Non-overlap: Truth and falsity are inverse operations that cancel each other out and do not and cannot overlap. You can no more have a proposition that is both true and false than you can have a number that is both positive and negative. This theory is in direct opposition to any glut theory, including dialetheism, which will say that truth and falsity can overlap and are not inverse operations that cancel each other out.
Support for Non-overlap: This theory explains, where gut theories fail to explain, the data of my intuitions (and I bet the intuitions of most people) surrounding the impossibility of everyday contradictions. If there is orange juice in my fridge, this is not merely strong evidence that it is not also the case that there is no orange juice in my fridge. Rather, this is proof that it cannot also be the case that there is no orange juice in my fridge. If a barber has shaved himself, this is proof that he has not also not shaved himself. If a person has casted a ballot, this is proof that they cannot also have not casted a ballot. And so on.
But why would the positive be a proof of an absence of a negative in these cases? Why do I feel so forced to believe that positivity entails an absence of negativity in these cases? Suggestion: Because Non-overlap is true and positivity and negativity are inverse operations and where truth picks out positivity, falsity picks out negativity.
Graham Priest says accounts of negation are contentious. (See: https://plato.stanford.edu/entries/dialetheism/#ArguNega.) Are they? Isn't Non-overlap the common account of negativity?
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