- Is Quantum Logic really temporal as Weizsäcker claims? Or that was his particular interpretation? Was Birkhoff's and von Neumann's original proposal of Quantum Logic temporal or atemporal?
Its quantum theory that Weisecker is claiming to be temporal, and this because he writes, right in the introduction:
I take a particular approach in starting from the idea of a quantum logic. This is in my view not a peculiar 'empirical' logic, but a specification of a
general logic of temporal statements, that is of statements on facts and possibilities.
In other words, he's taking the position that quantum physics as opposed to classical physics, is ontologically temporal, because it takes possibility as a basic ontology, whereas in classical physics it is a derived fact.
- When Weizsäcker says that Quantum Logic is not yet a logic because it contains no predicates of predicates, is he exaggerating his claim? I mean, I have read everywhere that Quantum Logic is just another type of logic but this is the first time I read that it is not really a logic. Weizsäcker himself says that it belongs to the lowest types of Russell's hierarchy of logical types. So, was he exaggerating his claim?
He's not exaggerating his claim. Quantum logic, as Birkhoff and von Neumann then articulated, is a travesty of a logic. However, the important point they were making is that perhaps classical notions of logic may need reinvestigating in the light of what quantum physics teaches us about the nature of change; and it is this point, which stands. (Having said this, it is a point that stood from at least Hegels day, and perhaps even earlier, since Aristotle - but quantum physics gave the question new urgency).
- Does Quantum Logic really not contain propositions about propositions? I have read that it can be formulated as a propositional logic. Wouldn't that mean the it would contain that? Was Weizsäcker talking about some other types of Quantum Logic (maybe his own version of it)?
Well, a little later from the introduction Weizsäcker writes:
In physics we can speak of an iteration of this process. The mathematics of Hilbert space presupposes a mathematical semantics of its symbols: the letter phi means a complex vector, the letter H means a self-adjoined linear operator, etc. Yet for the physicist this is still an uninterpreted 'formalism'...
It's a truth that is generally unackowledged by many formally minded physicists, that the formalism of Hilbert spaces isn't enough to describe even the very basic quantum physics of Bohr and Diracs day. This is why, Dirac, very astutely came up with his own formalism, which is aligned with von Neumanns Hilbert spaces, but actually goes beyond it. This is why, for the physicist, interested in physics rather than formalism, the formalism is 'uninterpreted'. Essentially, the correct, mathematically rigorous, formalism, for Quantum Mechanics, is yet to be sorted out (in the sense, we can teach it to under-graduates).
The link only gives the first two pages of Weizsäcker's paper, so I can't be more expansive than this. But it seems to me that Weizsäcker is far from endorsing quantum logic per se, and going by his table of contents:
- The Problem
- Classical and Temporal Logic
- Quantum Theory of Probability
- Reality in Quantum Theory
- Concluding Remarks
he is not particularly interested in quantum logic per se, but the nature of possibility, and how that, in some sense, already ontologises temporality, in a way that classical physics does not. Take for instance Newtons Laws of Motion, the paradigm of classical physics; it is well-known that this is time-reflective; however, this time-reflection is not valid in quantum physics - and this appears to be what he is focusing on.
