Talk:Strict conditional

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The article stated: "In logic, a strict conditional is a material conditional that is acted upon by the necessity operator from modal logic".

While that is one way to view it, it is contrary to the history.

C. I. Lewis' original modal logic systems had Possibly, not Necessity, as basic.

Lewis (like J. Barkley Rosser) defined material implication [ p implies q ] as ~(p&~q). (It is not the case that p is true and q otherwise). And he defined strict implication as ~M(p&~q) (It is not possible for p to be true and q otherwise).

So... I did a reword.

-- [[User:Nahaj] Nahaj 2005-08-25

[edit] Is the moon made of cheese?

I think that the example shown in this paper is slithgly misleading. The statement “the moon is made of cheese” used as the antecedent of all conditionals is typically false in all possible worlds that many are inclined to consider. While some people might believe that the moon is made of blue cheese, still this choice obscures the fact that strict conditionals can be used for facts that are assumed false but that would be more believable. For example, that the cervus elaphus canadensis is extinct is currently believed true, but yet one can consider the contrary as an actual possibility. I think that changing the antecedent to something that can be possible or not would improve the article. Suggestions? Comments? Paolo Liberatore (Talk) 18:58, 28 September 2005 (UTC)

Just a cultural note: I think possibly some subtle history is being missed here. When this issue was discussed after Principia Mathematica, by people that objected to the "material implication" given in it, "The moon is made of cheese" was the traditional example used in the discussions of what implication (or strict implication) should be. (And you see it sprinkled throughout papers in the early nineteen thirties.) Given some seventy years of tradition, I can fully understand why it was there. Nahaj 14:27, 27 October 2005 (UTC)

A question: what was the consequent used in the classical example? I mean, "if the moon is made of cheese then ..."? Paolo Liberatore (Talk) 20:05, 27 October 2005 (UTC)

To be honest, I don't remember. It would have to have been something true only by form. (It would not surprise me if it were 2+2=4). I'll be going back through some papers of the time next month, when I stumble over it I'll drop a note here. (: I assume you have a watch on the page. :) I think, by the way, that reading the papers of the time is a real eye opener on how far logic has come, and how the direction has changed. For example, Lewis' original papers on strict implication appeared mostly in "The Journal of Philosophy, Psychology, and Scientific Methods" and in "Mind; A quarterly review of Psychology and Philosophy", but most modern logicians probably don't consider Psychology the right forum. (And even as late as 1962 Anderson and Belnap's Journal of Symbolic Logic paper "A pure Calculus of Entailment" was funded in part by the [U.S.] office of Naval Research's Group Psychology branch. Nahaj 03:17, 28 October 2005 (UTC)

Not quite the reference you want... but close: "Implication and the Algebra of Logic" C. I. Lewis in Mind, New Series, Vol. 21, No. 84. (Oct., 1912), pp. 522-531. This is in a conjunction, making a point about implication. But, in 1912, it shows it was a standard example. (Nahaj)

Thanks for the reference. Yes, I have this page on my watchlist. Paolo Liberatore (Talk) 13:52, 28 October 2005 (UTC)

So far, what I've found is that around 1900 "The moon is made of green cheese" was the "canonical" example of a false statement, and used almost any time a false statement was needed for a discussion. The first use I can find of the use in the manner of the "Strict conditional" page example was in "On the Extension of the Common Logic", by Henry Bradford Smith in "The Journal of Philosophy, Psychology and Scientific Methods" Vol. 16, No. 14. (Jul. 3, 1919), and the consequent was "The angle-sum of a triangle equals two right angles". The consequent used varies over time and author, generally getting simpler over time. 2+2=4 starts appearing much much later. (And therefore probably can't be considered "classical" :) I assume that this answers your original question, and I'm not going to bother to research any further. Nahaj 16:50, 28 October 2005 (UTC)