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the "absurdist" concept of negation
According to the "absurdist" view, a rational discourse involves certain statements that are regarded as "absurd." These might vary according to the particular conversation: say, '0 = 1' or 'John ran from New York City to San Francisco in less than a minute' or 'A pig differs from all the other trees, only in that a pig has wings.' A statement in the discourse is summarily dismissed, if it implies an absurdity: that is, if we have an implication of the form '<statement X> implies <some absurdity>' then we immediately back away in horror and put a big taboo sign on <statement X>; this taboo sign is generally called negation, and the 'backing away in horror' rule is codified by an inference:
from '<statement X> implies <some absurdity>' infer 'not <statement X>'
Now certain issues arise
What statements are to be regarded as absurd? A general answer to that question might be 'An absurdity is any statement with too many consequences' -- in keeping with the saying, "Well, that proves entirely too much!" This is why '0 = 1' is regarded as absurd, for example
And what are the rules governing negation?
Two popular rules are double negation and excluded middle. Double negation asserts that 'not (not <statement X> )' has the same meaning as '<statement X>.' Excluded middle asserts that '<statement X> or not <statement X>' is always a harmless assumption in discourse. But neither double negation nor excluded middle is at all obviously correct under the "absurdist" interpretation of negation. Excluded middle, for example, suggests that, for any <statement X>, we are either in the convenient position of being able to assert definitively '<statement X>' or else in the convenient position of being able to assert definitively '<statement X> implies <some absurdity>' -- but we seldom in either of the convenient positions. Moreover, any number of other very desirable reasoning rules would require us to accept both double negation and excluded middle, whenever we accepted one of them. It is common to accept both, declaring that all statements must be either true or false
But this view, that all statements must be either true or false, leads immediately into new swampy territory, where we can easily be mired: first, because we really want to use logic in the sciences -- where statements are never really unambiguously 'true' but are more properly speaking only 'approximately true,' some being (at best) rather 'more true' than others; second, because we have suddenly complicated the problem of discussing 'negation' by introducing new terms ('true' and 'false'), which themselves require explanation. The meanings of 'true' and 'false' are not obvious; one might think 'false' represents an abstraction of '<some absurdity>', extended to include all statements which imply an absurdity; then perhaps 'true' represents a converse notion, according to which one begins from some axioms, and considers 'true' the statements derivable from the axioms; but then one should be careful the axioms themselves cannot lead to an absurdity -- which, unfortunately, is impossible to check in general. Boolos, in fact, has a nice little book, that studies the consequences of interpreting 'true' as 'provable from a set of axioms' and 'false' as 'provable from <the same> set of axioms,' but then there is usually a vast unclaimed territory, of statements which are neither 'true' nor 'false' -- in other words, excluded middle does not hold
It seems to me that many posters in this forum regard omnipotent beings as "absurd" -- since such beings would (by definition) have limitless consequences, thus certainly must have "too many consequences," and so must be rejected as "absurd" (under the general philosophical view that such notions "prove entirely too much"). I have some sympathy for this view, I suppose, but the conclusion I would reach is somewhat different: logic, wonderful tool that it is, has certain limits, and some issues simply cannot be addressed by mere logic.
In any case, I can see why the question in the OP ("Can &c&c?") should admit a 'yes' or 'no' answer: it does not seem to me to involve a statement which must be 'true' or 'false.' (And neither can I see any way one could test a purported answer to the question, nor can I imagine any use to which a supposed answer could be put)
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