14 research outputs found

    Conjunctive paraconsistency

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    Predicativity, the Russell-Myhill Paradox, and Church's Intensional Logic

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    This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church's intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms of Church's intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin's intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions.Comment: Forthcoming in The Journal of Philosophical Logi

    The Necessity of Mathematics

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    Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role

    Fixed-point models for paradoxical predicates

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    This paper introduces a new kind of fixed-point semantics, filling a gap within approaches to Liar-like paradoxes involving fixed-point models 脿 la Kripke (1975). The four-valued models presented below, (i) unlike the three-valued, consistent fixed-point models defined in Kripke (1975), are able to differentiate between paradoxical and pathological-but-unparadoxical sentences, and (ii) unlike the four-valued, paraconsistent fixed-point models first studied in Visser (1984) and Woodruff (1984), preserve consistency and groundedness of truth. Keywords:聽 Semantic Paradoxes 路 Fixed-point semantics 路 Many-valued logic 路 Kripke鈥檚 theory oftrut

    Fixed-point models for paradoxical predicates

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    This paper introduces a new kind of fixed-point semantics, filling a gap within approaches to Liar-like paradoxes involving fixed-point models 脿 la Kripke (1975). The four-valued models presented below, (i) unlike the three-valued, consistent fixed-point models defined in Kripke (1975), are able to differentiate between paradoxical and pathological-but-unparadoxical sentences, and (ii) unlike the four-valued, paraconsistent fixed-point models first studied in Visser (1984) and Woodruff (1984), preserve consistency and groundedness of truth. Keywords:聽 Semantic Paradoxes 路 Fixed-point semantics 路 Many-valued logic 路 Kripke鈥檚 theory oftrut

    Revenge: dialetheism and its expressive limitations

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    This thesis is about dialetheism and the problem of revenge. More broadly, it is about truth and what the logical paradoxes tell us about the logical behaviour of truth. One of the driving forces behind the contemporary study of truth and paradox is the problem of revenge: that many, perhaps all, available theories of truth, give rise to further paradoxes, invoking central notions of those theories, which demonstrate that the theory cannot express those notions. This sort of expressive limitation, especially if it involves the very notion invoked to diagnose what goes wrong in paradoxical sentences, would normally be thought a decisive point against a given theory of the paradoxes, were it not for the fact that the problem is so pervasive that every currently available theory has, at some point, been argued to suffer from it. Dialetheism, the view that some contradictions are true, has often been thought to be the only view which has a reasonable chance of avoiding the problem. Indeed, the surge of interest in the view since the first publication of Priest鈥檚 In Contradiction, in 1987, defending dialetheism, is probably due in large part to the seeming immunity to the revenge problem that Priest鈥檚 view possesses. Its virtue, in respect of revenge, is that its ability to accept, without collapse into incoherence, contradictions, allows it to accept any further revenge paradoxes as merely giving more sound arguments for dialetheia (true contradictions). This thesis argues that this appearance of revenge-immunity is mistaken. Dialetheism, too, has its revenge problems. The seeming virtue of dialetheism, that it can accept the contradictions generated by revenge paradoxes without incoherence, also has its drawbacks. This is because dialetheists are not only able, but compelled to accept the contradictions arising from the semantic paradoxes. This means that contradictions can arise in certain areas where they are undesirable. In particular, there are notions which seem to require consistency in order to be expressible. If we can demonstrate, using revenge paradoxes, that, on dialetheism, predicates putatively representing these notions would have to behave inconsistently, then we can demonstrate that dialetheists cannot express the notions. There are many ways one might wish to carve up the different varieties of dialetheism available. I have separated the view into two broad kinds: metatheoretically paraconsistent dialetheism, on the one hand, and metatheoretically consistent dialetheism, on the other. This distinction decides to which variety of revenge problem the version of dialetheism in question is subject. I take each in turn, and argue that they are each subject to expressive limitations brought about by revenge paradox

    Quantification and Paradox

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    I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected

    Quantifica莽茫o

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    O presente artigo tem como objetivo realizar uma introdu莽茫o geral ao t贸pico da quantifica莽茫o em linguagens formais e, especialmente, na l贸gica de predicados. Ele est谩 dividido em duas partes. Na primeira parte, apresento a sintaxe e a sem芒ntica dos quantificadores para a l贸gica de predicados. Na segunda parte, apresento um panorama de alguns dos principais problemas de ordem l贸gica e/ou filos贸fica envolvendo quantificadores, tais como a distin莽茫o entre interpreta莽玫es objetual e substitucional dos quantificadores, a abordagem quantificacional da no莽茫o de exist锚ncia, os crit茅rios quineanos de compromisso ontol贸gico e o problema da quantifica莽茫o irrestrita.This paper aims to provide a general introduction to the subject of quantification in formal languages and mainly in predicate logic. It is divided into two parts. The first one presents the syntax and semantics of the quantifiers for predicate logic. The second part offers an overview on some of the major problems of logical and/or philosophical order involving quantifiers, such as the distinction between objectual and substitutional interpretation of the quantifiers, the quantificational approach to the notion of existence, the Quinean criteria of ontological commitment, and the problem of unrestricted quantification.Funda莽茫o para a Ci锚ncia e a Tecnologiainfo:eu-repo/semantics/publishedVersio

    Replacing truth

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    Kevin Scharp proposes an original account of the nature and logic of truth, on which truth is an inconsistent concept that should be replaced for certain theoretical purposes. He argues that truth is best understood as an inconsistent concept; develops an axiomatic theory of truth; and offers a new kind of possible-worlds semantics for this theory
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