in the course of their ordinary pursuits-primarily in inquiry and in decision making. The principles and techniques recommended are explained and justified – not just stated; the aim is to teach orderly thinking, not the manipulation of symbols. The structure of material follows that of Quine’s Methods of Logic, and may be used as an introduction to that work, with sections on truth-functional logic, predicate logic, relational logic, and identity and description. Exercises are based on problems designed by authors including Quine, John Cooley, Richard Jeffrey, and Lewis Carroll.

Comment: This book is adequate for a first course on formal logic. Moreover, its table of contents follows that of Quine's "Methods of Logic", thus it can serve as an introduction or as a reference text for the study of the latter.

Fisher, Jennifer, and . On the Philosophy of Logic

2007, Cengage Learning.

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.

Grover, Dorothy, Joseph Kamp and Nuel Belnap. A Prosentential Theory of Truth

1975, Philosophical Studies 27(1): 73-125.

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.

Grover, Dorothy, and . Inheritors and Paradox

1977, Journal of Philosophy 74(10): 590-604

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.

Grover, Dorothy, and . How Significant is the Liar?

2008, In J. C. Beall & Bradley Armour-Garb (eds.), Deflationism and Paradox. OUP Oxford.

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.

Gupta, Anil, and . A Critique of Deflationism

1993, Philosophical Topics 21: 57-81.

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.

Comment: This would be very useful in a course on the nature of truth, or any course in which deflationary conceptions of truth are relevant. The paper is not technical and provides a good account of deflationism about truth. This would be suitable for undergraduates or graduates.

Gupta, Anil, and . Do the Paradoxes Pose a Special Problem for Deflationism?

2006, In J. C. Beall and Bradley Armour-Garb (eds.), Deflationism and Paradox, Oxford University Press. 133-147.

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.

Comment: This would be useful in a course on the nature of truth, or on paradoxes. This is slightly more specialised than 'A Critique of Deflationism' but still good reading material for an advanced undergraduate or graduate course. The paper is not easy, but clear and not very technical.

Hendricks, Vincent, and John Symons. Epistemic Logic

2006, Stanford Encyclopedia of Philosophy

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.

Maddy, Penelope, and . The Philosophy of Logic

2012, Bulletin of Symbolic Logic 18(4): 481-504.

Abstract: This talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic – what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics – Logicism, Intuitionism, Formalism, Realism – and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam are among the philosophers considered along the way.

Comment: This is a survey article which considers positions within philosophy of logic analogous to the views held by the various schools of the philosophy of mathematics. The article touches briefly on many positions and authors and is thus an excellent introduction to the philosophy of logic, specially for students already familiar with the philosophy of mathematics. The text is informal and it does not involve any proofs.