Post by Eugene 2.0 on Apr 25, 2021 16:03:23 GMT
Frege brought an example in which such formulas as, for instance,
∃x∃y s.t. 1000010000=y & xє{odd numbers} & x=y+k & k>0
have got no meaning, because we hadn't calculated it yet. But such it doesn't mean that such formulas have no sense, because we still might guess about it. While we wouldn't guess about such formulas as:
[∃*∀2∃*, all, (0)]
indeed, meaningless. And sometimes it appears to be true, but in particularly this case:
This was believed to be true for more than thirty years, and the result was used by other mathematicians to prove other results. But in the mid-1960s, Stål Aanderaa showed that Gödel's proof would not actually work if the formulas contained equality... References to Stål Aanderaa and to the article.
We can think of some formula to have meaning, but to get the answered is to prove the formula. And for that reason a meaningless formula is the formula that has no proof.
But what does it mean for a certain formula to have no proof? It means that there is no values which satisfies it. It's interesting to note that we can say about a sign or a thing that it has sense if it can be applied to something. If a sign or a thing can be used somewhere, even hypothetically, then that sign or thing isn't senseless.
And what about improvable formulas? Do they have any things for applying? - No, they do not. And that's why we can say about a certain improvable formula that because it's meaningless it has no sense. Any improvable formulas are meaningless, therefore all of such are senseless.
Need to note that there are meaningless things beyond proof technique, and for a certain thing to be meaningless is the same to have no sense of being used. So, that's why for any thing it's true that if this thing is meaningless, it is senseless.
∃x∃y s.t. 1000010000=y & xє{odd numbers} & x=y+k & k>0
have got no meaning, because we hadn't calculated it yet. But such it doesn't mean that such formulas have no sense, because we still might guess about it. While we wouldn't guess about such formulas as:
[∃*∀2∃*, all, (0)]
indeed, meaningless. And sometimes it appears to be true, but in particularly this case:
This was believed to be true for more than thirty years, and the result was used by other mathematicians to prove other results. But in the mid-1960s, Stål Aanderaa showed that Gödel's proof would not actually work if the formulas contained equality... References to Stål Aanderaa and to the article.
We can think of some formula to have meaning, but to get the answered is to prove the formula. And for that reason a meaningless formula is the formula that has no proof.
But what does it mean for a certain formula to have no proof? It means that there is no values which satisfies it. It's interesting to note that we can say about a sign or a thing that it has sense if it can be applied to something. If a sign or a thing can be used somewhere, even hypothetically, then that sign or thing isn't senseless.
And what about improvable formulas? Do they have any things for applying? - No, they do not. And that's why we can say about a certain improvable formula that because it's meaningless it has no sense. Any improvable formulas are meaningless, therefore all of such are senseless.
Need to note that there are meaningless things beyond proof technique, and for a certain thing to be meaningless is the same to have no sense of being used. So, that's why for any thing it's true that if this thing is meaningless, it is senseless.
