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.     

Predication and cognitive context: Between minimalism and contextualism

In this paper, we suggest a strategy for modelling cognitive context within a truth‐conditional semantics, using Asher's model of predication. This allows us to introduce the notion of type presupposition intended as a lexical constraint to the composition of the truth‐conditional content. More specifically, we suggest that this model of predication produces a notion of truth‐conditional meaning where the cognitive context fixes a set of lexical restrictions and forced modifications. We conclude that this model might offer an intermediate position between Minimalism and Contextualism: an account that provides intuitive truth conditions within a formal semantic theory.     

Keeping ‘True’: A Case Study in Conceptual Ethics

Suppose our ordinary notion of truth is ‘inconsistent’ in the sense that its meaning is partly given by principles that classically entail a logical contradiction. Should we replace the notion with a consistent surrogate? This paper begins by defusing various arguments in favor of this revisionary proposal, including Kevin Scharp’s contention that we need to replace truth for the purposes of semantic theorizing (and thus, in particular, to formulate the inconsistency theory of truth itself). Borrowing a certain conservative metasemantic principle from Matti Eklund, the article goes on to build a positive case for the opposite policy: retaining truth as-is. The thought is basically that bivalence for the bulk of what we say in the course of ordinary, scientific, and philosophical inquiry should suffice to justify keeping ‘true’. Two versions of the story are told: one more philosophical, drawing on an analogy to Lewis’ response to Putnam’s paradox; the other more technical, invoking a deviant strand of mathematical work on the semantic paradoxes.     

German philosophy, Freud, and the riddle of the woman

After Kant's critique of empiricism, subjectivist epistemologies cropped up in 19th-century German philosophy. Schopenhauer argued that the true essence of every object was an irrational and sexual will. This underlying will distorted a subject's knowledge of the world. Schopenhauer's notion of this true essence was analogous to his portrayal of women; they too were natural, irrational, and instinctual. Nietzsche postulated a will-to-power that structured and hence distorted a chaotic world. That structureless "real" world Nietzsche symbolized as the essential "truth of a woman," a truth which for Nietzsche was unknowable to the desirous male philosopher. Freud, while maintaining belief in empirical truth, developed a psychology of mis-knowledge which had much in common with Schopenhauer's epistemology. His theory of transference grew from a need to explain how female patients libidinally distorted the reality of their male analysts. Conversely, Freud's later writings on women are hampered by the author's realization of his own precarious and subjective position as man trying to know woman. These counter-transferential concerns ultimately made the woman's psychological essence an unknowable riddle for Freud.     

Two types of empirical adequacy: a partial structures approach

The notion of empirical adequacy has received recent philosophical attention, especially within the framework of the semantic approach. Empirical adequacy, as explicated in the semantic approach, concerns the relationship between empirical substructures and some phenomena. The aim here is to differentiate this notion of empirical adequacy from one concerning the relationship between data and phenomena. Distinguishing each notion of empirical adequacy emphasizes different aspects of scientific practice—one concerning theory-development from the basis of an established theory, the other concerning theory-development from the basis of data-fitting, where established theory may not foster further development. To illustrate this contrast, an example from financial economics is considered.     

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.     

Quine: Peter HyltonReference, Ontological Relativity, and Realism

Section I of this essay discusses Quine's views about reference,, contrasting them with those of Russell. For the latter, our language and thought succeed in being about the world because of our acquaintance with objects; the relation of reference—roughly, the relation between a name and its bearer—is thus fundamental. For Quine, by contrast, the fundamental relation by which our language comes to be about the world, and to have empirical content, is that between a sentence and stimulations of our sensory surfaces; reference, while important, is a derivative notion. Section II shows how this view of reference as derivative makes possible the notorious Quinean doctrine of ontological relativity. Section III raises the issue of realism. It argues that somewhat different notions of realism are in play for Quine and for Russell—for Russell, objects, and our knowledge of objects, play the fundamental role, while for quine objectivity and truth are fundamental, with ontology being derivative.     

