Disjunction and disjunctive syllogism

Canadian Journal of Philosophy

Volumn 28, Issue 1, 1998, Pages 21-32

  Milne, Peter ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 52849132052     PISSN: 00455091     EISSN: 19110820     Source Type: Journal    
DOI: 10.1080/00455091.1998.10715969     Document Type: Article

References (15)

1. 1962. Formale Logik 237–8. The Lewis argument might better be attributed to Albert of Saxony, who had it in all essentials some six centuries before Lewis, or perhaps to William of Soissons in the twelfth century. For the former see, e.g., J.M. Bochenski, second edition (Freiburg and Munich: Karl Alber for the latter, Christopher Martin, ‘William's Machine,’ Journal of Philosophy83 (1986) 564–72 (I owe this reference to Stephen Read).
2. 1992. Logic Primer Cambridge, Ma: The MIT Press. Colin Allen and Michael Hand, xii and 18–19
3. Prawitz, Dag. 1977. ‘Meaning and Proofs: On the Conflict between Classical and Intuitionist Logic,’. Theoria, 43: 2–40. See and ‘Proofs and the Meaning and Completeness of the Logical Constants,’ in J. Hintikka, I. Niiniluoto, and E. Saarinen, Essays on Mathematical and Philosophical Logic (Dordrecht: Reidel 1979) 25–40.
4. In order to read DS as a rule not just in which negation is eliminated but giving the meaning of negation one has to take it that not a single inference but the totality of instances of DS in which it occurs go to fix the meaning of a negated proposition: i.e., what fixes the meaning of −A is that, for every sentence B, −A and AvB suffice to yield B (as do −A and B v A).
5. Belnap, Nuel. 1962. ‘Tonk, Plonk and Plink,’. Analysis, 22: 130–4. reprinted in P.F. Strawson, Philosophical Logic (Oxford: Oxford University Press 1967) 132–7
6. Read, Stephen. 1988. Relevant Logic 31–4. Oxford: Blackwell. and Thinking About Logic (Oxford: Oxford University Press 1994), 60, 160, 163
7. Dummett, Michael. 1990. “ ‘The Source of the Concept of Truth,’ in ”. In Meaning and Method: Essays in Honor of Hilary Putnam Edited by: Boolos, George. 1–15. Cambridge: Cambridge University Press. at 7–8
8. Dummett, Michael. 1991. The Logical Basis of Metaphysics 256London: Duckworth. It should perhaps be noted that Dummett does describe DS as a fundamental form of argument, The Logical Basis, 293.
9. Dummett. ‘The Source,’ 7–8
10. Milne, Peter. 1994. ‘Classical Harmony: Rules of Inference and the Meaning of the Logical Constants,’. Synthese, 100: 49–94. See at 90, n. 31, for a proof that a conditional containing the Sasaki hook is locally weakest in the sense given in the text. As is well known, adding an intuitionist conditional to quantum logic collapses it to classical logic.
11. Tennant, Neil. 1990. Natural Logic Edinburgh: Edinburgh University Press. second edition
12. Milne. ‘Classical Harmony,’ 76
13. I mean this comparison of strength quite strictly, so that, for example, logics that contain DNE but lack other principles of intuitionist logic and may therefore intuitively be regarded as quite weak are neither stronger nor weaker than intuitionist logic. One is, of course, entitled to view the absence of DNE as a weakness of intuitionist logic. Discussion with Stephen Read prompted this footnote.
14. Read. Thinking about Logic 60
15. + , Segerberg's JX, rather than intuitionist logic, would have played a much more prominent role here had Allen and Hand chosen +-introduction and orthodox v-elimination as the rules governing their disjunction, admittedly a most unlikely event.