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Can truth be understood as math?

Posted: Mon May 27, 2019 4:54 am
by PeteOlcott
Could Truth be understood as the theorems of human knowledge where basic facts are its axioms?

∃Facts ⊆ Human_Knowledge ∃x ∈ Language(Human_Knowledge) (True(Facts, x) ↔ (Facts ⊢ x))

Re: Can truth be understood as math?

Posted: Mon May 27, 2019 9:19 am
by HexHammer
PeteOlcott wrote:
Mon May 27, 2019 4:54 am
Could Truth be understood as the theorems of human knowledge where basic facts are its axioms?

∃Facts ⊆ Human_Knowledge ∃x ∈ Language(Human_Knowledge) (True(Facts, x) ↔ (Facts ⊢ x))
No, then we wouldn't need humans for jobs, but could hire 100% robots which would do things faster, they could have high IQ conversations.

Re: Can truth be understood as math?

Posted: Mon May 27, 2019 12:35 pm
by Speakpigeon
PeteOlcott wrote:
Mon May 27, 2019 4:54 am
Could Truth be understood as the theorems of human knowledge where basic facts are its axioms?
∃Facts ⊆ Human_Knowledge ∃x ∈ Language(Human_Knowledge) (True(Facts, x) ↔ (Facts ⊢ x))
We know a few facts.
Facts are meaningful assertions we happen to know are true.
Sometimes we have the necessary vocabulary to talk about what we know: I can talk truthfully of the fact that I am in pain whenever I am in pain. However, most of the time, we talk about things which aren't facts we know and we do it as if they were facts we knew. The Moon is orbiting the Earth... Oh, well, how the Hell do I know that?!
Still, we know some facts so the notion of fact and truth are not in vain. A fact is true, by definition, and we happen to know some facts. So, we can at least make some assertions that are indeed true.
Now, a sentence x is true if it describes a fact. The sentence "I'm in pain" is true whenever I happen to be in pain.
Indeed, the fact that I am in pain implies that the sentence "I'm in pain" is true at this time. So, sometimes, some fact f implies some sentence x is true: fact ⊢ x. And then, of course, if one fact implies that sentence x is true, then all the facts together imply that x is true of some fact. And then, of course, you can make that your definition of truth. That in itself doesn't tell you which sentences are true and which are false, though.
EB