Necessity and Triviality

In this paper I argue that there are some sentences whose truth makes no demands on the world, being trivially true in that their truth-conditions are trivially met. I argue that this does not amount to their truth-conditions being met necessarily: we need a non-modal understanding of the notion of the demands the truth of a sentence makes, lest we be blinded to certain conceptual possibilities. I defend the claim that the truths of pure mathematics and set theory are trivially true, and hence accepting their truth brings no ontological commitment; I further defend the claim that the truths of applied mathematics and set theory do not demand the existence of numbers or sets. While the notion of a demand must not be reduced to anything modal, I nonetheless argue that sentences that are trivially true must also be necessary, lest we violate a very weak version of the principle that truth depends on the world. I further argue that all necessary truths are trivially true, lest we admit unexplained necessities. I end by showing one important consequence of this: I argue that if there are truthmakers for intrinsic predications, they must be states of affairs rather than tropes.     

Tokens, Dates And Tenseless Truth Conditions

There are two extant versions of the new tenseless theory of time: the date versionand the token-reflexive version. I ask whether they are equivalent, and if not, whichof them is to be preferred. I argue that they are not equivalent, that the date version isunsatisfactory, and that the token-reflexive version is correct. I defend the token-reflexive version against a string of objections from Quentin Smith. My defence involves a discussion of the ontological and semantic significance of truth conditions, and of the connection between truth and reality on the one hand, and that between truth and meaning on the other. I argue that Smith's objections to the token-reflexive theory stem from his confusing these two aspects of the notion of truth.     

Analyticity and Incorrigibility

The traditional point of view on analyticity implies that truth in virtue only of meaning entails a priori acceptability and vice versa. The argument for this claim is based on the idea that meaning as it concerns truth and meaning as it concerns competence are one and the same thing. In this paper I argue that the extensions of these notions do not coincide. I hold that truth in virtue of meaning — truth for semantic reasons—doesn't imply a priori acceptability, and that a priori reflection based only on knowledge of meaning—in the sense of competence—doesn't necessitate true conclusions.The main consequence of this view concerns conceptual analysis, as it presupposes we have a privileged—incorrigible in the face of empirical evidence—access to non-trivial truths about the world on the basis of mere a priori reflection founded on meaning. If, as I argue, such access is not incorrigible the project of conceptual analysis loses its special epistemological status.     

Truth as Translation – Part A

According to Tarski's Convention T, the adequacy of a truth definition is (implicitly) defined relatively to a translation mapping from the object language to the metalanguage; the translation mapping itself is left unspecified. This paper restates Convention T in a form in which the relativity to translation is made explicit. The notion of an interpreted language is introduced, and a corresponding notion of a translation between interpreted languages is defined. The latter definition is stated both in an algebraic version, and in an equivalent possible worlds version. It is a consequence of our definition that translation is indeterminate in certain cases. Finally, we give an application of our revised version of Convention T and show that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate. This is possible if only truth is based on a nonstandard translation mapping by which, e.g., the Liar sentence is translated to its own negation. In this part of the paper this existence result is proved only for languages without quantifiers; in Part B the result will be extended to first-order languages.     

Truth Values and Proof Theory

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.     

“If you’d wiggled A,then B would’ve changed”

This paper deals with the truth conditions of conditional sentences. It focuses on a particular class of problematic examples for semantic theories for these sentences. I will argue that the examples show the need to refer to dynamic, in particular causal laws in an approach to their truth conditions. More particularly, I will claim that we need a causal notion of consequence. The proposal subsequently made uses a representation of causal dependencies as proposed in Pearl (2000) to formalize a causal notion of consequence. This notion inserted in premise semantics for counterfactuals in the style of Veltman (1976) and Kratzer (1979) will provide a new interpretation rule for conditionals. I will illustrate how this approach overcomes problems of previous proposals and end with some remarks on remaining questions.     

Axiomatizing the Logic of Imagination

In a recent paper Berto introduces a semantic system for a logic of imagination, intended as positive conceivability, and aboutness of imaginative acts. This system crucially adopts elements of both the semantics of conditionals and the semantics of analytical implications in order to account for the central logical traits of the notion of truth in an act of imagination based on an explicit input. The main problem left unsolved is to put forward a complete set of axioms for the proposed system. In the present paper I offer a solution to this problem by providing a complete axiomatization of a generalization of the original semantics. The difficulty in proving completeness lies in the fact that the modalities that capture the notion of truth in an act of imagination are neither standard nor minimal, so that the construction of the canonical model and the proof of the truth lemma are to be substantially modified.

