intuitionistic math can help in quantum physics?
renevestergaard at icloud.com
Sat Apr 11 13:35:36 EDT 2020
I made a potentially-related observation in connection with "proofs of
life": classical reasoning is too permissive for reductionist subject
Reductionist here means that two distinct languages are used on each
their side of the consequence relation, and that the language of
premises ("on the left") pertains to more fundamental concepts than the
language of consequences ("on the right").
Classical logic admits excluded middle (specifically, stability, i.e.
"excluded middle on variables"), meaning that higher-level conclusions
can be reached that are not anchored in specific lower-level facts.
NB1 The above seems to point to minimal logic as the proper setting for
reductionist science. However, intuitionistic logic can be obtained by
admitting the law of weak excluded middle (and, specifically, weak
stability), which can be seen to amount logically to the open-system
assumption. From that perspective, the use of classical logic admits a
NB2 "Proofs of life" contains a reductionist reasoning system that
admits the cut rule, meaning considerations at the higher level can be
used to circumvent the need to consider lower-level facts.
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