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Sets, lies, and analogy: a new methodological take

Giulia Terzian
2020 Philosophical Studies  
The starting point of this paper is a claim defended most famously by Graham Priest: that given certain observed similarities between the set-theoretic and the semantic paradoxes, we should be looking  ...  on the one hand, and the use of inter-theoretic analogies on the other.  ...  , criterion of 'success' of a set-theoretic account (ditto for an account of truth, knowledge, social preferences, etc.).  ... 
doi:10.1007/s11098-020-01579-9 fatcat:icz7iuvlibexra2c3mjyran5vm

Indefinite Extensibility in Natural Language

Laureano Luna, Sherwood J. B. Sugden
2013 The Monist  
We also point out that object-object mapping theories of semantics, the usual account for the possibility of non intentional semantics, doesn't seem able to account for the indefinitely extensible productivity  ...  We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal  ...  In order to prove the proposition in the title we first introduce some definitions.  ... 
doi:10.5840/monist201396211 fatcat:4c6oowi6hbfvvg2oc7yfpezebi

Worlds and Propositions Set Free

Otávio Bueno, Christopher Menzel, Edward N. Zalta
2013 Erkenntnis: An International Journal of Scientific Philosophy  
The authors provide an object-theoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan.  ...  Next the authors show that an object-theoretic analysis of the Kaplan paradox reveals that there is no genuine paradox at all, as the central premise of the paradox is simply a logical falsehood and hence  ...  Without invoking sets, object theory offers an integrated account of worlds and propositions that assigns them clear existence and identity conditions without any threat of paradox.  ... 
doi:10.1007/s10670-013-9565-x fatcat:at5ltsh4jbaz7gwht2bd36aryu

Categorical Harmony and Paradoxes in Proof-Theoretic Semantics [chapter]

Yoshihiro Maruyama
2015 Advances in Proof-Theoretic Semantics  
Prooftheoretic semantics is a semantic enterprise to articulate an inferentialist account of the meaning of logical constants and inferences within the proof-theoretic tradition of Gentzen, Prawitz, and  ...  The present paper aims at contributing to developments of categorical proof-theoretic semantics, proposing the principle of categorical harmony, and thereby shedding structural light on Prior's "tonk"  ...  Acknowledgments I would like to thank Peter Schroeder-Heister for fruitful discussions in Oxford in spring 2012, which, inter alia, led to the table of degrees of paradoxicality of logical constants.  ... 
doi:10.1007/978-3-319-22686-6_6 fatcat:mzlptyfx7nddjalkuakf4bv4pi

A Yabloesque paradox in epistemic game theory

Can Başkent
2016 Synthese  
The Brandenburger-Keisler paradox is a self-referential paradox in epistemic game theory which can be viewed as a two-person version of Russell's Paradox.  ...  This paper gives a Yabloesque, non-self-referential paradox for infinitary players within the context of epistemic game theory.  ...  I acknowledge the constructive comments of the referees which helped improve the paper.  ... 
doi:10.1007/s11229-016-1231-9 fatcat:c73hhz6qpbfh3lxerzoqotdqbq

The "Villain" of Set Theory [review of Shaughan Levine, Understanding the Infinite]

Gary N. Curtis
1995 Russell: the Journal of Bertrand Russell Studies  
For instance, Cantor's initial response to the set-theoretic paradoxes is ad hoc (pp. 55-6) ..  ...  The problem for the interpretation of set theory is to find some principled way to delimit the collections so that no paradoxes resulc.  ... 
doi:10.15173/russell.v15i1.1882 fatcat:ydck6zujhrezlmcy2wxzvcwesu

A Note on Gabriel Uzquiano's "Varieties of Indefinite Extensibility"

Simon Hewitt
2018 Notre Dame Journal of Formal Logic  
♦φ tells us that φ is true on some subsequent reinterpretation of the set-theoretic vocabulary -while φ tells us that φ remains true on all subsequent reinterpretations of the set-theoretic vocabulary.  ...  A NOTE ON GABRIEL UZQUIANO'S 'VARIETIES OF INDEFINITE EXTENSIBILITY' SIMON HEWITT 1 Following Dummett, a number of philosophers have responded to the set-theoretic paradoxes by claiming that the concept  ... 
doi:10.1215/00294527-2018-0005 fatcat:nz2vkw2i2rbvldwjz47dtumq7e

