What Theories of Truth Should be Like (but Cannot be)

Leitgeb, Hannes

doi:10.1111/j.1747-9991.2007.00070.x

Cited by 56 publications

(63 citation statements)

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“…Thus, since the liar sentence isn't true, we might expect that we could say that this very fact is true; i.e., that it is true that the liar sentence is not true. Kripke's theory does not permit this: this is often known as a revenge problem (Leitgeb 2007). However, there is a way around this.…”

Section: Can There Really Be More Than One Notion Of Set?mentioning

confidence: 97%

Sets and supersets

Meadows

2015

Synthese

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It is a commonplace of set theory to say that there is no set of all wellorderings nor a set of all sets. We are implored to accept this due to the threat of paradox and the ensuing descent into unintelligibility. In the absence of promising alternatives, we tend to take up a conservative stance and tow the line: there is no universe (Halmos, in: Naive set theory, 1960). In this paper, I am going to challenge this claim by taking seriously the idea that we can talk about the collection of all the sets and many more collections beyond that. A method of articulating this idea is offered through an indefinitely extending hierarchy of set theories. It is argued that this approach provides a natural extension to ordinary set theory and leaves ordinary mathematical practice untouched.Keywords Philosophy of mathematics · Philosophy of set theory · Formal theories of truth · Absolute generality · Indefinite extensibility You're gonna need a bigger boat.(Jaws)The idea that there ought to be a set containing all of the sets is the focus of this paper. It is not a new idea. Moreover, I suspect that my way of addressing this issue will have occurred to many readers, although usually they they will have set it aside. I do not want to suggest that the techniques explored in this paper are of themselves particularly original; we shall see that related approaches have been explored from a technical angle for many years. Rather, what I am aiming to do is give this group of ideas a more philosophical twist by drawing out their underlying motivations and B Toby Meadows

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Section: Can There Really Be More Than One Notion Of Set?mentioning

confidence: 97%

Sets and supersets

Meadows

2015

Synthese

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“…For instance, the theory may be required to be ω-consistent (see Leitgeb 2007) or "symmetric" concerning its inner and outer logic, where the outer logic of a theory S is the set of S-provable sentences and the inner logic is the set of sentences ϕ with S T ϕ (see Leitgeb 2007). For instance, the theory may be required to be ω-consistent (see Leitgeb 2007) or "symmetric" concerning its inner and outer logic, where the outer logic of a theory S is the set of S-provable sentences and the inner logic is the set of sentences ϕ with S T ϕ (see Leitgeb 2007).…”

Section: Five Desideratamentioning

confidence: 99%

“…Some efforts have been made to carry out exercises similar to that of the present article: these include Sheard 1994 andLeitgeb 2007. But, for reasons that we hope to make clear, these efforts have remained less than fully satisfactory.…”

Section: Introductionmentioning

confidence: 96%

Unifying the Philosophy of Truth

Achourioti

Galinon

Martínez-Fernández

et al. 2015

Logic, Epistemology, and the Unity of Science

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Logic, Epistemology, and the Unity of Science aims to reconsider the question of the unity of science in light of recent developments in logic. At present, no single logical, semantical or methodological framework dominates the philosophy of science. However, the editors of this series believe that formal techniques like, for example, independence friendly logic, dialogical logics, multimodal logics, game theoretic semantics and linear logics, have the potential to cast new light on basic issues in the discussion of the unity of science.This series provides a venue where philosophers and logicians can apply specific technical insights to fundamental philosophical problems. While the series is open to a wide variety of perspectives, including the study and analysis of argumentation and the critical discussion of the relationship between logic and the philosophy of science, the aim is to provide an integrated picture of the scientific enterprise in all its diversity.More information about this series at

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“…Several authors have proposed different desiderata on a satisfactory theory of truth (cf. Halbach and Horsten 2005;Leitgeb 2007;Sheard 2002). We believe such lists often involve criteria which are only imported because truth seems to satisfy these criteria in natural language, without paying attention as to whether they play an important role in the expression of infinite conjunctions and disjunctions.…”

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confidence: 99%

“…Halbach and Horsten 2005;Leitgeb 2007). The inner logic of a truth system is the set of sentences the theory can prove to be true, while the outer logic is simply the set of its theorems.…”

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confidence: 99%

Disquotation and Infinite Conjunctions

Picollo

Schindler

2017

Erkenn

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One of the main logical functions of the truth predicate is to enable us to express so-called 'infinite conjunctions'. Several authors claim that the truth predicate can serve this function only if it is fully disquotational (transparent), which leads to triviality in classical logic. As a consequence, many have concluded that classical logic should be rejected. The purpose of this paper is threefold. First, we consider two accounts available in the literature of what it means to express infinite conjunctions with a truth predicate and argue that they fail to support the necessity of transparency for that purpose. Second, we show that, with the aid of some regimentation, many expressive functions of the truth predicate can actually be performed using truth principles that are consistent in classical logic. Finally, we suggest a reconceptualisation of deflationism, according to which the principles that govern the use of the truth predicate in natural language are largely irrelevant for the question of what formal theory of truth we should adopt. Many philosophers think that the paradoxes pose a special problem for deflationists; we will argue, on the contrary, that deflationists are in a much better position to deal with the paradoxes than their opponents. The ProblemMany philosophers maintain that the truth predicate can serve certain expressive roles of a quasi-logical nature, the most salient of which is to enable us to express so-called 'infinite conjunctions'. These are sentences of the form All Ps are true.where P is a predicate of the language that applies to infinitely many sentences. 1They are considered to express the infinitely many Ps at once or, as is often said, their infinite conjunction, without turning to infinitary or higher-order resources (cf. Quine 1970;Leeds 1978;Putnam 1978; Horwich 1998;Field 2007).(The phrase 'expressing infinite conjunctions' is taken from the literature-e.g. Putnam 1978; Gupta 1993-and of course in need of clarification. For the moment, the reader should take it as a technical term.) We call this function of the truth predicate the 'infinite-conjunction' function.As Quine (1970, chap. 1) points out, the universal quantifier serves a similar purpose. If the infinitely many sentences we want to express differ in one or several individual terms-e.g. ''0 is divisible by 2'', ''2 is divisible by 2'', ''4 is divisible by 2'', etc.-and the class of objects these terms denote is definable in the language by a suitable predicate (e.g. ''is an even number''), we can express the infinitely many sentences at once just generalising over those terms using this predicate-e.g. uttering ''All even numbers are divisible by 2''. However, if the infinitely many sentences we want to express don't differ just in one or more individual terms, this strategy is no longer available. In that case, the truth predicate, interacting with the universal quantifier, might do the job, as long as the sentences at issue share a property definable in the language. For instance, we can assert al...

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What Theories of Truth Should be Like (but Cannot be)

Cited by 56 publications

References 31 publications

Sets and supersets

Sets and supersets

Unifying the Philosophy of Truth

Disquotation and Infinite Conjunctions

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