On 16 Jun 2013, at 19:23, meekerdb wrote:

On 6/16/2013 12:24 AM, Bruno Marchal wrote:

On 15 Jun 2013, at 21:57, meekerdb wrote:

On 6/15/2013 12:40 AM, chris peck wrote:
Hi Rog

As you have described them a materialist could not be a "combination of both" rationalism and empiricism, because you have them as diametrically opposed. If "reason alone" is the source of knowledge, then experience isn't and can't be combined to be. Besides, Materialism is an ontological theory and doesn't give much of a hoot about how knowledge is aquired.

More to the point neither rationalism nor empiricism are branches of intuitionism.

Chris Peck is right here.



The moment of inspiration Penrose attributes to the mind connecting with a realm of ideas is neither an act of reason nor sensory experience. Moreover, If logic is to be "deductive" then, by definition, conclusions must never follow from unexplainable leaps of intuition.

Where does the persuasive power of logic come from? Why do you believe, "Either X or not-X" is true? Is it not a matter of intuition?

Yes, but not in the sense of the intuitionist.




Isn't logic just an attempt to formalize intuitive reasoning.

Only reasoning, where the intuition is used only in the choice of the axiom, and not in the reasoning.

Why not in the rules of inference too? Rejecting non-constructive proofs is a change in reasoning. I don't think there is such a sharp division between axioms and rules of inference as you imply.

I did not imply that. In most system, you can always limit the rules of inference by adding axioms. With enough axioms, and the modus ponens rule, you can derive all the other rules of inference. In particular, quantum logic, intuitionist logic and classical logic can be all formalized with only the modus ponens rules, and with the same rules for the quantifiers, just by suppressing some axioms in the Kleene's presentation of classical logic. You get quantum logic by replacing "p->(q->p)" by (p->q) -> (r->t) -> (p -> q) (limiting the a posteriori-axiom for implicative formula); you get intuitionist logic by abandoning ~~p -> p.

Bruno





Brent


Basically intuitionism reject the idea that there is an independent reality such that A v ~A applies to it. They accept only ~ ~(A V ~A).

If we limit reality to sigma_1 truth, like in the comp TOE, there is no genuine difference between intuitionism and platonism. But an intuitionist should still say no to the doctor, as the FPI is not constructive. "Washington V Moscow" needs a non-intuitionist "OR".

Bruno






Brent

If they do they have not been logically deduced, have they? And infact that is Penrose's point : leaps of intuition can not be modelled computationally. logic, ofcourse, can be. since, allegedly, minds can grope for and master facts beyond the scope of deduction, they must be qualitatively different from computer programs which can only deduce things logically.

You really seem to have things back to front in this post.

Regards

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http://iridia.ulb.ac.be/~marchal/




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http://iridia.ulb.ac.be/~marchal/



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