Supervaluation-Style Truth Without Supervaluations

Kripke’s theory of truth is arguably the most influential approach to self-referential truth and the semantic paradoxes. The use of a partial evaluation scheme is crucial to the theory and the most prominent schemes that are adopted are the strong Kleene and the supervaluation scheme. The strong Kleene scheme is attractive because it ensures the compositionality of the notion of truth. But under the strong Kleene scheme classical tautologies do not, in general, turn out to be true and, as a consequence, classical reasoning is no longer admissible once the notion of truth is involved. The supervaluation scheme adheres to classical reasoning but violates compositionality. Moreover, it turns Kripke’s theory into a rather complicated affair: to check whether a sentence is true we have to look at all admissible precisification of the interpretation of the truth predicate we are presented with. One consequence of this complicated evaluation condition is that under the supervaluation scheme a more proof-theoretic characterization of Kripke’s theory becomes inherently difficult, if not impossible. In this paper we explore the middle ground between the strong Kleene and the supervaluation scheme and provide an evaluation scheme that adheres to classical reasoning but retains many of the attractive features of the strong Kleene scheme. We supplement our semantic investigation with a novel axiomatic theory of truth that matches the semantic theory we have put forth.     

Paradoxes and Failures of Cut

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning—one which takes meaning to be constituted by assertibility and deniability conditions—and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system—ST—that conservatively extends classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered and responded to.     

Hobnobbing with the Nonexistent

Recent discussions of Geach sentences by Braun and Salmon are reprised. It is shown that the intractability of providing semantics for Geach sentences (using standard logical tools) is due to the assumption that quantifiers are ontologically committing. Representing the content of these statements is easy using neutral quantifiers. An important concern is consistent identity conditions for nonreferring terms. It may be thought that Meinongian-object approaches handle this better than Azzouni's no-objects-in-any-sense-at-all approach. This is shown to be false. How our truth-inducing practices determine truth values for empty-term statements is indicated—in particular, it is argued that our identification and distinguishing practices with “fictional entities” are parasitic on our practices with entities we take to be real. Examples from Austin—white dots on the horizon and specks—are among the test cases for the views developed here.     

带良好条件句的真理不动点理论

各种真理不动点理论的一个主要问题在于：它们通常缺乏像样的条件句。本文旨在提出两种新的想法去处理这个问题。在介绍克里普克的真理不动点理论之后,本文的作者探讨了对真理不动点理论的种种反对意见,并回答了其中的一部分。然后,作者说明了菲尔德的真理理论,并说明该理论如何在克里普克的真理不动点理论至上增加了条件句。不过,本文的作者争论说,菲尔德的条件句仍有许多不尽理想之处。为了弥补这些缺点,作者提出了两个想法：一个是在不动点理论至上增加亚当斯条件句,另一个则是在其上增加史多内克条件句。     

Adding a Conditional to Kripke’s Theory of Truth

Kripke’s theory of truth (Kripke, The Journal of Philosophy72(19), 690–716; 1975) has been very successful but shows well-known expressive difficulties; recently, Field has proposed to overcome them by adding a new conditional connective to it. In Field’s theories, desirable conditional and truth-theoretic principles are validated that Kripke’s theory does not yield. Some authors, however, are dissatisfied with certain aspects of Field’s theories, in particular the high complexity. I analyze Field’s models and pin down some reasons for discontent with them, focusing on the meaning of the new conditional and on the status of the principles so successfully recovered. Subsequently, I develop a semantics that improves on Kripke’s theory following Field’s program of adding a conditional to it, using some inductive constructions that include Kripke’s one and feature a strong evaluation for conditionals. The new theory overcomes several problems of Kripke’s one and, although weaker than Field’s proposals, it avoids the difficulties that affect them; at the same time, the new theory turns out to be quite simple. Moreover, the new construction can be used to model various conceptions of what a conditional connective is, in ways that are precluded to both Kripke’s and Field’s theories.     

