Non causa pro causa
Non causa pro causa
or false cause, is the fallacy, incident to the method of proof by reductio ad absurdum (q. v.), when a contradiction has been deduced from a number of assumptions, of inferring the negation of one of the assumptions, say M, where actually it is one or more of the other assumptions which are false and the contradiction could have been deduced without use of M. This fallacy was committed, e.g., by Burali-Forti in his paper of 1897 (see Paradoxes, logical) when he inferred the existence of ordinal numbers a, b such that a is neither less than, equal to, nor greater than b, upon having deduced what is now known as Burali-Forti’s paradox from the contrary assumption he had used without question the assumption that there is a class of all ordinal numbers. — A.C.