Board Thread:Questions and Answers/@comment-26429591-20170613035456/@comment-29375707-20170618220517

Paraconsistent logic is an area in logic that is part of the anticlassics, in which some principles of classical logic are violated. It is currently useful in areas such as computing and artificial intelligence (this link is in Portuguese, but this is due to Newton da Costa, who is also one of the founders of paraconsistent logic and also author of this article, to be Brazilian). Stanford Encyclopedia of Philosophy and the IEP also have articles on paraconsistent logic, and in addition, I would recommend reading Stanford's article on dialetheism, which deals a little bit with the subject. Paraconsistent logic is fairly recent, some of its founders are still alive.

As for Schrödinger's cat, as far as I remember, it is a demonstration of how the interpretation of quantum mechanics developed by Niels Bohr and Werner Heisenberg is strange. It is not literally a cat in a box, but a representation of quantum uncertainty in everyday objects.

And as regards the linguistic limitation to which I have referred, an example of this is the paradox of the liar, which can be expressed as follows:
 * $$(a)$$ Proposition $$(a)$$ is false.

Or:
 * $$(b)$$ Proposition $$(c)$$ is true.
 * $$(c)$$ Proposition $$(b)$$ is false.