[FOM] quantum logic

Antonino Drago drago at unina.it
Fri Apr 30 17:49:56 EDT 2010

> > Arnold Neumaier<Arnold.Neumaier at univie.ac.at>u>
Sent: Sunday, April 25, 2010 9:37 PM wrote:

> No serious mathematics can be deduced from quantum logic.
> The latter has no useful form of implication that would cooperate
> with conjunction in a way that lets one build up a theory in the
> usual stepwise fashion.

I contest this drastic apprasal.
Quantum logic, by allowing the reductio ad absudum in its weak version, may 
offer serious mathematics in the same way Lobachevski in Geometrische 
Untersuchungen... (see the Appendix to R. Bonola: Non-Euclidean Geometry, 
Dover) did when introduced his hyperbolic hypothesis by five theorems ad 
absurdum (no.s 17-22), one linked to another .
Of course, by means of this kind of arguing one does not build up a theory 
in the usual stepwise fashion; on this point I agree with Neumaier.
Best regards
Antonino Drago

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