Does quantum mechanics violate the laws of logic?

[Fanghur]

I was having a discussion with someone a little while ago and he made a claim that I found completely preposterous. He claimed that the laws of logic did not apply at the quantum level, which seems entirely self-refuting, as violating the laws of logic is by definition logically impossible. When I say the laws of logic, I am referring to the Law of Identity, which states that something is what it is and is not what it isn't (X = X), the Law of Non-contradiction, which states that in a true dichotomy of X or ~X, nothing can simultaneously be both X and ~X, and the Law of excluded Middle, which states that nothing can be neither X or ~X.

 

I know a fair bit about quantum mechanics, and absolutely nothing that I know about it violates any of these laws; of course, quantum mechanics does indeed violate our notions of common sense and human intuition, but the three laws of logic are necessarily true due to the impossibility of the contrary.

 

Did this person I was talking to simply have a misunderstanding of how quantum mechanics works?

[Joatmon]

I think you will just be arguing about definitions. There are rules of logic for the quantum level and also rules of classical logic. However they can be different(IMO)

 

http://en.wikipedia.org/wiki/Quantum_logic

[studiot]

 

the Law of excluded Middle, which states that nothing can be neither X or ~X.

 

Are you sure ?

 

What about tristate or Kleene's logic?

 

http://en.wikipedia.org/wiki/Three-valued_logic

 

I do believe it was the Bard himself who said

 

"There are more things, in Heaven and Earth, than Man has ever dreamed.

 

Edited July 7, 2013 by studiot

[EdEarl]

It is our innate ability to reason that allows us to postulate formal rules of logic, to hypothesize, to prove, and to communicate. When faced with a task, reason allows us to select a tool that helps, and to realize when a tool does not help.

 

Clearly, QM challenges our ability to understand, because it is not intuitive. Perhaps I am too ignorant to understand your question, because I do not know how to answer it.

 

Does quantum mechanics violate the laws of logic?

[swansont]

I was having a discussion with someone a little while ago and he made a claim that I found completely preposterous. He claimed that the laws of logic did not apply at the quantum level, which seems entirely self-refuting, as violating the laws of logic is by definition logically impossible. When I say the laws of logic, I am referring to the Law of Identity, which states that something is what it is and is not what it isn't (X = X), the Law of Non-contradiction, which states that in a true dichotomy of X or ~X, nothing can simultaneously be both X and ~X, and the Law of excluded Middle, which states that nothing can be neither X or ~X.

 

I know a fair bit about quantum mechanics, and absolutely nothing that I know about it violates any of these laws; of course, quantum mechanics does indeed violate our notions of common sense and human intuition, but the three laws of logic are necessarily true due to the impossibility of the contrary.

 

Did this person I was talking to simply have a misunderstanding of how quantum mechanics works?

 

I'm guessing the person was referring to superposition, which implies a violation. But then, these are classical logical laws, which applies in the physics sense as well, and there are several aspects of QM that seem absurd if you start with a classical physics premise.

[ydoaPs]

In addition to what swansont said, I'd like to point out a common category error in the OP.

 

When I say the laws of logic, I am referring to the Law of Identity, which states that something is what it is and is not what it isn't (X = X), the Law of Non-contradiction, which states that in a true dichotomy of X or ~X, nothing can simultaneously be both X and ~X, and the Law of excluded Middle, which states that nothing can be neither X or ~X.

Logic isn't about anything in the physical world outside of propositions. The propositional calculus is about propositions, that's it. It's not about rocks, or trees, or cabbages or kings. It's about ideas.

 

So, X isn't a thing, but an idea. The three things you mention are three forms of the same proposition.

 

pv~p

~(p&~p)

p->p

 

They're not "nothing can be neither p nor not p", "nothing can be both p and not p", and "if something is itself that it is itself". It is, however, "all propositions are either true or false", "no proposition is both true and false", and "if a proposition is true, then it is true".

[Fanghur]

Are you sure ?

 

What about tristate or Kleene's logic?

 

http://en.wikipedia.org/wiki/Three-valued_logic

 

I do believe it was the Bard himself who said

 

"There are more things, in Heaven and Earth, than Man has ever dreamed.

 

That is a different situation. Excluded Middle only applies to exhaustive and exclusive dichotomies in which there by definition can be no third option or hidden variable. And if you were to claim that 'true or false' were a true dichotomy, you would be incorrect. True or false is not a true dichotomy, 'true or not true', that's the true dichotomy. Therefore the Law of Excluded Middle still applies.

 

And YdoaPs, what you said is certainly true apart from the false dichotomy that I pointed out, however, the laws of logic are also descriptive of the nature and behaviour of existence. It is the nature of all things that exist that they are themselves and not something else; the Law of Identity is our conceptual description of this necessary fact about existence.

Edited July 7, 2013 by Fanghur

[studiot]

 

That is a different situation.

 

Exactly.

 

What 'laws of logic' ?

 

There is not an exclusive set!

[Fanghur]

 

Exactly.

 

What 'laws of logic' ?

 

There is not an exclusive set!

That is why I specifically named the ones I was referring to.

[studiot]

You certainly named them, but what makes you think they have universal applicability?

 

I showed you a system to which they do not apply.

[Fanghur]

You certainly named them, but what makes you think they have universal applicability?

 

I showed you a system to which they do not apply.

 

No you didn't, and in fact I specifically explained how they would apply even to that system of logic, or at the very least would not be violated by that system of logic, as they deal with dichotomies, and the system you named deals with trichotomies.

[D H]

When I say the laws of logic, I am referring to the Law of Identity, which states that something is what it is and is not what it isn't (X = X), the Law of Non-contradiction, which states that in a true dichotomy of X or ~X, nothing can simultaneously be both X and ~X, and the Law of excluded Middle, which states that nothing can be neither X or ~X.

 

Per the Copenhagen interpretation of QM, Schrödinger's cat is simultaneously alive and dead until the wavefunction collapses. Per the multiple worlds interpretation, the alive cat persists in some alternate reality after the observer sees the cat is dead. Either way, classical logic goes bye-bye.

 

There's nothing saying those laws are sacrosant. Fuzzy logic, for example, essentially is a rejection of the law of the excluded middle.

[studiot]

 

and the system you named deals with trichotomies.

 

 

 

Actually it doesn't.

 

In a dichotomy the outcomes are defined are one of two possibilities, there are no other alternatives.

In a trichotomy the outcomes are defined as being one of three possibilities, again there are no other alternatives.

 

In trisate logic there is an indeterminate outcome available. There is still a defined binary input.

 

The point of indeterminate is that it is not determinate.

[Fanghur]

But that doesn't mean that it doesn't actually have one.

[studiot]

Sure it does.

 

The point about a determinate outcome is that it is the same every time the experiment is repeated under the same conditions.

 

The point about an indeterminate outcome is that it may be the same every time, it may be differeent each time.

 

Further with a tristate logic chip the output may enter a state not recognised by succeeding circuitry.

Edited July 8, 2013 by studiot