Hitherto this has been the only mathematical outlet for the humour of mathematicians; and those who really had the interests of mathematics at heart saw with alarm the growing tendency towards scholasticism in mathematical jokes. Fortunately the discovery of logic by some mathematicians has removed this danger. Still to many mathematicians logic is still unknown, and to them--to Professor A. Schoenflies for example--modern mathematics, owing to its alliance with logic, appears to be sinking into scholasticism. It is true that the word "scholasticism" is not used by Professor Schoenflies in any intentionally precise signification, but merely as a vague epithet of disapproval, as the word "socialism" is used by the ordinary philistine, and this would certainly serve as a sufficient excuse. But no excuse is needed: these opinions are themselves a source of mathematical jokes. FOOTNOTES: [96] See Chapter XII. [97] _Encykl. der math. Wiss._, vol. iv., part i., p. 474. CHAPTER XXXVII THE PARADOXES OF LOGIC We have already[98] referred to the contempt shown by some mathematicians for exact thought, which they condemn under the name of "scholasticism." An example of this is given by Schoenflies in the second part of his publication usually known as the _Bericht über Mengenlehre_.[99] Here[100] a battle-cry in italics-- "_Against all resignation, but also against all scholasticism!_"-- found utterance. Later on, Schoenflies[101] became bolder and adopted a more personal battle-cry, also in italics, and with a whole line to itself: "_For Cantorism but against Russellism!_" "Cantorism" means the theory of transfinite aggregates and numbers erected for the most part by Georg Cantor. Shortly speaking, the great sin of "Russellism" is to have gone too far in the chain of logical deduction for many mathematicians, who were perhaps, like Schoenflies,[102] blinded by their rather uncritical love of mathematics. Thus it comes about that Schoenflies[103] denounces Russellism as "scholastic and unhealthy." This queer blend of qualities would surely arouse the curiosity of the most _blasé_ as to what strange thing Russellism must be.[104]