ABSTRACT
There is a mistaken generalized idea that antinomies are essentially dependent on negation. In fact, many antinomies have nothing to do with negation but rather with some basic, more general notion of opposition relative to which negation is only a particular case. We present here a logic of opposition as an instrument with which to place antinomicity in its most general setting. In the process, several arguments will be made about the foundations of mathematics which go beyond the issue of antinomicity and which reflect the present and future changes that are and will be taking place in mathematics as a whole, mostly related to the enormous impact that computers are effecting on the way mathematics is practiced from day to day.
