*Moritz Schulz*

- Published in print:
- 2017
- Published Online:
- March 2017
- ISBN:
- 9780198785958
- eISBN:
- 9780191831713
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198785958.003.0008
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The chapter discusses how one can escape Lewis-style triviality results for counterfactuals on the epsilon-based semantics described in chapter 6. Starting with D. Lewis’s positive observation on ...
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The chapter discusses how one can escape Lewis-style triviality results for counterfactuals on the epsilon-based semantics described in chapter 6. Starting with D. Lewis’s positive observation on imaging, the results by R. Wiliams and H. Leitgeb are discussed.Less

The chapter discusses how one can escape Lewis-style triviality results for counterfactuals on the epsilon-based semantics described in chapter 6. Starting with D. Lewis’s positive observation on imaging, the results by R. Wiliams and H. Leitgeb are discussed.

*Neil Tennant*

- Published in print:
- 2017
- Published Online:
- October 2017
- ISBN:
- 9780198777892
- eISBN:
- 9780191823367
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198777892.003.0010
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Ironically Anderson and Belnap argue for the rejection of Disjunctive Syllogism by means of an argument that appears to employ it. We aim to establish a ‘variable-sharing’ result for Classical Core ...
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Ironically Anderson and Belnap argue for the rejection of Disjunctive Syllogism by means of an argument that appears to employ it. We aim to establish a ‘variable-sharing’ result for Classical Core Logic that is stronger than any such result for any other system. We define an exigent relevance condition R(X,A) on the premise-set X and the conclusion A of any proof, exploiting positive and negative occurrences of subformulae. This treatment includes first-order proofs. Our main result on relevance is that for every proof of A from X in Classical Core Logic, we have R(X,A). R(X,A) is a best possible explication of the sought notion of relevance. Our result is optimal, and challenges relevantists in the Anderson–Belnap tradition to identify any strengthening of the relation R(X,A) that can be shown to hold for some subsystem of Anderson–Belnap R but that can be shown to fail for Classical Core Logic.Less

Ironically Anderson and Belnap argue for the rejection of Disjunctive Syllogism by means of an argument that appears to employ it. We aim to establish a ‘variable-sharing’ result for Classical Core Logic that is stronger than any such result for any other system. We define an exigent relevance condition R(X,A) on the premise-set X and the conclusion A of any proof, exploiting positive and negative occurrences of subformulae. This treatment includes first-order proofs. Our main result on relevance is that for every proof of A from X in Classical Core Logic, we have R(X,A). R(X,A) is a best possible explication of the sought notion of relevance. Our result is optimal, and challenges relevantists in the Anderson–Belnap tradition to identify any strengthening of the relation R(X,A) that can be shown to hold for some subsystem of Anderson–Belnap **R** but that can be shown to fail for Classical Core Logic.