Anti-realism is a doctrine about logic, language, and meaning that is based on the work of Wittgenstein and Frege. In this book, Professor Tennant clarifies and develops Dummett's arguments for anti-realism and ultimately advocates a radical reform of our logical practices.

I present a general theory of abstraction operators which treats them as variable-binding term- forming operators, and provides a reasonably uniform treatment for definite descriptions, set abstracts, natural number abstraction, and real number abstraction. This minimizing, extensional and relational theory reveals a striking similarity between definite descriptions and set abstracts, and provides a clear rationale for the claim that there is a logic of sets (which is ontologically non- committal). The theory also treats both natural and real numbers as answering (...) to a two-fold process of abstraction. The first step, of conceptual abstraction, yields the object occupying a particular position within an ordering of a certain kind. The second step, of objectual abstraction, yields the number sui generis, as the position itself within any ordering of the kind in question. (shrink)

Reviewed Works:Gaisi Takeuti, Proof Theory.Georg Kreisel, Proof Theory: Some Personal Recollections.Wolfram Pohlers, Contributions of the Schutte School in Munich to Proof Theory.Stephen G. Simpson, Subsystems of $\mathbf{Z}_2$ and Reverse Mathematics.Solomon Feferman, Proof Theory: A Personal Report.

This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

From the point of view of proof-theoretic semantics, we examine the logical background invoked by Neil Tennant's abstractionist realist account of mathematical existence. To prepare the way, we must first look closely at the rule of existential elimination familiar from classical and intuitionist logics and at rules governing identity. We then examine how well free logics meet the harmony and uniqueness constraints familiar from the proof-theoretic semantics project. Tennant assigns a special role to atomic formulas containing singular terms. This, we (...) find, secures harmony and uniqueness but militates against the putative realism. (shrink)

The Taming of the True continues the project Neil Tennant began in Anti-realism and Logic of investigating and defending anti-realism. Tennant’s earlier book anticipated a second volume, in which issues related to empirical discourse would be addressed in greater detail. The Taming of the True provides this sequel. It also attempts a ground-clearing project, by addressing challenges to some of the presuppositions and implications of Tennant’s anti-realist position. Finally, it takes an opportunity to revisit some of the issues examined in (...) the earlier book, in light of the evolving debate over realism and anti-realism. (shrink)

The Taming of the True poses a broad challenge to realist views of meaning and truth that have been prominent in recent philosophy. Neil Tennant argues compellingly that every truth is knowable, and that an effective logical system can be based on this principle. He lays the foundations for global semantic anti-realism and extends its consequences from the philosophy of mathematics and logic to the theory of meaning, metaphysics, and epistemology.

Provability, Computability and Reflection.

This is a new major and systematic monograph on the realism debate, written by a very skillful and sophisticated defender of anti-realism. The realism debate is conceived here as a primarily semantic controversy concerning the possibility of forming propositions or sentences about the world whose truth or falsity might be unknowable to us. Realists of various persuasions take it to be perfectly possible, while nonrealists of all sorts deny this. Tennant distinguishes two basic forms of nonrealism in his book: irrealism (...) and antirealism. According to semantic irrealism, there are no such entities as propositions, or objective and determinate meanings for sentences to possess. Semantic antirealists generally do not agree with such a radical conclusion. They argue for the objectivity and determinacy of meaning, although at the same time they insist that both meaning and truth attributable to propositions or sentences has to be epistemically constrained, that is, grasping a meaning has to be manifestable and truth has to be in principle knowable. While developing in greater detail his own version of antirealism that respects those two constraints, Tennant combines the knowability requirement with the claim that truth need not be bivalent, which in turn leads him to replace classical logic based on bivalence by a nonclassical constructive logic, namely, intuitionistic relevant logic. Tennant attempts to show that this logic has much wider application than one might suppose. It suffices not only for mathematics but also adequately captures the basic inferential practices of empirical sciences. It would be hard to overestimate the significance of that attempt, since if successful it undermines the charge that anti-realism is a doctrine that cannot really be extended beyond the domain of mathematical discourse. The general strategy taken in this respect by Tennant is not, as has been common so far, to strengthen the notion of empirical verification or confirmation of a sentence in such a way as to make it a close analogue of the notion of mathematical proof. “Rather, one should attend to the main feature of natural scientific theorizing to which Popper drew our attention: our scientific theories can at best be falsified, not verified”. In other words, in the case of empirical discourse the perfect analogue of the antirealist notion of constructive provability is the notion of constructive falsifiability. (shrink)

The aim here is to describe how to complete the constructive logicist program, in the author’s book Anti-Realism and Logic, of deriving all the Peano-Dedekind postulates for arithmetic within a theory of natural numbers that also accounts for their applicability in counting finite collections of objects. The axioms still to be derived are those for addition and multiplication. Frege did not derive them in a fully explicit, conceptually illuminating way. Nor has any neo-Fregean done so.