Deflationary Truth and Pathologies

By a classical result of Kotlarski, Krajewski and Lachlan, pathological satisfaction classes can be constructed for countable, recursively saturated models of Peano arithmetic. In this paper we consider the question of whether the pathology can be eliminated; we ask in effect what generalities involving the notion of truth can be obtained in a deflationary truth theory (a theory of truth which is conservative over its base). It is shown that the answer depends on the notion of pathology we adopt. It turns out in particular that a certain natural closure condition imposed on a satisfaction class—namely, closure of truth under sentential proofs—generates a nonconservative extension of a syntactic base theory (Peano arithmetic).     

Deflationism beyond arithmetic

The conservativeness argument poses a dilemma to deflationism about truth, according to which a deflationist theory of truth must be conservative but no adequate theory of truth is conservative. The debate on the conservativeness argument has so far been framed in a specific formal setting, where theories of truth are formulated over arithmetical base theories. I will argue that the appropriate formal setting for evaluating the conservativeness argument is provided not by theories of truth over arithmetic but by those over subject matters ‘richer’ than arithmetic, such as set theory. The move to this new formal setting provides deflationists with better defence and brings a broader perspective to the debate.

     

How Truth Behaves When There’s No Vicious Reference

In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth “its consequence that truth behaves like an ordinary classical concept under certain conditions—conditions that can roughly be characterized as those in which there is no vicious reference in the language.” To clarify this remark, they define Thomason models, nonpathological models in which truth behaves like a classical concept, and investigate conditions under which a model is Thomason: they argue that a model is Thomason when there is no vicious reference in it. We extend their investigation, considering notions of nonpathologicality and senses of “no vicious reference” generated both by revision theories of truth and by fixed-point theories of truth. We show that some of the fixed-point theories have an advantage analogous to that which Gupta and Belnap claim for their approach, and that at least one revision theory does not. This calls into question the claim that the revision theories have a distinctive advantage in this regard.     

Axiomatic Theories of Partial Ground I

This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that the theory is a proof-theoretically conservative extension of the theory PT of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground.     

Theories of Truth without Standard Models and Yablo’s Sequences

The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω-inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, I show that in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω- inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth.     

Conservative Theories of Classical Truth

Some axiomatic theories of truth and related subsystems of second-order arithmetic are surveyed and shown to be conservative over their respective base theory. In particular, it is shown by purely finitistically means that the theory PA ÷ "there is a satisfaction class" and the theory FS of [2] are conservative over PA.     

意义理论

Research into logical syntax provides us the knowledge of the structure of sentences, while logical semantics provides a window into uncovering the truth of sentences. Therefore, it is natural to make sentences and truth the central concern when one deals with the theory of meaning logically. Although their theories of meaning differ greatly, both Michael Dummett’s theory and Donald Davidson’s theory are concerned with sentences and truth and developed in terms of truth. Logical theories and methods first introduced by G. Frege underwent great developments during the past century and have played an important role in expanding these two scholars’ theories of meaning. Translated by Ma Minghui from Zhexue Yanjiu 哲学研究 (Philosophical Research), 2006, (7): 53–61     

Reliabilism and antirealist theories of truth

In order to shed light on the question of whether reliabilism entails or excludes certain kinds of truth theories, I examine two arguments that purport to establish that reliabilism cannot be combined with antirealist and epistemic theories of truth. I take antirealism about truth to be the denial of the recognition-transcendence of truth, and epistemic theories to be those that identify truth with some kind of positive epistemic status. According to one argument, reliabilism and antirealism are incompatible because the former takes epistemic justification to be recognition-transcendent in a certain sense that conflicts with the latter’s denial of the recognition-transcendence of truth. I show that, because the recognition-transcendence of reliabilist justification is significantly weaker than the recognition-transcendence required by a realist conception of truth, antirealist theories of truth that deny the strong transcendence of truth do not threaten the externalist character of reliabilism. According to the second argument, reliabilism cannot be combined with an epistemic truth theory because reliabilists analyze positive epistemic status in terms of truth but epistemic theorists analyze truth in terms of positive epistemic status. However, I argue that reliabilists who wish to adopt an epistemic theory of truth can avoid circularity by appealing to a multiplicity of positive epistemic statuses.     

