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Physicist Eugene Wigner argued that

the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious

and that

there is no rational explanation for it

as it it indicated in his essay “The Unreasonable Effectiveness of Mathematics”. His words have been interpreted by many philosophers and physicists (Like Max Tegmark) as suggesting that the universe IS mathematics.

In this book*: “The Pythagorean World: Why Mathematics Is Unreasonably Effective In Physics”, the author indicates that Wigner’s view of mathematics is not as inclusive as Graham Priest’s, since it does not include paraconsistent logic (Priest is a philosopher who has worked extensively in this area).

But what does this exactly mean? What does it mean that Wigner did not include Paraconsistent logics in this view? Does it mean that he simply did not explicitly mention them in his essay?

*Link to the book

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    Perhaps it means the Wigner is not tolerant of contradictions. And part of the mystery that Wigner has detected is that a powerful method of progressing math and science is to NOT be tolerant of contradictions.
    – puppetsock
    Jan 14 '20 at 18:06
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    Like puppetsock l see no reason for Wigner to consider paraconsistent logic or accept true contradictions. Dialethism is a minority sport. .
    – user20253
    Mar 31 '20 at 11:42
  • @PeterJ why do you see no reasons for that?
    – vengaq
    Apr 3 '20 at 18:39
  • @vengaq - I know of no instance of a true contradiction so see no argument for modifying logic. I see it as a strength that Wigner ignores paraconsistent logic.
    – user20253
    Apr 4 '20 at 13:21
  • It's worth knowing that the VonNeumann-Wigner interpretation has been probably the most perniciously misleading serious interpretations of quantum mechanics. Many scientists disagree with Wigner, enough to be a whole trope: en.wikipedia.org/wiki/…
    – CriglCragl
    Mar 25 at 22:12
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Wigner might have been a very great physicist, but the mysteriousness of why numbers are important in physics is not at all mysterious. The very word 'geometry' betrays its earthy origins. Physics and number met first in geometry, and they have continued together ever since. Given that this meeting was over ten millenia ago, its not at all strange by now, that we have a great deal to show just how much overlap there is between the two.

Shame on Wigner, he should have thought about it more. Then again, he did remark that the Native Americans made way for the colonising Europeans as a weaker race (implied) made way for the 'stronger'. I suppose racial theorising was all the rage back then. Not a word about genocide, concentration camps, broken treaties, venality married to stupidity and ignorance and an almost insatiable greed...

Mr Wigner, you can't make up for all that by thinking your name rather sounds like wig-wam...

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A paraconsistent logic is a logic that does not validate the principle of explosion ("from a contradiction, anything follows"). A paraconsistent plurality of worlds will therefore be open to nontrivial worlds in which there are true contradictions.

Cantor identified both God and "inconsistent multiplicities" as examples of absolute infinity. The latter were structures like "the ordinal of all ordinals," or a naive V, which would be rather "tall" or "large" such that saying there were V-many worlds would be saying that there were as many worlds as could be. A paraconsistent naive V would therefore "seem larger" than a consistent refined V (where the class of all sets doesn't have a commensurable "size," exactly). (See also the SEP article on impossible worlds.)

As far as physics goes, Wigner's eschewal of paraconsistency would be Wigner not applying inconsistent mathematics to physics, or not thinking it applied, or something along these lines.

EDIT: or maybe the idea is that the application of inconsistent mathematics to physics is not as "mysterious" as the application of consistent mathematics supposedly is?

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