Re: Question about Basic Law V


lugita15@xxxxxxxxx wrote:
Rupert wrote:
Fuckwit wrote:
On 3 Sep 2006 20:41:26 -0700, "Rupert" <rupertmccallum@xxxxxxxxx> wrote:


You need to clarify further how you are going to get the system to talk
about things like predicates.

2nd order logic.


In 2nd-order logic we talk about sets. It's not clear how you'd apply
the notion of "recursively enumerable" to them. If you refer to
predicates by their Goedel numbers then the notion of "recursively
enumerable" is applicable, but there is a difficulty in passing from a
predicate to the set it defines.

True, this is how we understand second-order logic today.
Nevertheless, Frege did not have such an interpretation. Instead, he
called his second order variables "concepts," and interpreted them to
be predicates, not sets. Instead, he considered sets, or extensions in
his phraseology, to be under the domain of first-order quantification,
i.e. he considered extensions as objects. To him, two concepts F and
G, even if exactly the same objects fall under them, may still be
different concepts. For instance, the concept "being a prime number"
is different from "for all F being a prime number," in that the first
one is predicative while the second one is not.
Any further help would be greatly appreciated.
Thank You in Advance.

[...] If you spell out the details of Frege's system I may be able to
tell you in more detail how this would come out.

See:
http://plato.stanford.edu/entries/frege-logic/


Fuckwit

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