Truth and Assertability

Deflationists say that the equivalence between ‘p is true’ and p is all there is to the meaning of ‘true’. “Use” theories generally construe meaning as acceptance conditions. I argue: (i) there are certain obvious objections to a deflationary theory of truth so formulated; but (ii) they can be overcome if we employ a graded notion of use, i.e. a notion of assertability; but (iii) there appear to be certain further difficulties which cannot be overcome in this way.     

Supervaluations and the Propositional Attitude Constraint

For the sentences of languages that contain operators that express the concepts of definiteness and indefiniteness, there is an unavoidable tension between a truth-theoretic semantics that delivers truth conditions for those sentences that capture their propositional contents and any model-theoretic semantics that has a story to tell about how indetifiniteness in a constituent affects the semantic value of sentences which imbed it. But semantic theories of both kinds play essential roles, so the tension needs to be resolved. I argue that it is the truth theory which correctly characterises the notion of truth, per se. When we take into account the considerations required to bring model theory into harmony with truth theory, those considerations undermine the arguments standardly used to motivate supervaluational model theories designed to validate classical logic. But those considerations also show that celebration would be premature for advocates of the most frequently encountered rival approach – many-valued model theory.     

The Dual Foundation of Qualitative Truth Approximation

The main formal notion involved in qualitative truth approximation by the HD-method, viz. ‘more truthlike’, is shown to not only have, by its definition, an intuitively appealing ‘model foundation’, but also, at least partially, a conceptually plausible ‘consequence foundation’. Moreover, combining the relevant parts of both leads to a very appealing ‘dual foundation’, the more so since the relevant methodological notions, viz. ‘more successful’ and its ingredients provided by the HD-method, can be given a similar dual foundation. According to the resulting dual foundation of ‘naive truth approximation’, the HD-method provides successes (established true consequences) and counterexamples (established wrongly missing models) of theories. Such HD-results may support the tentative conclusion that one theory seems to remain more successful than another in the naive sense of having more successes and fewer counterexamples. If so, this provides good reasons for believing that the more successful theory is also more truthlike in the naive sense of having more correct models and more true consequences. In the dual foundation of ‘refined truth approximation’, HD-results remain of the same two kinds, but ‘more successful’ is taken in the refined sense of accommodating counterexamples while saving relevant successes, in which case ‘more truthlike’ can be taken in the refined sense of improving relevant models while saving relevant consequences. In this way one gets a realistic dual account of qualitative truth approximation by the HD-method. The model foundation can also be extended to the methodological notions, but not in a very plausible way. The consequence foundation only seems specifiable for naive truth approximation, in which case it is plausible. In sum, the dual foundation is superior to both. This revised version was published online in July 2006 with corrections to the Cover Date.     

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。     

Verisimilitude and Belief Change for Conjunctive Theories

Theory change is a central concern in contemporary epistemology and philosophy of science. In this paper, we investigate the relationships between two ongoing research programs providing formal treatments of theory change: the (post-Popperian) approach to verisimilitude and the AGM theory of belief change. We show that appropriately construed accounts emerging from those two lines of epistemological research do yield convergences relative to a specified kind of theories, here labeled “conjunctive”. In this domain, a set of plausible conditions are identified which demonstrably capture the verisimilitudinarian effectiveness of AGM belief change, i.e., its effectiveness in tracking truth approximation. We conclude by indicating some further developments and open issues arising from our results.     

Truth in the Tractatus

My paper takes issue both with the standard view that the Tractatus contains a correspondence theory and with recent suggestions that it features a deflationary or semantic theory. Standard correspondence interpretations are mistaken, because they treat the isomorphism between a sentence and what it depicts as a sufficient condition of truth rather than of sense. The semantic/deflationary interpretation ignores passages that suggest some kind of correspondence theory. The official theory of truth in the Tractatus is an obtainment theory – a sentence is true iff the state of affairs it depicts obtains. This theory differs from deflationary theories in that it involves an ontology of states of affairs/facts; and it can be transformed into a type of correspondence theory: a sentence is true iff it corresponds to, i.e. depicts an obtaining state of affairs (fact). Admittedly, unlike correspondence theories as commonly portrayed, this account does not involve a genuinely truth-making relation. It features a relation of correspondence, yet it is that of depicting, between a meaningful sentence and its sense – a possible state of affairs. What makes for truth is not that relation, but the obtaining of the depicted state of affairs. This does not disqualify the Tractatus from holding a correspondence theory, however, since the correspondence theories of Moore and Russell are committed to a similar position. Alternatively, the obtainment theory can be seen as a synthesis of correspondence, semantic and deflationary approaches. It does justice to the idea that what is true depends solely on what is the case, and it combines a semantic explanation of the relation between a sentence and what it says with a deflationary account of the agreement between what the sentence says and what obtains or is the case if it is true     

Point-Free Geometry and Verisimilitude of Theories

A metric approach to Popper’s verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of the difficulties arising from the known definitions of verisimilitude.     

