Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how

On 5/11/2024 11:47 AM, Ross Finlayson wrote:

On 05/11/2024 07:40 AM, Jim Burns wrote:

[...]

>
In the logical, the purely logical,
the syntax "is" the semantics.

If what makes logic impure is
to be about something,
then it would make some sense to say that
pure logic has no semantics
...which leads, by default?
to syntax being the missing semantics, I guess?
Sorry, I will not sign your petition.
Syntax and semantics are more different than
cabbages and kings.
It seems to me that
the purest of ultra.pure logic is actually
_about_ claims,
analogous to geometry being _about_ points,
lines, plane.figures, and so on.
It is an unbreakable law that
the sum of the squares of the two shorter sides
of a right.triangle is equal to
the square of the third and longest side.
It is an unbreakable law that
a finite sequence of only not.first.false claims
holds only true claims.
It is an unbreakable law that
Q preceded by P and P⇒Q is not.first.false.