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Re: goedel

Re. the following:
 
the ultimate validity of any theorem should stand or fall - in respect of real world phenomena - not only on the coherency of the proof, but on the truth, falsity or applicability of the axioms upon which the proof is predicated.

Comment:

This mistakes Map (Theory) for Territory (Real World).

In physics, "...a theory is just a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make.  It exists only in our minds and does not have any other reality (whatever that might mean)." (Stephen W. Hawking, A Brief History of Time, Bantam Books, 1988, p. 9)

In economics, the modus operandi of ergodists and econometricians alike is predicated on the pre-supposition that the universe of volitional phenomena is, ultimately, indistinguishable from that of non-volitional physical phenomena - that Free Will is an illusion.

Gunnar

 
----- Original Message -----
Sent: Sunday, October 06, 2002 9:14 AM
Subject: Re: goedel



>From: Paul Davidson
>To: "William B. Ryan"
>Subject: Re: goedel
>Date: Sat, 05 Oct 2002 11:47:34 -0400
>
>At 10:01 AM 10/5/2002 -0500, you wrote:
>
>>You said yesterday that something cannot be an axiom unless if it

>>is "subject to falsification."

[Ryan 10-06-02]  As noted earlier, I should have written here "if" instead of "unless if."

>>Where did you get that idea?
>>
>>How do you know that an axiom cannot be falsified without trying?
>>
>>Because you do not succeed does not mean in principle it is not
>>falsifiable.
>
>
>Funny but my dictionary indicates that an axiom is a "universal

>truth" for which no proof is required.

[Ryan 10-06-02]  Then no proof is required for the ergodic axiom.  :)

That is the definition in many dictionaries.  It is a poor definition.

All it really means is that the proof of a theorem based upon certain axioms does not require proof of the axioms.

Therefore, the ultimate validity of any theorem should stand or fall - in respect of real world phenomena - not only on the coherency of the proof, but on the truth, falsity or applicability of the axioms upon which the proof is predicated.

The "axiomatic method" is that as theorems are generated they become axioms, or building blocks, for the generation of ever more extended theorems, which themselves become axioms for even more extended theorems. 

The underlying axioms that started the process become hidden from view, or forgotten.

 

 

>Paul Davidson
>Editor, Journal of Post Keynesian Economics
>503 SMC
>University of Tennessee
>Knoxville, Tn 379996-0550
>phone Number: (865) 974-4221
>fax number: (865) 974-1686
>http://econ.bus.utk.edu/davidsonextra/Davidson.html

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