     

Radical quotation and real repetition

In this essay I argue for a constructivist account of the entities composing the object languages of Davidsonian truth theories and a quotational account of the reference from metalinguistic expressions to interpreted utterances. I claim that ‘radical quotation’ requires an ontology of repeatable events with strong similarities to Derrida's account of iterable events. In part one I summarise Davidson's account of interpretation and Olav Gjelsivk's arguments to the effect that the syntactic individuation of linguistic objects is only workable if interpreters make richer assumptions about semantic properties than Davidson can tolerate. In part two I show that the objectivist account of syntactic objects which Gjelsivk's arguments presuppose is incompatible with one corollary of Davidsonian semantic indeterminacy: namely, the relativity of language to interpretative scheme. In place of this an account of radical interpretation is presented in which a quotational theory of metalinguistic reference furnishes the requisite relativity. In part three I argue that this account requires that particular utterance events must be repeatable to be radically quotable and give reasons why particularity and repeatability are not incompatible.     

On A Neglected Path to Intuitionism

According to Quine, in any disagreement over basic logical laws the contesting parties must mean different things by the connectives or quantifiers implicated in those laws; when a deviant logician ‘tries to deny the doctrine he only changes the subject’. The standard (Heyting) semantics for intuitionism offers some confirmation for this thesis, for it represents an intuitionist as attaching quite different senses to the connectives than does a classical logician. All the same, I think Quine was wrong, even about the dispute between classicists and intuitionists. I argue for this by presenting an account of consequence, and a cognate semantic theory for the language of the propositional calculus, which (a) respects the meanings of the connectives as embodied in the familiar classical truth-tables, (b) does not presuppose Bivalence, and with respect to which (c) the rules of the intuitionist propositional calculus are sound and complete. Thus the disagreement between classicists and intuitionists, at least, need not stem from their attaching different senses to the connectives; one may deny the doctrine without changing the subject. The basic notion of my semantic theory is truth at a possibility, where a possibility is a way that (some) things might be, but which differs from a possible world in that the way in question need not be fully specific or determinate. I compare my approach with a previous theory of truth at a possibility due to Lloyd Humberstone, and with a previous attempt to refute Quine’s thesis due to John McDowell.     

Review

I argue in this paper that anyone who accepts the ontology of scientific realism can only accept a pragmatic theory of truth, i.e., a theory on which truth is what it is epistemically right to believe. But the combination of realism with such a theory of truth is a form of internal realism; therefore, a scientific realist should be an internal realist. The strategy of the paper is to argue that there is no adequate semantic or correspondence theory of truth compatible with a realist ontology, that a redundancy theory cannot account for the value of truth, and that the only kind of truth theory which can account for the value of truth, and is compatible with a realist ontology, is a pragmatic theory. The kind of truth theory I wish to defend is objective and naturalistic, and the ontology is realistic. My position is, therefore, one of objective, naturalistic realism.     

Thought experiments and conceptual revision

The idea that claims about the physical world might be arrived through a priori reasoning has a long history in physics. But it is clear that empiricist notions of the nature of science, and in particular the empirical nature of physics, have held sway in this century. Yet, in the idea of thought experiments in science, we might find the survival of earlier a priori reasoning to the truth of claims about the physical world. This paper challenges the notion that science can be understood as a purely empirical endeavor and points out what reforms would be necessary for teaching the image of science to our young.     

Wittgenstein as philosopher of culture

Interest in Wittgenstein came to Norway in a period of unrest on the Norwegian philosophical scene. The dominant Oslo School of empirical semantics was dissolved during the same period, not because it refused to take the locutionary/ illocutionary distinction seriously enough, but mainly because of its blind spot, caused by its exaggerated honesty. This paper argues that the semantic theory of ‘proposition and occurrence’ led the empirical semanticist into an intellectual attitude, overlooking language as part of a cultural landscape. Through overlooking this possibility, the empirical semanticist became an animal without a habitat. The way out was an interpretation of the notion of a language‐game which makes Wittgenstein a philosopher of culture.