Strict conditional: Difference between revisions

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In [[logic]], a '''strict conditional''' (symbol: <math>\Box</math>, or ⥽) is a conditional governed by a [[modal operator]], that is, a [[logical connective]] of [[modal logic]]. It is [[logical equivalence|logically equivalent]] to the [[material conditional]] of [[classical logic]], combined with the [[Logical truth|necessity]] operator from [[modal logic]]. For any two [[proposition]]s ''p'' and ''q'', the [[well-formed formula|formula]] ''p'' → ''q'' says that ''p'' [[material conditional|materially implies]] ''q'' while <math>\Box (p \rightarrow q)</math> says that ''p'' [[logical consequence|strictly implies]] ''q''.<ref>[[Graham Priest]], ''An Introduction to Non-Classical Logic: From if to is'', 2nd ed, Cambridge University Press, 2008, {{ISBN|0-521-85433-4}}, [https://books.google.com/books?id=rMXVbmAw3YwC&pg=PA72 p. 72.]</ref> Strict conditionals are the result of [[C. I. Lewis|Clarence Irving Lewis]]'s attempt to find a conditional for logic that can adequately express [[indicative conditional]]s in natural language.<ref>{{cite book|last1=Lewis|first1=C.I.|author1-link=ClarenceC. I. Lewis|last2=Langford|first2=C.H.|author2-link=Cooper Harold Langford|year=1959|orig-year=1932|title=Symbolic Logic|edition=2|publisher=[[Dover Publications]]|isbn=0-486-60170-6|page=124}}</ref><ref>Nicholas Bunnin and Jiyuan Yu (eds), ''The Blackwell Dictionary of Western Philosophy'', Wiley, 2004, {{ISBN|1-4051-0679-4}}, "strict implication," [https://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}}, [https://books.google.com/books?id=nQliRGPVpTwC&pg=PA127 p. 127–136].</ref>

==Avoiding paradoxes==