Date: Apr 5, 2013 12:40 PM
Author: namducnguyen
Subject: Re: Matheology § 224

On 05/04/2013 10:10 AM, Frederick Williams wrote:
> 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?


But you have not spelled out (presented) a _valid_ finite a language
structure! See below.

> 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.

But what exactly is A?

And what exactly what did you technical mean by "ingredients of ... [a]
> [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.]

Since virtually when we talk about a structure _of any use_ in textbooks
or otherwise (such as in my example for L(0,<) which my request
originates from), _can you_ give an example with some non-logical
symbols involved?

Specifically an example for L(0,<) I originally requested of you?

It'd not help you anyway if you don't (and you seem to be ignorant of
that fact): since if you don't have any non-logical symbol for your L,
Shoenfield's stipulation iii (you've alluded to above) means _your_
_alleged structure A_ can _not be defined_ at all!
> Nam will now fail to explain his "since Godel" remark, thereby
> demonstrating both his ignorance and his dishonesty.

You're bluffing of course. What you have is a simple 3-element set
{1,2,3} that you _labeled_ as "|A|": you've _NOT_ defined, spelled out,
what A be!

So, sorry that I have to wait _until you do define exactly what A be_ .

There is no remainder in the mathematics of infinity.