The Problem of Deep Competitors and the Pursuit of Epistemically Utopian Truths

According to standard scientific realism, science seeks truth and we can justifiably believe that our successful theories achieve, or at least approximate, that goal. In this paper, I discuss the implications of the following competitor thesis: Any theory we may favor has competitors such that we cannot justifiably deny that they are approximately true. After defending that thesis, I articulate three specific threats it poses for standard scientific realism; one is epistemic, the other two are axiological (that is, pertaining to the claim that science seeks truth). I also flag an additional axiological “challenge,” that of how one might justify the pursuit of a primary aim, such as truth. Bracketing epistemic realism, I argue that the axiological threats can be addressed by embracing a refined realist axiological hypothesis, one that specifies a specific subclass of true claims sought in science. And after identifying three potential responses to the axiological “challenge,” I contend that, while standard axiological realism appears to lack the resources required to utilize any of the responses, the refined realist axiology I embrace is well suited to each.     

Restoring Continuity in Theory Change: The Kepler-to-Newton Case

In the on-going debate between scientific realism and its various opponents, a crucial role in challenging the realist claim that success of scientific theories must be attributed to their approximate truth is played by the so-called pessimistic meta-induction: Arguing that the history of science boils down to a succession of theories which, though successful at a time, were eventually discarded only to be replaced by alternative theories which in turn met with the same fate, it purports to show that the empirical success of scientific theories cannot have any bearing on claims about their truth-likeness. Yet, the same historical record suggests a possible strategy to counter this argument. Far from being a barren wasteland, it contains cases which point to the need of adopting a selective attitude when passing judgments about truth-likeness of theories. In this vein, Psillos has proposed the so-called divide et impera move. It consists in pointing out that responsibility for the success of a theory should be attributed to an indispensable core element in it, acting in unison with other elements reflecting the concrete historical conditions under which the theory was formulated. In what follows it is argued that the discovery of Kepler’s first two laws and the transition to Newtonian mechanics provides a notable case to exhibit the divide et impera move. All the more so, since—as will be shown—Kepler himself employs a variant of this move, a fact that sheds light on the philosophical implications of his theories. As a result, it will be argued that the appropriate selective attitude towards theories becomes solidly warranted if wedded to the diachronic element in the process of a theory’s development.     

Theorizing about truth outside of one’s own language

A theory of truth is language-transcendent if it ascribes truth conditions to truth-bearers that are not expressible in (or translatable to) our natural language; a theory is language-immanent if it is not language-transcendent. In this paper, I argue for the following theses. (1) Whether the correct theory of truth is language-transcendent or language-immanent will have significant consequences for general philosophy. Prima facie, a language-transcendent theory is preferable. However, (2) language-transcendent theories tend to require substantive metaphysical commitments concerning truth. Deflationist theories are particularly interesting in this context. I argue that, if deflationism is to remain consistent with its motivations, then it must opt for a language-immanent conception of truth.

     

A deflationary theory of reference

The article first rehearses three deflationary theories of reference, (1) disquotationalism, (2) propositionalism (Horwich), and (3) the anaphoric theory (Brandom), and raises a number of objections against them. It turns out that each corresponds to a closely related theory of truth, and that these are subject to analogous criticisms to a surprisingly high extent. I then present a theory of my own, according to which the schema “That S(t) is about t” and the biconditional “S refers to x iff S says something about x” are exhaustive of the notions of aboutness and reference. An account of the usefulness of “about” is then given, which, I argue, is superior to that of Horwich. I close with a few considerations about how the advertised theory relates to well-known issues of reference, the conclusions of which is (1) that the issues concern reference and aboutness only insofar as the words “about” and “refer” serve to generalise over the claims that are really at issue, (2) that the theory of reference will not settle the issues, and (3) that it follows from (2) that the issues do not concern the nature of aboutness or reference.