A note on Horwich's notion of grounding

Thomas Schindler
2018 Synthese  
Horwich (Deflationism and paradox, Oxford University Press, Oxford, pp 75-84, 2005) proposes a solution to the liar paradox that relies on a particular notion of grounding-one that, unlike Kripke's (J  ...  Philos 72:690-716, 1975) notion of grounding, does not invoke any "Tarski-style compositional principles".  ...  This work was supported by the German Research Foundation (DFG, "Reference Patterns of Paradox") and was written while the author held a Junior Research Fellowship by Clare College, University of Cambridge  ... 
doi:10.1007/s11229-018-1780-1 fatcat:5w2ek7vja5hrta4il24kvuhgei

Revamping Hypothetico-Deductivism: A Dialectic Account of Confirmation

Gregor Betz
2012 Erkenntnis: An International Journal of Scientific Philosophy  
We use recently developed approaches in argumentation theory in order to revamp the hypothetico-deductive model of confirmation, thus alleviating the well-known paradoxes the H-D account faces.  ...  Dialectic confirmation generalises hypothetico-deductive confirmation and mitigates the raven paradox, the grue paradox, the tacking paradox, the paradox from conceptual difference, and the problem of  ...  In order to solve the paradox from conceptual difference, we will show that, according to the dialectic account, H 1 is confirmed by the piece of evidence e although H 1 doesn't imply e.  ... 
doi:10.1007/s10670-012-9406-3 fatcat:55q3zp4x55anrglzxafgmkrcmq

A paradox about sets of properties

Nathan Salmón
2021 Synthese  
Despite appearances Ex is not a truth of logic. 11 However, Ex is a trivial set-theoretic consequence (via Separation) of the apparent truism that every property is an element of some set or other.  ...  A Family of Paradoxes The paradox of property sets belongs to a broad Russellian family of paradoxes, which includes both set-theoretic paradoxes and semantic paradoxes.  ... 
doi:10.1007/s11229-021-03353-8 fatcat:ggfauxkrdzd55b6iabbwosax6e

On Putnam and His Models

Timothy Bays
2001 Journal of Philosophy  
To use Putnam's terminology, the paradox shows that it is impossible to pin down the "intended interpretation" of set-theoretic language using only (first-order) axioms.  ...  of set-theoretic sentences.  ...  That is, for some formula in the language of set theory, φ(x, y 1 , . . . , yn), and some sequence, a 1 , . . . , an, of sets, we can consider the class of all sets b such that φ(b, a 1 , . . . , an) is  ... 
doi:10.2307/2678439 fatcat:3c6eo5mm7rdnjoj2smia7epbbm

A New Unified Account of Truth and Paradox

N. Tennant
2015 Mind  
Some (more finely) tuned proof-theoretical ideas Complementing the proof-theoretic account of paradox is the prooftheoretically motivated account I have offered of how to relevantize proofs (including  ...  in order to handle (or avoid) the problem of paradox.  ...  to undertake whatever rational revision of one's beliefs might be called for. 9  ... 
doi:10.1093/mind/fzu179 fatcat:dlf6xksza5dpdhqlr3vnylljre

Skolem's Paradox and Platonism

Carlo Cellucci
1970 Crítica. Revista Hispanoamericana de Filosofía  
The thesis that Skolem's paradox necessarily implies that all set theoretic notions are relative is justified only on the basis of an abstract conceptionof mathematics rejecting the existence of an intuitive  ...  He appeared to take no account of the relativity of set-theoretical concepts pointed out by Skolem [. . .] , assuming that such concepts as sum set, power set, cardinal number, etc., had an absolute significance  ... 
doi:10.22201/iifs.18704905e.1970.88 fatcat:v24vcvnt75dejhzawdtjn63fuu

Book reviews

Justin Leiber, Robert M. French, John A. Barnden, Syed S. Ali, Richard Wyatt, Timothy R. Colburn, Brian Harvey, Norman R. Gall, Susan G. Josephson, Francesco Orilia, Achille C. Varzi
1996 Minds and Machines  
We think that this hope is fully justified, although some problems remain that future research in this field should take into account.  ...  The following assumptions constitute the typical background in which the truth paradoxes arise: (i) classical first-order logic, (ii) a language allowing for self-reference, and (iii) the "semantic" Tarskian  ...  In order to use M to interpret L + , we start from an arbitrary hypothesis concerning the interpretation of the new predicates and set off a revision process in an attempt to interpret each of them as  ... 
doi:10.1007/bf00388919 fatcat:rm6dbfpu55etrnox6bpo6iswbe

Page 8370 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
And the formal structure of the paradox of the largest cardinal is the same as that of the antinomy of infinite number, which he formulated some two years earlier, in 1899.  ...  in descriptive set theory. (3) As metamath- ematical methods became incorporated into mathematics, they led not only to extra-theoretic closure results about earlier problems but also to intra-theoretic  ... 
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