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?

Sure.

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]

structure"?

>

> [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_ .

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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI

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