```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 languagestructure! 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 textbooksor otherwise (such as in my example for L(0,<) which my requestoriginates from), _can you_ give an example with some non-logicalsymbols 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 ofthat 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.                                       NYOGEN SENZAKI----------------------------------------------------
```