# If statement p is false. And i say p is false, then p is true?

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 – Mathematicslover Apr 24 at 11:10
• – Sujit Bhattacharyya Apr 24 at 11:14
• i mean if i assume p is false and this clears out to be false then p must be true – Mathematicslover Apr 24 at 11:14
• "Why does false, false result in true ?" What does it mean ? – Mauro ALLEGRANZA Apr 24 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 at 11:47

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

$$q=\neg p$$

:)

• 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 – Mathematicslover Apr 24 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 $\neg q=p$ – Eureka Apr 24 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 :/ – Mathematicslover Apr 24 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. – Eureka Apr 24 at 11:18
• could you please so kind and sum it up again clearly and in simple english ? – 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.)

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