Talk:Logical possibility

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"1+1=3 and 0=1 are false in all possible worlds." - 1+1=3 is false in, say, decimal arithmetics. But 1 rectangle plus 1 rectangle can equal 3 rectangles, and thus, "1+1=3 [is] false in ALL posible worlds" is false. :) - Nick15 02:17, 30 October 2006 (UTC)

I think you miss the point. What is usually meant by "1 + 1 = 3" is false, even if some of those other things it could mean in other contexts are true. Michael Hardy 02:19, 30 October 2006 (UTC)

I do not feel that the first person perspective is appropriate. Perhaps those sections should be re-written. ~Anonymous

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]]== 1 + 1 = 3 ==

You will hold me a pedant for removing the photograph and the accompanying caption. Remark, however, that it is logical impossibility that is under discussion, and logical impossibility admits of no quaint games. All terms must be defined until they are unambiguous. For example, it is easily evident that we use different digits to denote different numbers (different cows, different laws, &c.). It is not at all easily evident that "1 + 1 = 3" cannot be taken as the basis of a system without contradictions - even if we assign the symbols almost their usual meanings. 1 + 1 = 3 won't serve you any way, but change 3 to 0 and you obtain the system of integers modulo 2, also the two-element group. --VKokielov 03:58, 10 May 2007 (UTC)

Other groups are irrelevant. What "1 + 1 = 3" normally means is about addition of cardinalities of finite sets, and it is indeed logically impossible. Michael Hardy 04:01, 10 May 2007 (UTC)
Yes, but when the terms are undefined? We pass across the wrong idea. --VKokielov 13:26, 10 May 2007 (UTC)


"For example, it may be logically possible for the laws of nature to be different from what they actually are. The debate over whether it really is logically possible is beyond the scope of this article."

I find this, and the subsequent couple of sentences highly misleading, since it suggests that there is a live debate as to whether the laws of nature are logically necessary. There isn't. ---- NoizHed (talk) 21:13, 16 November 2007 (UTC)
(To clarify - no-one thinks the laws of nature are logically necessary. ---- NoizHed (talk) 21:14, 16 November 2007 (UTC))