The Semantic Paradoxes: A Diagnostic Investigation

Chihara, Charles S.

doi:10.2307/2184846

Cited by 136 publications

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“…This contrasts with views on which our competence with Btrue^consists in cognizing the kind of highly complex theories proposed as solutions to the Liar, or in a corresponding set of dispositions (see, e.g. Chihara (1979)). As we will see, however, not all facts about our reactions to the paradoxes have obvious explanations.…”

Section: Accounting For the Acceptance Facts Related To The Paradoxesmentioning

confidence: 87%

“…Still, I know of no argument against it. By contrast, Chihara (1979) and Eklund (2002a) have adduced rather clear and simple arguments in its favour. Also, it seems odd to me that meaning-constitutivity, in the present sense, should entail truth, whether conceptually or metaphysically; truth and meaning-constitutivity in this sense are, after all, rather different properties.…”

Section: Objections Relating To Meaning-constitutivitymentioning

confidence: 99%

“…I: 12), Chihara (1979Chihara ( , 1984, Yablo (1993), Barker (1998), Burgess (2002), Eklund (2002a, b), Ludwig (2002), Azzouni (2003Azzouni ( , 2006Azzouni ( , 2007Azzouni ( , 2013, Patterson (2007a, b, 2009), and Scharp (2007, 2013a.…”

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Trivial Languages

Båve

2017

Acta Anal

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I here present and defend what I call the Triviality Theory of Truth (TT), to be understood in analogy with Matti Eklund's Inconsistency Theory of Truth (IT). A specific formulation of (TT) is defended and compared with alternatives found in the literature. A number of objections against the proposed notion of meaningconstitutivity are discussed and held inconclusive. The main focus, however, is on the problem, discussed at length by Gupta and Belnap, that speakers do not accept epistemically neutral conclusions of Curry derivations. I first argue that the facts about speakers' reactions to such Curry derivations do not constitute a problem for (TT) specifically. Rather, they follow from independent, uncontroversial facts. I then propose a solution which coheres with (TT) as I understand it. Finally, I consider a normative reading of their objection and offer a response.The idea that the Liar paradox shows that Bour language is inconsistent^, what is now called the Inconsistency Theory of Truth (IT), goes back at least to Tarski. 1 How exactly to understand the idea that our language is inconsistent is a matter of ongoing debate. I will here expound what I take to be the best rendering of this phrase, by which I mean least contentious explication, which nevertheless captures most of what its adherents take it to involve. However, it is not (IT), but the related Triviality Theory of Truth (TT) that will be the main focus of this paper. As we will see, this theory raises some new questions and has been questioned on grounds irrelevant to (IT). In a nutshell, (TT) says of Curry's paradox (and of the Liar paradox plus ex contradictione quodlibet) what (IT) says about the Liar, namely, that the principles used in the respective paradoxical derivations are

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Section: Accounting For the Acceptance Facts Related To The Paradoxesmentioning

confidence: 87%

Section: Objections Relating To Meaning-constitutivitymentioning

confidence: 99%

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Trivial Languages

Båve

2017

Acta Anal

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“…This opens a broader issue, to what extent standard logic, and predicative language based on it, are able to provide a consistent conceptual system-the so called inconsistency theory of truth [16,17]. The topic is different from the issues generated by Godel's second theorem since it is not just about the lack of completeness proof, and its impossibility.…”

