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Klement, Kevin C.

doi:10.1023/a:1022619903237

Cited by 10 publications

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References 17 publications

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“…For a discussion of several responses to these and related problems, seeKlement (2002, ch. 7) and(2003a).…”

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Grundgesetze and the Sense/Reference Distinction

Klement¹

2019

Essays on Frege's Basic Laws of Arithmetic

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Frege developed the theory of sense and reference while composing his Grundgesetze and considering its philosophical implications. The Grundgesetze is thus the most important test case for the application of this theory of meaning. I argue that evidence internal and external to the Grundgesetze suggests that he thought of senses as having a structure isomorphic to the Grundgesetze expressions that would be used to express them, which entails a theory about the identity conditions of senses that is relatively fine-grained, though still coarser than some other commentators have suggested. While this interpretation does not make Frege’s ontological commitment to the denizens of a “third realm” as profligate as some have alleged, it is sufficiently bloated to lead to Cantorian paradoxes and diagonal contradictions independent of his Basic Law V.

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“…For a discussion of several responses to these and related problems, seeKlement (2002, ch. 7) and(2003a).…”

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confidence: 99%

Grundgesetze and the Sense/Reference Distinction

Klement¹

2019

Essays on Frege's Basic Laws of Arithmetic

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“…In some of my recent work, I have attempted to highlight all the possible ways someone with broadly Fregean commitments could escape from such paradoxes (Klement 2002(Klement , 2003. With regard to the particular Cantorian construction sketched above, the most initially promising responses would be (1) denying there is any such concept as O¢, (2) denying that there is any sense O¢* presenting the concept O¢ (since, if there is no such sense, there can be no thoughts about O¢), (3) denying that the concept O¢ is the only concept that the thought that everything is O¢ generalizes over, and (4) denying that the thought that everything is O¢ is of the appropriate logical type for the question as to whether it falls under O¢ to be meaningful.…”

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Does Frege have too many thoughts? A Cantorian problem revisited

Klement¹

2005

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standard probabilistic practice of saying that E provides evidence for H just in case P(H|E) > P(H).) Whether one's resulting credence in the theory of quantum mechanics would be so low that one would reject quantum mechanics would depend on details like one's prior probability for Theory X. Even with a probability shift in favour of Theory X, one's credences could still be such that quantum mechanics is judged vastly more probable than Theory X.Just as the observation of the decay can provide evidence for Theory X and against quantum mechanics, the observation that we are in a small civilization can provide evidence for or against various physical theories. For example, consider Theory Y, which predicts that all civilizations are small. The fact that our civilization is small could constitute evidence in favour of Theory Y and against inflationary theory. But depending on such factors as one's prior probability for Theory Y, one's credences could still be such that inflationary theory is judged vastly more probable than Theory Y. Thus, that our civilization is small could lead one to decrease one's credence in inflationary theory, but nevertheless that credence could still be high.The issue we are discussing in the previous paragraph is a general issue about theory comparison in science; if that is the core of Olum's paper then there is nothing surprising here. It would be surprising if there were a conflict between anthropic reasoning and observation, but Olum's argument fails to show that this is the case.

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

Walsh

2015

J Philos 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.

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Cited by 10 publications

References 17 publications

Grundgesetze and the Sense/Reference Distinction

Grundgesetze and the Sense/Reference Distinction

Does Frege have too many thoughts? A Cantorian problem revisited

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

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