Re: Definition of finite.



The proof that is in my head ( which might be erronous ) is the
following:

Since y equinumerous to y
Since y is a natural number
Then y is a finite set.

That is correct.

But this proves the finitude of y
in terms of y itself, and it is that's why
I claim this definition to be 'essentially'
circulr.

It's not circular. The reason you think it is circular is that you
still haven't studied the basic logic you need to study.

We will prove the finiitude of ANY set y in terms of properties of y
itself. If y is a natural number, then it just happens that the
property we is IMMEDIATE in the proof. Immediacy is not circularity.

Hey Moe, you know that I know all of that.
My point is a little bit deeper than this.
This immediancy you call, to me it is
a form of circularity, it is a kind of subtle
circularity. It is not desirable to define
such an important concept like 'finite'
in this way.

Remember I said that Tarski's definition
is 'essentially' circular. I didn't say
it is formally circular.

This definition of finite , I mean the one
with the R and conv(R) that you've mentioned
is much better than Tarski's quasy-circular
definition. actually this definition using R
and conv(R) is my definition of x is finite
number 2.

Anyhow I think we'll discuss this subject later.
I need to define 'essentially' circular in a clear
manner so that we can have a frutiful clear
discussion about it.

.