Quote:
Originally Posted by tame_deuces
"A exists and does not exist" is not a contradictory statement. In case it isn't intuitive why: For it to be contradictory, you need to establish a rule that is broken.
In the future when you want to be sarcastic about people's understanding, you should take more care to use the terminology you are employing properly.
And yes, this is important. In physics for example, some phenomena can behave like two different things at once in certain models - those models do not contradict themselves nor some accepted universal principle.
I don't think this is quite right. Starting with the physics example, I assume you are referring to the so-called wave/particle duality, so that you might say "an electron is a wave and is not a wave". You are using that formulation to assert that this statement is not actually contradictory because in QM the behavior of electrons really does have both wavelike and non-wavelike characteristics.
The problem is that, even though this second statement is true, the first is not, depending on whether or not the copula is taken to be exhaustive, as it usually is. That is, if "is" means something like equality in algebra, then it really is contradictory to say that A is B and is also not-B, but that's not what is actually going on in QM. It's actually much more correct to say that "electrons are neither waves nor particles," but that both the "wave" and "particle" concepts, and their associated models, are oversimplifications from classical mechanics that partly capture the behavior of electrons, but not so much as to make it true that an electron
is a wave in an exhaustive sense. The problem is that the phrasing "an electron is a wave" suggests that exhaustive sense, which is why "an electron is a wave and is not a wave" is a contradiction. Basically, there is a map/territory problem.
This isn't a question of there being some external rule to be broken, it's just a question of the foundations of logic and the concepts of identity and equality. The general formula A is B and A is not B is a contradiction given the most basic conceptual definitions of identity and equality. What makes the wave/particle duality non-contradictory is that it is, in fact, not actually a duality. The reason we describe it as such is an historical accident. The concepts of wave and particle in physics are not comprehensive and essential identities in the way that classical logic requires in order to function.
On the other hand, it has been argued that the real problem with formulations like "A exists and does not exist" is that
existence isn't properly a predicate. That's a separate issue, but using the normal rules of logic "A is B and is not B" is contradictory. Examples from physics don't actually disprove that, instead they have to do with the limits of our logical (conceptual) formulations of empirical phenomena.