Truth in Fiction,Impossible Worlds,and Belief Revision

We present a theory of truth in fiction that improves on Lewis's [1978] ‘Analysis 2’ in two ways. First, we expand Lewis's possible worlds apparatus by adding non-normal or impossible worlds. Second, we model truth in fiction as (make-believed) belief revision via ideas from dynamic epistemic logic. We explain the major objections raised against Lewis's original view and show that our theory overcomes them.     

Filtering Theories of Truth: Compositionality as a Criterion

The traditional way to filter out the implausible candidate solutions to the semantic paradoxes is to appeal to the so-called “cost/benefit analyses.” Yet it is often tedious and controversial to carry out such analyses in detail. Facing this, it would be helpful for us to rely upon some principles to filter out at least something, if not everything, from them. The proposal in this paper is thereby rather simple: We may use principles of compositionality as a “filter” for this purpose. The paper has four sections. In Section 2, the author uses the filter to examine Kripke’s fixed-point theory and to thereby show how it works. In Section 3, the author gives more examples from the classical theories of truth to demonstrate the power of the filter. In Section 4, the author addresses the skepticism concerning whether there is any consistent or non-trivial theory of truth that can survive this filtering procedure. A “nearly sufficient” condition for a theory of truth to survive this test is discussed in order to show that at least some consistent or non-trivial theories of truth do indeed survive the filtering procedure.     

Against Stepping Back: A Critique of Contextualist Approaches to the Semantic Paradoxes

A number of philosophers have argued that the key to understanding the semantic paradoxes is to recognize that truth is essentially relative to context. All of these philosophers have been motivated by the idea that once a liar sentence has been uttered we can ‘step back’ and, from the point of view of a different context, judge that the liar sentence is true. This paper argues that this ‘stepping back’ idea is a mistake that results from failing to relativize truth to context in the first place. Moreover, context-relative liar sentences, such as ‘This sentence is not true in any context’ present a paradox even after truth has been relativized to context. Nonetheless, the relativization of truth to context may offer us the means to avoid paradox, if we can justifiably deny that a sentence about a context can be true in the very context it is about.     

Satisfying Predicates: Kleene's Proof of the Hilbert–Bernays Theorem

The Hilbert–Bernays Theorem establishes that for any satisfiable first-order quantificational schema S, one can write out linguistic expressions that are guaranteed to yield a true sentence of elementary arithmetic when they are substituted for the predicate letters in S. The theorem implies that if L is a consistent, fully interpreted language rich enough to express elementary arithmetic, then a schema S is valid if and only if every sentence of L that can be obtained by substituting predicates of L for predicate letters in S is true. The theorem therefore licenses us to define validity substitutionally in languages rich enough to express arithmetic. The heart of the theorem is an arithmetization of Gödel's completeness proof for first-order predicate logic. Hilbert and Bernays were the first to prove that there is such an arithmetization. Kleene established a strengthened version of it, and Kreisel, Mostowski, and Putnam refined Kleene's result. Despite the later refinements, Kleene's presentation of the arithmetization is still regarded as the standard one. It is highly compressed, however, and very difficult to read. My goals in this paper are expository: to present the basics of Kleene's arithmetization in a less compressed, more easily readable form, in a setting that highlights its relevance to issues in the philosophy of logic, especially to Quine's substitutional definition of logical truth, and to formulate the Hilbert–Bernays Theorem in a way that incorporates Kreisel's, Mostowski's, and Putnam's refinements of Kleene's result.     

There are Kinds and Kinds of Kinds: Ben-Yami on the Semantics of Kind Terms

Hanoch Ben-Yami has argued that the theory of the semantics of natural kind terms proposed by Kripke and Putnam is false and has proposed an allegedly novel account of the semantics of kind terms. In this article, I critically examine Ben-Yami’s arguments. I will argue that Ben-Yami’s objections do not show that Kripke and Putnam’s theory is false, but at most that the specific versions of it held by Kripke and Putnam have some weaknesses. Moreover, I will argue that Ben-Yami’s account is not a novel account but it is only an unsatisfactory version of Kripke and Putnam’s theory.     

