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*To*: "The Van Til List" <vantil-list@XC.Org>*Subject*: Re: Logical formalisms*From*: David Byron <david.byron@aya.yale.edu>*Date*: Thu, 29 Jul 1999 06:25:11 -0400*In-Reply-To*: <LYR231513-27561-1999.07.29-01.40.43--david.byron#yale.edu@XC.Org>*References*: <LYR230528-27022-1999.07.28-19.13.07--jamesanderson#xc.org@XC.Org><LYR231513-26955-1999.07.28-18.01.52--david.byron#yale.edu@ XC.Org>*Reply-To*: "The Van Til List" <vantil-list@XC.Org>

At 04:40 AM 7/29/99 , James Anderson wrote: >On 28 Jul 99, at 22:13, David Byron wrote: > >> In classical logic, presuppositions are trivial and wimpy. > >I'm sure I ought to know this by now, but -- why is this so? Consider the following: A presupposes B if and only if [a] B is true whenever A is true and [b] B is true whenever A is false According to this definition, B must be true for A to have any truthvalue at all. An instance of this relationship might go this way: The proposition A{"Euclid stopped beating his wife a month ago"} cannot be valuated as true unless Euclid had a wife and had been beating her. But it also cannot be valuated as false unless Euclid had a wife and had been beating her (and had not yet stopped!). So, the possibility of truthvaluating A{"Euclid stopped beating his wife a month ago"} depends on the truth of the proposition B:"Euclid had a wife and had been beating her". If B is false, then A is neither true nor false; the question of its truthvalue doesn't arise. All of this seems to agree with our intuitions and our usage in natural language; for which reason we tend to reply to loaded questions such as "Has Euclid stopped beating his wife yet?" not with a simple "yes" or "no" but with a *corrective* "Euclid has no wife," or "Euclid has never beat his wife". Now, the problem with this definition of logical presupposition is that if A "presupposes" B in the manner described, and if (by the principle of bivalence) A is either true or false in *every* possible world, then it follows that B is "true in every possible world". This means by definition that B is a logical truth. But in a bivalent system, when *any* other proposition is either true or false, then a truth of logic is true. Consequently, in a bivalent system, the relationship of "presupposition" described above holds between any proposition and any logically true proposition, but never otherwise. Cheers, David Byron david.byron@aya.yale.edu --- You are currently subscribed to vantil-list as: jamesanderson@xc.org

**References**:**Re: Logical formalisms***From:*David Byron <david.byron@aya.yale.edu>

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