Date: Apr 5, 2013 12:10 PM
Author: Frederick Williams
Subject: Re: Matheology § 224

Nam Nguyen wrote:
> On 05/04/2013 6:22 AM, Frederick Williams wrote:

> > Nam Nguyen wrote:
> >>
> >> On 04/04/2013 10:55 PM, fom wrote:

> >>>
> >>> Who knows what is and what is not -- even
> >>> in the simple realm of mathematics -- claims
> >>> a certain knowledge that is revealed rather
> >>> than discerned.

> >>
> >> So, since Godel, is the knowledge of the natural numbers
> >> a revealed or discerned one?
> >>
> >> Revealed by whom? Discerned from what?

> >
> > Why do you write "since Godel"? What is his relevance to the matter?
> >

> There's no point for technically discussing (or arguing) with you,
> in any thread.
> Until you present a simple example of a 3-element-universe structure of
> your own, bye.

And if do that, you'll explain your "since Godel" remark? Let's try
that. My structure is a structure in the sense of Shoenfield,
Mathematical logic, ASL/A K Peters, 2000, section 2.5. Since
Shoenfield's structures make reference to a first order language L, I'll
define that first. L is as defined by Shoenfield in section 2.4 with no
function symbols and one binary predicate symbol =. The ingredients of
the structure A are
i) |A| = {1,2,3}.
ii) No functions.
iii) No predicates.

[For the benefit of others who may not be familiar with Shoenfield, no
predicate is required to interpret the binary predicate symbol = which
must, nevertheless, be in the language.]

Nam will now fail to explain his "since Godel" remark, thereby
demonstrating both his ignorance and his dishonesty.

When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting