I tried to read the paper by Hillary Putnam, but there were too many difficult equations — Dusty of Sky
I tried to read the paper by Hillary Putnam, but there were too many difficult equations, so I'm hoping that someone here can make his case in more ordinary language. — Dusty of Sky
Putnam gives an example of the double-slit experiment on pp180-181. On his view, the photon goes through (slit A1 or slit A2) and hits region R, yet it is not the case that the photon (goes through slit A1 and hits region R) or (goes through slit A2 and hits region R). — Andrew M
I can't conceive how an observation which violates principle of distributivity could be possible. What would that even look like? Putnam is an accomplished and respected philosopher, so I'm sure there's something I'm missing. I'll try to read the paper again at some point and hope I have better luck with it. But if you think you understand what he's saying, please try to explain. — Dusty of Sky
Addendum: after glancing at the equations on pp180-181, I see that he's using probability. I don't have a good grasp of probabilistic logic, but my understanding is that it adds a number of layers of complexity and uncertainty to classical logic. I may be wrong, but I think that the principles of probabilistic logic are quite contentious among logicians. Perhaps quantum mechanics only violates ordinary principles of probabilistic logic, not classical logic. — Dusty of Sky
Mathematically, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic.
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For Putnam, the elements of L(H) represent categorical properties that an object possesses, or does not, independently of whether or not we look. Inasmuch as this picture of physical properties is confirmed by the empirical success of quantum mechanics, we must, on this view, accept that the way in which physical properties actually hang together is not Boolean. Since logic is, for Putnam, very much the study of how physical properties actually hang together, he concludes that classical logic is simply mistaken: the distributive law is not universally valid. — Quantum Logic and Probability Theory - SEP
Perhaps quantum mechanics only violates ordinary principles of probabilistic logic, not classical logic. — Dusty of Sky
That’s because the photon doesn’t go through A1 OR A2, it goes through A1 AND A2. — Pfhorrest
Putnam is saying that the photon going through (slit A1 or slit A2) and hitting region R describes an interference experiment. That is, you don't know which slit the photon went through but, on conventional realist assumptions, it went through one slit or the other. However the photon need not hit region R if you do measure which slit it went through. Now we know this already since this is just what QM predicts. But Putnam's claim is that those two experimental observations are the left-hand-side and right-hand-side of the principle of distributivity, and so violate it. — Andrew M
However I will maintain that there is a sense in which we choose, amongst possible logical systems, that which best fits what it is we are trying to explain.
SO what might very loosely be described as the empirical component of logic is no more than choosing a logic that fits our purpose, when our purpose is describing how things are — Banno
I don't think this necessarily contradicts the principle of distributivity. It seems that measuring which slit the photon goes through affects the conditions of the experiment. So if you don't measure, then both ((A1 or A2) and R) and ((A1 and R) or (A2 and R)) are true. If you do measure, then both are at least potentially false because not-R can be true. Am I still missing something? — Dusty of Sky
1 / | \ A1 A2 R \ | / 0
(A1 or A2) and R = 1 and R = R
(A1 and R) or (A2 and R) = 0 or 0 = 0
Also, here's a derivation of one side of the principle of distributivity. The principle follows from more basic logical principles, so if you reject distributivity, you must also reject at least one of the other principles used in this derivation. — Dusty of Sky
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