Strict conditional: Difference between revisions

Revision as of 14:29, 14 January 2012

Revision as of 00:28, 15 January 2012

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==Problems==

Although the strict conditional is much closer to being able to express natural language conditionals than the material conditional, it has its own problems with antecedents that are necessarily true (such as 2 + 2 = 4) or necessarily false.<ref>Roy A. Sorensen, ''A Brief History of the Paradox: Philosophy and the labyrinths of the mind'', Oxford University Press, 2003, ISBN 0195159039, [http://books.google.com/books?id=PB8I0kHeKy4C&pg=PA105 p. 105.]</ref> The following sentence, for example, is not correctly formalized by a strict conditional:

: If Bill Gates graduated in Medicine, then 2 + 2 = 4.

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: <math>\Box</math> (Bill Gates graduated in Medicine <math>\rightarrow</math> 2 + 2 = 4)

In modal logic, this formula means that, in every possible world where Bill Gates graduated in medicine, it holds that 2 + 2 = 4. Since 2 + 2 is equal to 4 in all possible worlds, this formula is true, although it does not seem that the original sentence should be. Similarly,A problemssimilar cansituation arisearises with antecedents2 that+ are2 necessarily true or false.<ref>Roy A.= Sorensen5, ''Awhich Briefis Historynecessarily of the Paradox: Philosophy and the labyrinths of the mind'', Oxford University Press, 2003, ISBN 0195159039, [http://books.google.com/books?id=PB8I0kHeKy4C&pg=PA105 p. 105.]</ref> A similar situation arises withfalse:

: If 2 + 2 = 5, then Bill Gates graduated in Medicine.