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Switch to: References
Citations of:
How to Ekman a Crabbé-Tennant
Synthese 199 (Suppl 3):617-639 (2018)
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For the past 40 years, Neil Tennant has defended a proof-theoretic criterion of self-referential paradoxicality. According to this criterion, the defining characteristic of paradoxes is that, when formulated within a natural deduction system, they produce derivations that cannot be normalized. This paper raises doubts about Tennant’s approach. Recently, Tennant has suggested that Russell’s paradox might not truly fit his criterion. I will argue that the reasoning that rules out Russell’s paradox can similarly be applied to some semantic paradoxes. Therefore, if (...) |
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We begin with a brief explanation of our proof-theoretic criterion of paradoxicality—its motivation, its methods, and its results so far. It is a proof-theoretic account of paradoxicality that can be given in addition to, or alongside, the more familiar semantic account of Kripke. It is a question for further research whether the two accounts agree in general on what is to count as a paradox. It is also a question for further research whether and, if so, how the so-called Ekman (...) |
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In this dissertation, we shall investigate whether Tennant's criterion for paradoxicality(TCP) can be a correct criterion for genuine paradoxes and whether the requirement of a normal derivation(RND) can be a proof-theoretic solution to the paradoxes. Tennant’s criterion has two types of counterexamples. The one is a case which raises the problem of overgeneration that TCP makes a paradoxical derivation non-paradoxical. The other is one which generates the problem of undergeneration that TCP renders a non-paradoxical derivation paradoxical. Chapter 2 deals with (...) |
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It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the same conclusion would have to be identified. In this paper it will be shown that the question, which reductions we accept in our system, is not only important if we see them as generating a theory of proof identity but is also (...) |
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In this autobiographical sketch, which is followed by a bibliography of my writings, I try to relate my intellectual development to problems, ideas and results in proof-theoretic semantics on which I have worked and to which I have contributed. |
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Dag Prawitz (1971) put forward the idea that an admissible reduction process does not affect the identity of proofs represented by derivations in natural deduction. The idea relies on his conjecture that two derivations represent the same proof if and only if they are equivalent in the sense that they are reflexive, transitive and symmetric closure of the immediate reducibility relation. Schroeder-Heister and Tranchini (2017) accept Prawitz’s conjecture and propose the triviality test as the criterion for admissible reductions. In the (...) |
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