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Why does false, false result in true ? As i stated. I do not love mathematics is not true is <=> i love mathematics. How could we explain that with logic ? Double negation ? could we say that saying false is the same thing as taking the negation ? and double-negation results in elimnation ? Please help and provide a good answer.

  • instead of downvoting i would appreciate an answer. Really do not know what people hope to achieve with simply downvoting –  Apr 24 '19 at 11:10
  • Here are some useful links
    : https://math.stackexchange.com/questions/931234/is-proof-by-contradiction-same-thing-as-a-rightarrow-b-is-true-when-a-is?rq=1 https://math.stackexchange.com/questions/1697691/this-statement-is-false?rq=1 https://math.stackexchange.com/questions/1699654/this-statement-is-false-propositional-logic     – Sujit Bhattacharyya Apr 24 '19 at 11:14
  • i mean if i assume p is false and this clears out to be false then p must be true –  Apr 24 '19 at 11:14
  • "Why does false, false result in true ?" What does it mean ? – Mauro ALLEGRANZA Apr 24 '19 at 11:46
  • To say that "I do not love mathematics" is not TRUE is to say that "I do not love mathematics" is FALSE. But if it is false that I do not love mathematics, this means that I love mathematics. Fullstop. – Mauro ALLEGRANZA Apr 24 '19 at 11:47
  • @MauroALLEGRANZA i mean if i assume p is false and this clears out to be false then p must be true –  Apr 24 '19 at 11:54
  • Maybe you're looking for this: https://en.wikipedia.org/wiki/Double_negation – Matti P. Apr 24 '19 at 12:06

2 Answers2

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No you are getting a bit confused: if $p$ is false, the "$p$ is false" is another statement $q$, not $p$ itself. And clearly:

$$q=\neg p$$

:)

Kandinskij
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  • do you know what i mean ? i mean if i assume p is false and this clears out to be false then p must be true –  Apr 24 '19 at 11:14
  • Yes clearly if $q=\neg p$ than if the stament $q$ is false.$\neg q=\neg \neg p$ , which for double negation is $\neg q=p$ – Kandinskij Apr 24 '19 at 11:15
  • eureka do you have books or literature to recommend, i do not wanna ask always here, as i get to many downvotes :/ –  Apr 24 '19 at 11:17
  • @ÖmerF.Yi I don't know books, however this is formal logic. You shouldn't leave this site, it's amazing. You should just learn to be more clear and to write a good post. – Kandinskij Apr 24 '19 at 11:18
  • could you please so kind and sum it up again clearly and in simple english ? –  Apr 24 '19 at 11:20
  • @ÖmerF.Yi the comment or the answer? – Kandinskij Apr 24 '19 at 11:23
  • the answer. i appreciate long versions with clear english –  Apr 24 '19 at 11:24
  • does is false means simply taking the negation of a statement ? –  Apr 24 '19 at 11:31
  • @ÖmerF.Yi yes if it's true that it is false. – Kandinskij Apr 24 '19 at 13:55
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If $p$ is false, and you say "$p$ is false", then the statement "$p$ is false" is true, but $p$ is still false.
If you say "$p$ is false", and it turns out that this is wrong, then the statement "$p$ is false" is false, and $p$ is true$^1$.
"$p$" and "$p$ is false" are two diffeerent statements.

$^1$ (This is assuming that all statements are either true or false, as classical logic does; there are logics which assume more than two truth values or truth-value gaps.)

Natalie Clarius
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