Pat Mefford’s Question about the Impossibility of the Contrary

Atheist Pat Mefford asked a strange question in the context of a discussion about the impossibility of the contrary. I would love to try and answer it. However, Pat is a smart guy, and I need him to dumb it down for me.

What if I insisted on a multi-value logic? Such as Kleene’s 3-valued logic that has a third value that is an intermediate between true and false?

Is Pat claiming A v ~A is false? Or that it is undefined? I’m not sure. Comments are welcome.



Maybe not that it’s false, or true, but something in between. Was this three value logic to be applied directly to the impossibility of the contrary? If so, how would that help the atheist view anyhow? Is it only because I’m stupid that a three value logic just makes things unintelligible to me in questions of truth or falsity?

B.C. Askins

Without more context its hard to know what he means, but Kleene’s ternary logic doesn’t have “an intermediate between true and false.” It contains a third value described as “undefined,” not “intermediate.” Insisting on such a logic would probably have zero net effect on a discussion of the IOC, but (as I said) without context it’s hard to know what’s going on. There are other multi-valued logics which propose “truth degrees” (between false(0) and true(1)) but I don’t think Kleene’s system (referring to partial recursive function contexts) falls into that category. Two cents…

Patrick Mefford

Hi Chris,

A multi-value logic is looking to assign values to a statement beyond just true or false. For example the proposition “Chris will go to Church on Sunday or he will not go to Church on Sunday” is a true proposition. I don’t have a problem with this but someone who is a presentist (like William Lane Craig) who thinks that only the present is real will have concerns that there is no truth maker in the future that assigns value to either side of the disjunction (because the future doesn’t exist) and so the proposition is neither false nor true, it is indeterminate.

The strategy behind multi-value logics is going to different for each, so the other values are going to range from indeterminate, paradoxical, meaningless, as third values, or there could be six values with three different strengths of “true” and three different strengths of “false”.

C.L. Bolt

Thanks for this Pat. When I get some spare time I will attempt a response.

[BLOCKED BY STBV] The Liar Paradox and Presuppositional Apologetics « B.C. Askins

[…] of VanTilian Presuppositional (sometimes voguely referred to as Covenantal) Apologetics. Chris asked Pat for clarification, then responded here and here. Pat raises the “Liar Paradox” as an objection to Chris’ […]

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