Editorial Introduction

I survey some important semantical and axiomatic theories of self-referential truth. Kripke's fixed-point theory, the revision theory of truth and appraoches involving fuzzy logic are the main examples of semantical theories. I look at axiomatic theories devised by Cantini, Feferman, Freidman and Sheard. Finally some applications of the theory of self-referential truth are considered.     

Theories of Truth Which Have No Standard Models

This papers deals with the class of axiomatic theories of truth for semantically closed languages, where the theories do not allow for standard models; i.e., those theories cannot be interpreted as referring to the natural number codes of sentences only (for an overview of axiomatic theories of truth in general, see Halbach[6]). We are going to give new proofs for two well-known results in this area, and we also prove a new theorem on the nonstandardness of a certain theory of truth. The results indicate that the proof strategies for all the theorems on the nonstandardness of such theories are "essentially" of the same kind of structure.     

Remarks on Compositionality and Weak Axiomatic Theories of Truth

The paper draws attention to an important, but apparently neglected distinction relating to axiomatic theories of truth, viz. the distinction between weakly and strongly truth-compositional theories of truth. The paper argues that the distinction might be helpful in classifying weak axiomatic theories of truth and examines some of them with respect to it.     

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.     

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.     

Reasoning about conscious experience with axiomatic and graphical mathematics

We cast aspects of consciousness in axiomatic mathematical terms, using the graphical calculus of general process theories (a.k.a symmetric monoidal categories and Frobenius algebras therein). This calculus exploits the ontological neutrality of process theories. A toy example using the axiomatic calculus is given to show the power of this approach, recovering other aspects of conscious experience, such as external and internal subjective distinction, privacy or unreadability of personal subjective experience, and phenomenal unity, one of the main issues for scientific studies of consciousness. In fact, these features naturally arise from the compositional nature of axiomatic calculus.     

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.     

Foundations of educational psychology: Howard Gardner's neoclassical psyche

This article is a theoretical examination of the implications of Howard Gardner's work in developmental and educational psychology (1983, 1993, 1999a, 1999b) for the structure of the psyche. The author accepts as axiomatic, in the context of this article, Gardner's educational manifesto (1999a) that all students should be taught disciplinary understandings of truth, beauty, and goodness. Rational inferences are then made indicating that the psyche that Gardner intends to educate and help develop is in the form of a neoclassical psyche and that it is structured by the capacities to know truth, to love beauty, and to will goodness.     

Truth in Applicative Theories

We give a survey on truth theories for applicative theories. It comprises Frege structures, universes for Frege structures, and a theory of supervaluation. We present the proof-theoretic results for these theories and show their syntactical expressive power. In particular, we present as a novelty a syntactical interpretation of ID₁ in a applicative truth theory based on supervaluation.     

真理、符合与收缩论

The central claim of this essay is that many deflationary theories of truth are variants of the correspondence theory of truth. Essential to the correspondence theory of truth is the proposal that objective features of the world are the truthmakers of statements. Many advocates of deflationary theories (including F. P. Ramsay, P. F. Strawson and Paul Horwich) remain committed to this proposal. Although T-sentences (statements of the form “s is true iff p”) are presented by advocates of deflationary theories of truth as truisms or analytic truths, T-sentences are often understood as entailing commitment to the central proposal of the correspondence theory.     

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.

     

Comparing Fixed-Point and Revision Theories of Truth

In response to the liar’s paradox, Kripke developed the fixed-point semantics for languages expressing their own truth concepts. (Martin and Woodruff independently developed this semantics, but not to the same extent as Kripke.) Kripke’s work suggests a number of related fixed-point theories of truth for such languages. Gupta and Belnap develop their revision theory of truth in contrast to the fixed-point theories. The current paper considers three natural ways to compare the various resulting theories of truth, and establishes the resulting relationships among these theories. The point is to get a sense of the lay of the land amid a variety of options. Our results will also provide technical fodder for the methodological remarks of the companion paper to this one.     

Verisimilitude and belief change for nomic conjunctive theories

In this paper, we address the problem of truth approximation through theory change, asking whether revising our theories by newly acquired data leads us closer to the truth about a given domain. More particularly, we focus on “nomic conjunctive theories”, i.e., theories expressed as conjunctions of logically independent statements concerning the physical or, more generally, nomic possibilities and impossibilities of the domain under inquiry. We define both a comparative and a quantitative notion of the verisimilitude of such theories, and identify suitable conditions concerning the (partial) correctness of acquired data, under which revising our theories by data leads us closer to “the nomic truth”, construed as the target of scientific inquiry. We conclude by indicating some further developments, generalizations, and open issues arising from our results.     

The Chrysippus intuition and contextual theories of truth

Contextual theories of truth are motivated primarily by the resolution they provide to paradoxical reasoning about truth. The principal argument for contextual theories of truth relies on a key intuition about the truth value of the proposition expressed by a particular utterance made during paradoxical reasoning, which Anil Gupta calls “the Chrysippus intuition.” In this paper, I argue that the principal argument for contextual theories of truth is circular, and that the Chrysippus intuition is false. I conclude that the philosophical motivation for contextual theories of truth fails.

Bolzanian knowing: infallibility,virtue and foundational truth

The paper discusses Bernard Bolzano’s epistemological approach to believing and knowing with regard to the epistemic requirements of an axiomatic model of science. It relates Bolzano’s notions of believing, knowing and evaluation to notions of infallibility, immediacy and foundational truth. If axiomatic systems require their foundational truths to be infallibly known, this knowledge involves both evaluation of the infallibility of the asserted truth and evaluation of its being foundational. The twofold attempt to examine one’s assertions and to do so by searching for the objective grounds of the truths asserted lies at the heart of Bolzano’s notion of knowledge. However, the explanatory task of searching for grounds requires methods that cannot warrant infallibility. Hence, its constitutive role in a conception of knowledge seems to imply the fallibility of such knowledge. I argue that the explanatory task contained in Bolzanian knowing involves a high degree of epistemic virtues, and that it is only through some salient virtue that the credit of infallibility can distinguish Bolzanian knowing from a high degree of Bolzanian believing.     

Truth and Consciousness

Many work on flushing out what our consciousness means in cognitive and phenomenological terms, but no one has yet connected the dots on how consciousness and truth intersect, much less how our phenomenal consciousness can form the ground for most of our models of truth. Here, I connect those dots and argue that the basic structure of our phenomenal consciousness grounds the nature of truth as concordance, to harmonize in agreement, and that most extant theories on truth are well explained in that grounding. Said another way, the unifying and bifurcating intentional structure of phenomenal consciousness is the non-epistemic ground of truth, such that most theories of truth can be explained as particular expressions of concordance based upon the differing aspects of that ground.     

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.

     

DEFLATIONISM,CONSERVATIVENESS AND MAXIMALITY

We discuss two desirable properties of deflationary truth theories: conservativeness and maximality. Joining them together, we obtain a notion of a maximal conservative truth theory – a theory which is conservative over its base, but can’t be enlarged any further without losing its conservative character. There are indeed such theories; we show however that none of them is axiomatizable, and moreover, that there will be in fact continuum many theories of this sort. It turns out in effect that the deflationist still needs some additional principles, which would permit him to construct his preferred theory of truth.     

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.     

Axiomatic justifications of the utility principle: A formal investigation

It is argued that existing axiomatic theories of utility do not provide the utility principle or the principle of maximising expected utility with a formal justification. It is also argued that these theories only put mild constraints on a decision-maker in a decision-context. Finally, it is argued that the prospects are not particularly bright for finding formal non-circular arguments for the utility principle that do not rely on the law of large numbers.