George Boole and the Calculus of Thought (2018)
3quarksdaily.com
3quarksdaily.com
And yet.. quantum mechanics managed to break the most certain of all principles. Or actually.. the man who says "I always lie", does he belong to the group of people who always lie, or does he not belong to it?
The universe we live in turns out to be an interesting place, at least.
(3) Sentence (3) is false.
(Or, "What I am saying right now is a lie.")
That's because you're conflating "spin" for "angular motion" in classical physics. They just aren't the same thing, as particle spin clearly has different properties.
No, it's called spin because it's a quantum mechanical form of angular momentum that simply has no analog in classical physics, and some physicists at the time suggested a physical interpretation that was consistent with an older form of quantum theory.
> In the quantum world it's still possible to be in both states or places at once - and that's where the quantum weirdness is. Nobody would care or talk about it if being in two spin states at the same time wasn't more strange than wearing a shoe and a tie at the same time.
Again, because they are conflating it with classical notions. Superposition has classical, deterministic interpretations which feature none of this apparent "weirdness".
Though natural language logic remains the same.
> Or actually.. the man who says "I always lie", does he belong to the group of people who always lie, or does he not belong to it?
The Russell-type paradox is more interesting than the liar-type paradoxes since it is not susceptible to the same resolutions (though can be avoided with a theory of types).
So, Aristotle holds, because the page is not "blank" and "not blank" at the same time.
That's false. Quantum logic satisfies the principle of non-contradiction (the logical property described in the quotation from Aristotle).
The mistake you're making is misinterpreting the superposition of p and ~p, which is a combination of being p with some probability and ~p with some probability, with the simultaneous possession of p and ~p with certainty in both cases. Quantum mechanics doesn't say the latter is possible.
What Quantum Mechanics actually postulates is that even talking about those properties makes little sense if somebody doesn't look at them (it's more of the tree falling with nobody to hear paradox), and once you look you may get one of the properties with some probability.