In this paper we shall introduce two types of contextual-hierarchical approaches to the strengthened liar problem. These approaches, which we call the ‘standard’ and the ‘alternative’ ch-reconstructions of the strengthened liar problem, differ in their philosophical view regarding the nature of truth and the relation between the truth predicates T r n and T r n+1 of different hierarchy-levels. The basic idea of the standard ch-reconstruction is that the T r n+1-schema should hold for all sentences of \. In contrast, (...) the alternative ch-reconstruction, for which we shall argue in section four, is motivated by the idea that T r n and T r n+1 are coherent in the sense that the same sentences of \ should be true according to T r n and T r n+1. We show that instances of the standard ch-reconstruction can be obtained by iterating Kripke’s strong Kleene jump operator. Furthermore, we will demonstrate how instances of the alternative ch-reconstruction can be obtained by a slight modification of the iterated axiom system KF and of the iterated strong Kleene jump operator. (shrink)

Peter Milne has tried to refure Truthmaker Maximalism. the thesis that every truth has a truthmaker, by producing a simple and direct counterexample to it, the sentence M: This sentence has no truthmaker. I argue that, contrary to what Milne argues, on Truthmaker Maximalism M is equivalent to the Liar, which gives the truthmaker maximalist a way to defend his position from Milne's counterexample: to argue that M expresses no proposition.

What makes necessary truths true? I argue that all truth supervenes on how things are, and that necessary truths are no exception. What makes them true are proofs. But if so, the notion of proof needs to be generalized to include verification-transcendent proofs, proofs whose correctness exceeds our ability to verify it. It is incumbent on me, therefore, to show that arguments, such as Dummett's, that verification- truth is not compatible with the theory of meaning, are mistaken. The answer is (...) that what we can conceive and construct far outstrips our actual abilities. I conclude by proposing a proof-theoretic account of modality, rejecting a claim of Armstrong's that modality can reside in non-modal truthmakers. (shrink)

First paragraph: Truthmaker theory maintains that for every truth there is something, some thing, some entity, that makes it true. Balking at the prospect that logical truths are made true by any particular thing, a consequence that may in fact be hard to avoid (see Restall 1996, Read 2000), this principle of truthmaking is sometimes restricted to (logically) contingent truths. I aim to show that even in its restricted form, the principle is provably false.

A proof employing no semantic terms is offered in support of the claim that there can be truths without truthmakers. The logical resources used in the proof are weak but do include the structural rule Contraction.

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

This paper introduces a new approach to the theory of truthmaking. According to this approach, there are multiple forms of truthmaking. Here, I characterize and motivate a specific version of this approach, which I call a ‘Pluralist Theory of Truthmaking.’ It is suggested that truthmaking is a plural, variegated phenomenon wherein different kinds of truths, e.g., positive truths, negative truths, counterfactual truths, etc., are made true in different ways. While the paper only aims to lay the groundwork for a Pluralist (...) Theory of Truthmaking, I show how the theory can be applied to positive and negative truths. The upshot of this application is that truthmaking pluralism allows us to provide negative truths with ‘non-suspicious’ truthmakers. Finally, it is argued that Truthmaker Maximalists would do well to endorse truthmaking pluralism, as it offers a new strategy for upholding Maximalism while diminishing controversial ontological commitments. (shrink)

This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context drawn from linguistics and philosophy of language, we can see the Liar sentence to be context dependent. Once this context dependence is properly understood, it is argued, a hierarchical structure emerges which is neither ad (...) hoc nor unnatural. (shrink)

At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on the (...) philosophical topics related to truth. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth. (shrink)

Truth and Ontology concludes that some truths do not depend on being in any substantive way at all.

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

Truths are determined not by what we believe, but by the way the world is. Or so realists about truth believe. Philosophers call such theories correspondence theories of truth. Truthmaking theory, which now has many adherents among contemporary philosophers, is the most recent development of a realist theory of truth, and in this book D. M. Armstrong offers the first full-length study of this theory. He examines its applications to different sorts of truth, including contingent truths, modal truths, truths about (...) the past and the future, and mathematical truths. In a clear, even-handed and non-technical discussion he makes a compelling case for truthmaking and its importance in philosophy. His book marks a significant contribution to the debate and will be of interest to a wide range of readers working in analytical philosophy. (shrink)

Definitional and axiomatic theories of truth -- Objects of truth -- Tarski -- Truth and set theory -- Technical preliminaries -- Comparing axiomatic theories of truth -- Disquotation -- Classical compositional truth -- Hierarchies -- Typed and type-free theories of truth -- Reasons against typing -- Axioms and rules -- Axioms for type-free truth -- Classical symmetric truth -- Kripke-Feferman -- Axiomatizing Kripke's theory in partial logic -- Grounded truth -- Alternative evaluation schemata -- Disquotation -- Classical logic -- Deflationism (...) -- Reflection -- Ontological reduction -- Applying theories of truth. (shrink)

Consider a certain red rose. The proposition that the rose is red is true because the rose is red. One might say as well that the proposition that the rose is red is made true by the rose’s being red. This, it has been thought, does not commit one to a truthmaker of the proposition that the rose is red. For there is no entity that makes the proposition true. What makes it true is how the rose is, and how (...) the rose is is not an entity over and above the rose. It is against this view that I shall argue in this paper. I shall argue that a significant class of true propositions, including inessential predications like the proposition that the rose is red, are made true by entities. "No truthmaking without truthmakers" is my slogan. Although I have my view about what kinds of entities are truthmakers, I shall not argue for or presuppose that view here. All I shall argue for here is that if a proposition is made true by something, it is made true by some thing, but my argument will leave it open what kind of thing that thing is: it could be a fact or state of affairs, a trope, or any other sort of entity. (shrink)