Talk:Counterexample

Opening Statements

The opening statement “In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule.” is inaccurate. An exception implies that the the rule under question is valid in some or most cases. The existence of a counterexample has no such implications. Also the statement “In mathematics, counterexamples are often used to prove the boundaries of possible theorems” is equally misleading. Counterexample cannot be used to establish boundaries (whatever that means). I'll wait a few days, and if there are no replies or edits, I'll modify these statements. 24.14.155.208 (talk) 20:15, 3 February 2014 (UTC)

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Uruk-Hai...

/chortle Kaz 19:55, 17 Jan 2005 (UTC)

Not Pc

/chortle Indigenius 01:11, 2 June 2006 (UTC)

Brazilian logic

Removed: However, it does not work in Brazilian logic, where contradictions aren't necessarily false. Counterexamples can exist in Brazilian logic, but the above argument must be checked to ensure that the contradiction produced actually is false in the particular case at hand.

According to the page referenced, the law of non-contradiction holds in Brazilian logic. (I have my suspicions about the contents of that page too, but $\neg \phi (t)\to \neg \forall x:\phi (x)$ works in linear logic with quantifiers, and R# is stronger than that.) -Dan 16:33, 21 November 2005 (UTC)

fix-up

The definition for the mathematics should be about something, everyone understands. Just get a better example instead of "Orcs" 24.12.8.97 20:50, 25 September 2006 (UTC)

Local or global

The following text was removed:

A counterexample may be local or global in an argument called bia.

If an editor can complete the thought, with a reference, it may improve the article.Rgdboer (talk) 21:47, 18 January 2015 (UTC)

2602:306:BDCA:ACE0:19DA:FC75:4D66:5B9E (talk) 19:40, 24 February 2016 (UTC)

Reasoning Counterexamples Are Based On

Do counterexamples come from inductive or abductive reasoning? I'm asking because I have determined that deductive reasoning means following the right conclusion and therefore ascertains no counterexamples whatsoever. Cbsteffen (talk) 19:42, 24 February 2016 (UTC)

Question about non-counterexamples

Correct me if I'm wrong, but if something is not a counterexample, then do we say it is an "example"? For example, can we say that 7 and 10 are examples to the statement "All prime numbers are odd"? 173.76.246.128 (talk) 18:26, 17 August 2020 (UTC)

We say that 7 is an example of an odd prime. 10 is no more an example (or counterexample) relating to odd primes than is pi. Slgaiser (talk) 13:28, 3 July 2021 (UTC)