A Minimalist Theory of Truth

This article, after briefly discussing Alfred Tarski's influential theory of truth, turns to a more recent theory of truth, a deflationary, or minimalist, theory. One of the chief elements of a deflationary, or minimalist, theory of truth is that it replaces the question of what truth is with the question of what “true” does. After setting out the central features of the minimalist theory of truth, the article explains the motivation for opting for such a position. In addition, it provides some reasons for thinking that such a theory of truth is “minimal” or “deflationary” in the way that contemporary truth theorists have claimed it to be.     

Believing at Will is Possible

There are convincing counter-examples to the widely accepted thesis that we cannot believe at will. For it seems possible that the truth of a proposition depend on whether or not one believes it. I call such scenarios cases of Truth Depends on Belief (TDB) and I argue that they meet the main criteria for believing at will that we find in the literature. I reply to five objections that one might level against the thesis that TDB cases show that believing at will is possible, namely that (1) mind-reading is impossible, (2) in TDB cases, one's belief is caused by one's desire, (3) in TDB scenarios, one chooses not a belief but something else, (4) TDB cases are reducible to Feldman cases, and that (5) if truth depends on belief, we are on the road to a regress. Of course, TDB scenarios hardly, if ever, occur in real life. For three reasons, they are nonetheless important. First, they show that the thesis that it is conceptually impossible to believe at will is simply false. Second, they provide us with an important constraint on any version of the thesis that it is psychologically impossible to believe at will. Third, they show us that, contrary to what several philosophers claim or imply, believing at will should not be identified with believing irrespective of—what one considers to be—the truth, nor should believing irrespective of the truth be considered a necessary condition for believing at will.     

Truth as Translation – Part B

This is the second part of a paper dealing with truth and translation. In Part A a revised version of Tarski's Convention T has been presented, which explicitly refers to a translation mapping from the object language to the metalanguage; the vague notion of a translation has been replaced by a precise definition. At the end of Part A it has been shown that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate – this is possible if truth is based on a nonstandard translation mapping. However, this result has only been proved for languages without quantifiers. In Part B we now extend the result to first-order languages, and we show that this can be done in three different ways. In each case, the addition of a truth predicate to an interpreted language with a high degree of expressiveness leads to changes in the ontology of the language.     

WARRANTED ASSERTIBILITY AND THE NORMS OF ASSERTORIC PRACTICE: WHY TRUTH AND WARRANTED ASSERTIBILITY ARE NOT COINCIDENT NORMS

Crispin Wright has argued that truth and warranted assertibility are coincident but non‐co‐extensive norms of assertoric practice and that this fact inflates deflationary theories of truth. Wright's inflationary argument has generated much discussion in the literature. By contrast, relatively little has been said about the coincidence claim that is the focus of this paper. Wright's argument for the claim that truth and warranted assertibility are coincident norms is first presented. It is then suggested that the argument trades on an ambiguity in ‘justified’ and ‘warrantedly assertible’. Finally, it is argued that, once the ambiguity is removed, there is reason to reject the claim that truth and epistemic warrant are coincident norms of assertoric practice. One important result is that no epistemic theory of truth can satisfy what Wright takes to be a key platitude about assertion.     

Two Key Differences between Science and Philosophy

C. S. Peirce made the following claim: If science reveals truth, then consensus among scientists can be expected in the limit. This article does not dispute this claim; it simply assumes it. On the basis of this assumption, the following question is asked: Is it possible to extend Peirce's claim to philosophy in a natural way? It is argued that two important differences between science and philosophy strongly militate against such an extension. Does this mean that there is no truth to be found in philosophy? Are there, perhaps, different kinds of truth (scientific, philosophical, religious, and so on)? But such questions, though related to the present investigation, are nevertheless well beyond the scope of this article.     

