(urth) I, even I, would celebrate, in rhymes inept the great...

[Norwood, Frederick Hudson]

Jeffery Wilson:  I do say A is A.  That's called the reflexive property of equality.  And, yes, I've read the Lewis Carroll bit.  Even wrote a poem about it.

Said the mathematician Kurt Godel,
There are obstacles we'll never hurdle,
There's a theorem that's true
But no proof can you do,
'Till Achilles outraces the turtle.

Modern mathematics has dealt with the paradox.  See, for example, Logic for Mathematicians by Hamilton.

Brendon Fuhs:  Sure, you can say any consequence of a true statement is false, but I think you've just changed the meaning of the word "true", not invented a new logic.

Rick Norwood




-----Original Message-----
From: Urth [mailto:urth-bounces at lists.urth.net] On Behalf Of Jeffery Wilson clueland.com
Sent: Thursday, October 16, 2014 12:40 AM
To: The Urth Mailing List
Subject: Re: (urth) I, even I, would celebrate, in rhymes inept the great...

On 10/15/2014 1:28 PM, Norwood, Frederick Hudson wrote:
> I notice that none of the "we can never know anything absolutely"
> team on this thread has accepted my challenge to explain how A can be 
> true, and A implies B can be true, and yet B can be false.

That is known as modus ponens (the method that affirms), but that's short for modus ponendo ponens (the method that affirms by affirming), and as the longer Latin name implies, its truth is complicated by an infinite regress, as dramatized by another famed fantasy author:

http://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achilles

If you consider a true statement about abstracted symbols to be an absolute truth, why not save steps and just say "A is A"? That remains valid regardless of the values of A or B or the validity of modus ponens.

--
Jeff Wilson - < jwilson at clueland.com >
A&M Texarkana Computational Intelligence Lab < http://www.tamut.edu/cil > _______________________________________________
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