Quantum logic: Can the logical statement P 鈭?卢P ever be false?

Probably. In Quantum computing, there is something called a ';cat state'; (named after the Schrodinger's Cat problem). In this state, both p and 卢p are true, and thus p %26amp; 卢p is true. (I'm letting p mean ';All the qubits are |0%26gt;).





If p %26amp; 卢p is true, then ~(p v ~p) is also true. You can use DeMorgan's equivalences to convince yourself of this, assuming they still apply in quantum logic (and they might not... I'm not sure which is why I say ';probably'; as my answer).





And of course, if ~(p v ~p) is true then p v ~p is false.





On a side note, the issue you're raising was also mentioned by W.V.O. Quine in his paper ';Two Dogmas of Empiricism.'; He claimed that the laws of logic might need to be revised in light of the problems quantum mechanics raised for the Law of the Excluded Middle.Quantum logic: Can the logical statement P 鈭?卢P ever be false?
As a quantum state, it can be uncertain until observed. The waveform is uncollapsed, therefore it may not be in either state.





It is, essentially, both P and !P.Quantum logic: Can the logical statement P 鈭?卢P ever be false?
it's always true
I don't think so.





What is more, I think quantum logic isn't quite right because they would have to accept (if they accept ~(P or ~P)) logical contradictions. I think any system of logic, or for that matter any way of understanding something which allows for contradiction is not just odd but absurd. I think it is just a psychological fact that people cannot conceive that P while also at the same time properly conceive that ~P (this is not to say that, therefore, logic is a psychological thing, rather it is just to say that conceiving a contradiction is impossible).





It may be that quantum logic can describe what we think is going on at some quantum level, yet, I think if we do this we dispense of necessary truths that are required for a general understanding of anything whatever.





So, if we accept that 'S is both a C at time T and S is not a C at time T' we are saying, then, we are saying contradictions are in some sense possible - BUT the only sense in which they are possible is just this: a particular object can have incompatible properties, say the quanta S has the property P at time t and has property Q at time t, where P and Q are incompatible. I don't think is a logical contradiction per se, but it seems like it is at first glace.


It would be more like a logical contradiction if it had property P at T and did not have property P at T...this, I think, is not psychologically conceivable.