Section: Ontological Implications Of Metacomputable Revisitedmentioning

confidence: 99%

Metacomputable

Bołtuć

2017

Entropy

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Abstract:The paper introduces the notion of "metacomputable" processes as those which are the product of computable processes. This notion seems interesting in the instance when metacomputable processes may not be computable themselves, but are produced by computable ones. The notion of computability used here relies on Turing computability. When we talk about something being non-computable, this can be viewed as computation that incorporates Turing's oracle, maybe a true randomizer (perhaps a quantum one). The notions of "processes" is used broadly, so that it also covers "objects" under the functional description; for the sake of this paper an object is seen as computable if processes that fully describe relevant aspects of its functioning are computable. The paper also introduces a distinction between phenomenal content and the epistemic subject which holds that content. The distinction provides an application of the notion of the metacomputable. In accordance with the functional definition of computable objects, sketched out above, it is possible to think of objects, such as brains, as being computable. If we take the functionality of brains relevant for consideration to be their supposed ability to generate first-person consciousness, and if they were computable in this regard, it would mean that brains, as generators of consciousness, could be described, straightforwardly, by Turing-computable mathematical functions. If there were other, maybe artificial, generators of first-person consciousness, then we could hope to design those as Turing-computable machines as well. However, thinking of such generators of consciousness as computable does not preclude the stream of consciousness being non-computable. This is the main point of this article-computable processes, including functionally described machines, may be able to generate incomputable products. Those processes, while not computable, are metacomputable-by regulative definition introduced in this article. Another example of a metacomputable process that is not also computable would be a true randomizer, if we were able to build one. Presumably, it would be built according to a computable design, e.g., by a machine designed using AutoCAD, that could be programmed into an industrial robot. Yet, its product-a perfect randomizer-would be incomputable. The last point I need to make belongs to ontology in the theory of computability. The claim that computable objects, or processes, may produce incomputable ones does not commit us to what I call computational monism-the idea that non-computable processes may, strictly speaking, be transformed into computable ones. Metacomputable objects, or processes, may originate from computable systems (systems will be understood here as complex, structured objects or processes) that have non-computable admixtures. Such processes are computable as long as those non-computable admixtures are latent, or otherwise irrelevant for a given functionality, and they are non-computable if the admixtures become active and relevant. O...

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“…Recent work in the theory of truth has worked to make the distinction between these perspectives clearer (Eklund, 2002;Azzouni, 2007;Patterson, 2006;Chihara, 1979). However, it is also possible to discern a similar thread in Tarski's (1944).…”

Section: Infmentioning

confidence: 99%

Naive Infinitism: The Case for an Inconsistency Approach to Infinite Collections

Meadows¹

2015

Notre Dame J. Formal Logic

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ABSTRACT. This paper expands upon a way in which we might rationally doubt that there are multiple sizes of infinity. The argument draws its inspiration from recent work in the philosophy of truth and philosophy of set theory. More specifically, elements of contextualist theories of truth and multiverse accounts of set theory are brought together in an effort make sense of Cantor's troubling theorem. The resultant theory provides an alternative philosophical perspective on the transfinite, but has limited impact on everyday mathematical practice.This relativity of cardinalities is very striking evidence of how far abstract formalistic set theory is removed from all that is intuitive.One can indeed construct systems that faithfully represent set theory down to the last detail. But as soon as one applies the finer instruments of investigation all this fades away to nothing. Of all the cardinalities only the finite ones and the denumerable one remain. Only these have real meaning; every thing else is formalistic fiction. (von Neumann, 1967) The aim of this paper is to take seriously the idea that we have, in some sense, misunderstood the message of Cantor's theorem; or at the least, that in hindsight we have driven headlong into the transfinite when we could have paused a moment longer to consider an alternative. My goal is to demonstrate that Cantor's theorem can be understood more like the liar paradox, as a kind of fork in the road. The crucial idea is that, in admitting there are multiple sizes of infinity, we have done irreparable damage to our naïve conception of the infinite. My goal in this paper is to demonstrate that we may coherently reject the multiplicity of infinite cardinalities and to illustrate the value of this perspective. (Hodges, 1998). This paper is not intended as a contribution to that corpus. My contention is that actually, it is not so difficult to make intelligible something like the view suggested above. The difficulty, rather, lies in showing that it is interesting.The paper is broken into three main sections: the Setup; the Case of the Missing Bijection;and Problems. The first section dominates the paper. The goal here is to lay out the problem as clearly as possible. We articulate the problem in two passes. The first pass formulates a version of Cantor's theorem from a pre-set-theoretic framework, after which we initiate discussion as to its interpretation. We then introduce and formulate an analogy between Cantor's theorem and the liar paradox. In the second pass, we take up a version of third order arithmetic and from there argue that like the liar paradox, we may consider Cantor's theorem as presenting us with a fork in the philosophical road. In the second section, we discuss a problem opened in the first section. We sketch a response to it which sheds some light on a possible link between contemporary contextualist accounts of truth and multiverse approaches to set theory. Finally, we address some of obvious problems for the view proposed. THE SETUPLet us suppose, for the sak...

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The Semantic Paradoxes: A Diagnostic Investigation

Cited by 136 publications

References 0 publications

Trivial Languages

Trivial Languages

Metacomputable

Naive Infinitism: The Case for an Inconsistency Approach to Infinite Collections

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