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.


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

$$q=\neg p$$


  • $\begingroup$ 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 $\endgroup$ – Mathematicslover Apr 24 at 11:14
  • $\begingroup$ Yes clearly if $q=\neg p$ than if the stament $q$ is false.$\neg q=\neg \neg p$ , which for double negation is $\neg q=p$ $\endgroup$ – Eureka Apr 24 at 11:15
  • $\begingroup$ eureka do you have books or literature to recommend, i do not wanna ask always here, as i get to many downvotes :/ $\endgroup$ – Mathematicslover Apr 24 at 11:17
  • $\begingroup$ @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. $\endgroup$ – Eureka Apr 24 at 11:18
  • $\begingroup$ could you please so kind and sum it up again clearly and in simple english ? $\endgroup$ – Mathematicslover Apr 24 at 11:20

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.)

  • $\begingroup$ hen the statement "𝑝 is false" is false, and 𝑝 is true. im asking for that why is this ? $\endgroup$ – Mathematicslover Apr 24 at 18:48
  • $\begingroup$ That's just the meaning of the word "false"... $\endgroup$ – lemontree Apr 24 at 18:49
  • $\begingroup$ false means taking the negation ? since p is wrong the nefation would be true, right ? $\endgroup$ – Mathematicslover Apr 24 at 18:52
  • $\begingroup$ @Ömer F. Yi Yes. $\endgroup$ – lemontree Apr 24 at 18:53
  • $\begingroup$ brilliant, that was my question. $\endgroup$ – Mathematicslover Apr 24 at 18:54

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