N. A. Vasil’ev’s Logic and the Problem of Future Random Events

The solution of the problem of the future random events truth is considered in Vasil’ev’s logic. N. A. Vasil’ev graded the logic according to two levels—the level of facts, i.e. time fixed events, and the level of notions or rules, governing these facts. The mathematical construction previously suggested for imaginary Vasil’ev’s logic, extends to the early variant of his logic—a logic of notions. In the paper, we investigate the meaning of problematic and uncertain assertions introduced by Vasil’ev. As a result, we developed a model of Vasil’ev’s logic of facts that resolves also the truth problem of future random events. The imaginary logic has also been extended to the level of notions, and the law of the excluded eighth is gotten in it. The correspondence between Vasil’ev’s terms “some” and “all” and modern quantifiers is discussed.     

Kant on Truth-Aptness

Many scholars claimed that, according to Immanuel Kant, some judgements lack a truth-value: analytic judgements, judgements about items of which humans cannot have experience, judgements of perception, and non-assertoric judgements. However, no one has undertaken an extensive examination of the textual evidence for those claims.

Based on an analysis of Kant's texts, I argue that: ? according to Kant, only judgements of perception are not truth-apt. All other judgements are truth-apt, including analytic judgements and judgements about items of which humans cannot have experience.

? Kant sometimes states that truth-apt judgements are actual bearers of truth or falsity only when they are taken to state what is actually the case. Kant calls these judgements assertoric. Other texts ascribe truth and falsity to judgements, regardless of whether they are assertoric.

Kant's views on truth-aptness raise challenges for correspondentist and coherentist interpretations of Kant's theory of truth; they rule out the identification of Kant's crucial notion of objective validity with truth-aptness; and they imply that Kant was not a verificationist about truth or meaning.     

The seventh servant: The implications of a truth drive in Bions theory of 'O'

Drawing upon Bion's published works on the subjects of truth, dreaming, alpha‐function and transformations in ‘O’, the author independently postulates that there exists a ‘truth instinctual drive’ that subserves a truth principle, the latter of which is associated with the reality principle. Further, he suggests, following Bion's postulation, that ‘alpha‐function’ and dreaming/phantasying constitute unconscious thinking processes and that they mediate the activity of this ‘truth drive’ (quest, pulsion), which the author hypothesizes constitutes another aspect of a larger entity that also includes the epistemophilic component drive. It purportedly seeks and transmits as well as includes what Bion (1965, pp. 147‐9) calls ‘O’, the ‘Absolute Truth, Ultimate Reality, O’ (also associated with infi nity, noumena or things‐in‐themselves, and ‘godhead’) (1970, p. 26). It is further hypothesized that the truth drive functions in collaboration with an ‘unconscious consciousness’ that is associated with the faculty of ‘attention’, which is also known as ‘intuition’. It is responsive to internal psychical reality and constitutes Bion's ‘seventh servant’. O, the ultimate landscape of psychoanalysis, has many dimensions, but the one that seems to interest Bion is that of the emotional experience of the analysand's and the analyst's ‘evolving O’ respectively (1970, p. 52) during the analytic session. The author thus hypothesizes that a sense of truth presents itself to the subject as a quest for truth which has the quality and force of an instinctual drive and constitutes the counterpart to the epistemophilic drive. This ‘truth quest’ or ‘drive’ is hypothesized to be the source of the generation of the emotional truth of one's ongoing experiences, both conscious and unconscious. It is proposed that emotions are beacons of truth in regard to the acceptance of reality. The concepts of an emotional truth drive and a truth principle would help us understand why analysands are able to accept analysts’ interpretations that favor the operation of the reality principle over the pleasure principle—because of what is postulated as their overriding adaptive need for truth. Ultimately, it would seem that Bion's legacy of truth aims at integrating fi nite man with infi nite man.     

Reasoning and rationalization

Contra Lewis, it is argued that the correspondence theory is a genuine rival theory of truth: it goes beyond the redundancy theory; it competes with other theories of truth; it is aptly summarized by the slogan 'truth is correspondence to fact'; and it really is a theory of truth.