Thread by @LGcommaI

#ScheibePopperAndQuantumLogic-2
"This paper is NOT written in order to vindicate #QuantumLogic. Rather it is written to rebut a mistaken criticism of quantum logic. The criticism is due to Popper ([1968]) and it concerns a classical paper by #Birkhoff and #vonNeumann ([1936]).
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>As is well known, this latter paper inaugurated the study of two rather different though interconnected kinds of problem, namely
(1) the philosophical problem whether quantum mechanics involves a non-classical #logic, the so-called #QuantumLogic
(2) the mathematical problem of
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>characterising the basic structure of quantum mechanics, i.e. Hilbert space, by physically plausible axioms of a LATTICE THEORETICAL KIND.

As was to be expected, the philosophical problem concerning the logic of #QuantumMechanics has remained controversial, whereas
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>there has been considerable progress in solving the mathematical problem of axiomatisation (cf. Varadarajan [1968]).
But until recently one thing has NEVER been called in question, in either the philosopher's or the mathematician's camp, namely that
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>Birkhoff and von Neumann's paper really points to well-defined problems. Only #Popper[1902–1994] had doubts in this respect. Having repeatedly read his paper of 1968, I can only summarise his criticism as saying, 𝘩𝘰𝘳𝘳𝘪𝘣𝘪𝘭𝘦 𝘥𝘪𝘤𝘵𝘶: in their paper of 1936[,]
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>#Birkhoff[1911–1996] and #vonNeumann talked about something which really does not exist and the non-existence of which can, moreover, be shown by means of rather trivial mathematical considerations.

Since this account may sound like a #caricature of Popper's criticism,
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>let me quote from his own summary, according
to which
'#Birkhoff[1911–1996] and von #Neumann's famous paper ... culminates in a proposal which clashes with each of a number of assumptions made by the authors' (p. 682).

Popper also says that

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