Talk:Law of excluded middle

law of excluded middle should only be used when the boundaries are known (how many choices there are)
If we have to decide between P and P), that means that we're not even 100% sure which one is true (exists). Therefore there's also the possibility to ask to decide between R and R) and so on...; if we have to decide

between P, P), R and R) than obviously we have more than two choices, therefore the law of excluded middle

cannot be applied here - where we don't even know the boundaries (i.e. how many choices do we have).

Clarification: Example 1: Maybe we can ask someone to decide whether Socrates is supernatural or not supernatural (even this can be argued, see below)...

Example 2: but we cannot ask someone to decide whether God exists or does not exists without asking someone to decide whether 1 God exists or 10 Gods exists. I know 10 Gods is might not be 1 God negated, but how can we assume that if we don't even know which one is true AND we don't even know our boundaries (how many choices we have to choose from)

Argument on Example 1: If somehow Socrates becomes supernatural for a fraction of a second, does that qualify him as supernatural? — Preceding unsigned comment added by Rodamn (talk • contribs) 2008-03-04T19:23:27 (UTC)

The founding a priori necessary fact: (l) p w ~p ,that is to say,the law of excluded middle.
Let the symbol (l) represent a priori necessity. (l) p w ~p means that the fact p and the fact not-p are a priori necessarily contradictory. On the one hand, they are necessarily in-compatible in reality, on the other hand they cannot be both excluded from reality. Hence the fact p ≡ p. That means that the fact p is the fact excluding the fact not-p as the fact not-p is the fact excluding p. The author of this remark refers the potential reader to An inquiry into meaning and truth, chapter 20 by Bertrand Russell and to what is devoted to the said chapter entitled The law of excluded middle in the following papers:

KNOLmnc 1 To defend his views about modal logic and strict implication, Jean-François Monteil utilizes the chapter of Bertrand Russell’s An inquiry into meaning and truth entitled The law of excluded middle.

KNOLmnc 1 Modal logic. The three ingredients of strict implication. Calcutta. — Preceding unsigned comment added by 78.234.2.195 (talk) 2013-12-13T16:49:06 (UTC)

"This statement is not false"
The part ""This statement is not false", can be assigned true." is unclear/misleading. It can also be assigned false without leading to any contradiction right? How is this resolved? I think this should be expanded on. — Preceding unsigned comment added by Abenthy (talk • contribs) 2021-07-21T10:24:46 (UTC)

General Edits
The first section provides a definition for the law of excluded middle, but does not preview other sections, which I think could be useful for general comprehension of the article. The last sentence of the lead section ("A commonly cited counterexample uses statements unprovable now, but provable in the future to show that the law of excluded middle may apply when the principle of bivalence fails.[3]") is also confusing, as the counterexample is not explained. In the history section, most of the text is block quotes instead of synthesis, and the grammar for some sentences throughout the history section could be improved. The "Consequences of the law of excluded middle in Principia Mathematica" section uses lemmas not known to the reader just looking at this article; perhaps the proof could have links to relevant lemmas and theorems? Additionally, the criticism sections is not so much criticism as it is a description of how perception and usage of the law of excluded middle evolved over time; I would suggest changing the title or modifying the content to include arguments against the law (ex. the last sentence in the section). Riyeng (talk) 16:42, 1 September 2022 (UTC)