Talk:Logical possibility

"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

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))

Why So Classical?

Upfront, I admit I'm not super knowledgeable about formal logic. Anyway, one thing that sort of bugs me about this article is that it seems to have a bias towards classical logics, given it starts out by saying "A logically possible proposition is one that can be asserted without implying a logical contradiction". But there are, of course, systems of formal logic which are tolerant of contradictions, like Paraconsistent logics. Also, the article seems to mix up Logical Possibility with Metaphysical possibility when it says "This is to say that a proposition is logically possible if there is some coherent way for the world to be, under which the proposition would be true.", which sounds like metaphysical possibility So shouldn't the article be rephrased to something more along the lines of how the Stanford Encyclopedia of Philosophy frames this, treating Logical Possibility as consistent with the axioms of a system of logic? (http://stanford.library.usyd.edu.au/archives/sum2010/entries/modality-epistemology/) MindForgedManacle (talk) 01:33, 24 July 2015 (UTC)

Edit Fighting

What is with the editing dispute over this article? Wizengamut (talk) 16:26, 27 December 2015 (UTC)

Is P ∧ ¬P logically possible?

Under the conventional rules of propositional logic, the proposition P ∧ ¬P is a logical consequence of another proposition, viz. ¬P ∧ P. According to the definition in the lead, we have to conclude that P ∧ ¬P is logically possible.  --Lambiam 19:18, 3 June 2020 (UTC)

I think the article should start more or less as follows:

In modal logic, a logical proposition is possible if it is true in some possible world. The universe of "possible worlds" depends on the axioms and rules of the logical system in which one is working, but given some logical system, any logically consistent collection of statements is a possible world. The modal diamond operator $\lozenge$ is used to express possibility: $\lozenge P$ denotes "proposition $P$ is possible".

 --Lambiam 19:48, 3 June 2020 (UTC)

While the term "logical possibility" is used, I'm not sure it has an accepted definition. If we can't find a canonical RS that defines this concept, then I don't think we should have an article on it. — Charles Stewart (talk) 09:22, 8 July 2020 (UTC)

The lead gives the ref https://stanford.library.sydney.edu.au/archives/sum2014/entries/modality-epistemology/ after its definition, but the SEP articles has the term "logical possibility" occur twice without definition. I don't think this counts as a source for the term. — Charles Stewart (talk) 09:27, 8 July 2020 (UTC)

Apparently C.S. Peirce used the term (from http://www.commens.org/dictionary/term/logical-possibility), but his definition varied: the most familiar-sounding to me of these is "Logical possibility refers to a state of information in which nothing would be known of positive facts, except so much as is necessary to know the meanings of words and sentences." but I would usually call this conceptual possibility. — Charles Stewart (talk) 09:35, 8 July 2020 (UTC)

And Peirce was following Leibniz, who appears to have distinguished between real and logical possibility when talking about how we might conceive of possible worlds. I'm convinced we should have an article on it, and also that the current article is OR. — Charles Stewart (talk) 09:46, 8 July 2020 (UTC)