The Lacanian Delusion
It is true that some mathematicians --- Brouwer's school of ``intuitionists'' --- disdain reductio proofs, and Lacan may have caught some echo of this. They are motivated, however, not by any acceptance of contradictions, but by unease about applying the law of the excluded middle to infinite sets. (The principle of non-contradiction holds that any statement is either true or false; the law of the excluded middle, with which it is often confused, holds that, for any object x and any property A, either ``x is A'' is true or ``x is not A'' is true.) This rules out many sorts of proof by contradiction, which must be replaced by proofs by explicit construction, greatly complicating the development of branches of mathematics like the real numbers. (For a brief summary, see Kleene, Introduction to Metamathematics, sec. 13.) --- All of this is, however, taking us blessedly far from Lacan; let us return to our sheep.