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Topic: Torkel Franzen argues
Replies: 25   Last Post: May 17, 2013 3:52 PM

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Newberry

Posts: 969
Registered: 6/4/07
Torkel Franzen argues
Posted: Apr 24, 2013 9:28 PM
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Torkel Franzen argues that all the axioms of ZFC are manifestly true
the logic apparatus is truth preserving therefore all is good and the
system is consistent.

First of all if this is true the the anti-machinists such as Lucas or
Penrose are right because Franzen has just made an argument a machine
cannot do.

So the axioms are manifestly true and the rules are truth preserving.
The argument seems impeccable. What could possibly be wrong with it?
For example is it possible that the logical apparatus contributes some
spurious truths in addition to preserving them? This

(x)((x+3 < x) --> (x = x+4)) (1)

does not look manifestly true to me. Where did it come from? From the
axioms? At this point discussion with the indoctrinated people becomes
difficult. They just repeat that (1) is true under all
interpretations. They are not able to see the problem. In fact this
has nothing to do with any interpretations. The same problem occurs at
the propositional level:

(P & ~P) --> Q (2)

is notoriously counter-intuitive. It is called PARADOX of material
implication, and it motivated research into relevance logics. So don't
tell me that it is all based on manifest truth. In fact I have shown
in another thread
https://groups.google.com/forum/?hl=en&fromgroups#!topic/sci.logic/lDJcgOg4vco
that the proof that the truths of first order arithmetic are not
recursively enumerable is NOT likely to hold if we use Strawson-like
semantics.



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