FOM: polylogic: three points
Prof. Antonino Drago
drago at unina.it
Tue Mar 9 16:24:49 EST 1999
The question about polylogic is valid per se - apart the question =
whtether Marx supported or not polymathematics.=20
First point. I ask: Which relevance of the translation =
Kolmogoroff-Glyvenko-Goedel? If it is relevant, then the intuitionistic =
logic is essentially different from classical logic, as Goedel stated =
ina paper just after his celebrated theorem. Then, polylogic follows
Second point. I ask: Is KGG translation complete? The case of the =
predicate claculus makes apparent the negative answer (see the different =
versions in the several textbooks). Then, its philosophical version is =
an incommensurable phenomenon, a fact emphasised by both Kuhn and =
Feyerabend as unavoidable in science, as concerning couple of scientific =
theories or paradigms; although they have been unable to offer a sharp =
definition of this phenomenon. In this case foudnations of logic and =
foundations of mathematics share a basic phenomenon of foudnation of =
physics.
Third point. In the original texts by mathematicians of some new =
theories there exist double negated sentences playing crucial roles in =
the respective theories: L. Carnot, Lobachevskii, Galois, Klein, =
Poincar=E9, Goedel (apart Lavoisier, S. Carnot, Avogadro, Planck, =
Einstein, Heisenberg...). For instance, never Lobachevskii wrote "There =
exist two parallel lines"; rather he always stated sentences like the =
following: "No contradiction follows from the hypothesis..."; "It is not =
absurd to take as the angle of parallelism....". It is apparent that in =
his time the corresponding affirmative versions of these statements =
lacked of scientific evidence. The language of mathematicians include =
these double negations in a crucial though covert way: why it is said =
"in-variant", i.e. not-unchanged, instead of equal or constant?
Antonino Drago
adrago at na.infn.it =20
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