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In [[logic]], a '''strict conditional''' is a [[materialmodal conditionaloperator]], that is, acteda upon[[logical byconnective]] of [[modal logic]]. It is [[logical equivalence|logical equivalent]] to the [[material conditional]] of classical logic, combined with the [[Logical truth|necessity]] operator from [[modal logic]]. For any two propositions[[proposition]]s <math>p</math> and <math>q</math>, the [[well-formed formula|formula]] <math>p \rightarrow q</math> says that <math>p</math> materially implies <math>q</math> while <math>\Box (p \rightarrow q)</math> says that <math>p</math> [[logical consequence|strictly implies]] <math>q</math>.<ref>Graham Priest, ''An Introduction to Non-Classical Logic: From if to is'', 2<sup>nd</sup> ed, Cambridge University Press, 2008, ISBN 0-521-85433-4, [http://books.google.com/books?id=rMXVbmAw3YwC&pg=PA72 p. 72.]</ref> Strict conditionals are the result of [[Clarence Irving Lewis]]'s attempt to find a conditional for logic that can adequately express [[indicative conditional]]s in natural language.<ref>Nicholas Bunnin and Jiyuan Yu (eds), ''The Blackwell Dictionary of Western Philosophy'', Wiley, 2004, ISBN 1-4051-0679-4, "strict implication," [http://books.google.com/books?id=OskKWI1YA7AC&pg=PA660 p. 660.]</ref> They have also been used in studying [[Molinism|Molinist]] theology.<ref>Jonathan L. Kvanvig, "Creation, Deliberation, and Molinism," in ''Destiny and Deliberation: Essays in Philosophical Theology'', Oxford University Press, 2011, ISBN 0-19-969657-8, [http://books.google.com/books?id=nQliRGPVpTwC&pg=PA127 p. 127–136.]</ref>
==Avoiding paradoxes==
==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 consequents[[consequent]]s that are [[Logical truth|necessarily true]] (such as 2 + 2 = 4) or antecedents that are necessarily false.<ref>Roy A. Sorensen, ''A Brief History of the Paradox: Philosophy and the labyrinths of the mind'', Oxford University Press, 2003, ISBN 0-19-515903-9, [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.
* [[Indicative conditional]]
* [[Material conditional]]
* [[Logical implicationconsequence]]
* [[Corresponding conditional]]
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