Dorothy Wrinch (1894–1976) was a productive and intelligent philosopher, mathematician, and biochemist who contributed to a wide array of fields. She published in economics and probability, x-ray crystallography and protein structures, the cardinal arithmetic of Principia Mathematica‘s second volume, and, of course, philosophy. One of her particular interests was the relation between philosophy and logic, and logic’s role in the scientific method.
Wrinch holds many distinctions. She was the first woman to teach mathematics to men at Cambridge. She was a single mother in academia during a period that was doubtless especially hostile to women in the workplace. In 1930, she also wrote a pseudonymous book, The Retreat from Parenthood, that was no doubt partly informed by this experience, and one that might be viewed as a counterpart to Russell’s 1928 Marriage & Morals. Wrinch wrote a thesis on logic, sadly now lost so far as I know, under Bertrand Russell’s supervision, though this was unofficial because Russell had been sacked due to his pacifist activities during the World War I; officially, G. H. Hardy was Wrinch’s thesis supervisor. She also got into a bitter dispute with Linus Pauling over the structure of proteins, a dispute now known as the “cyclol controversy.” These biographical details are covered in Marjorie Senechal’s superb I Died for Beauty: Dorothy Wrinch and the Cultures of Science.
Here I want to focus on a hilarious episode from 1917, that one time Wrinch threw mad shade at a Professor L. P. Saunders, who was criticizing Russell’s 1914 Lowell Lectures, known to us at Our Knowledge of the External World: As a Field for Scientific Method in Philosophy. Wrinch, then a graduate student studying mathematics at the University College London, was responding to Saunders’ critical piece on Russell’s Our Knowledge.
Saunders argues, somewhat bizarrely, that if facts involving sense-data and the laws of logic are certain, then nothing else is certain:
Mr. Russell, I have to point out, regards the laws of logic and sense-data as the hardest of hard facts; thus, in the end, the other hard facts…are not really “certain”. It is fair, therefore, to say that the only facts that are known, according to Mr. Russell, are sense-data and the laws of logic…
Mr. Russell, like all empiricists, does not take his own position with sufficient seriousness. He tells you, in effect, that sense-data alone are certain facts; and in violent contradiction to this he asks you to accept a great many other statements (viz., the statements constituting his position as such, statements about it, and statements about other philosophies) as true! And yet one would have thought it unnecessary to have to point out that if sense-data are the only really certain (i.e. certain) facts, that then nothing else is certain. Unfortunately, although this is, in one sense, quite clear, it is also, in another sense, not clear, seeing that this statement itself claims to be true. How Mr. Russell came to overlook this is very difficult to understand. (Saunders 1917: 49-50)
Of course, Russell’s view by no means implies that whatever is implied by the laws of logic in conjunction with facts about sense-data are not part of the certain facts. Surely, whatever is logically implied by these is also certain. Wrinch rightly picks up on this point, finding Saunders’ reasoning ridiculous and saying as much in her 1917 reply:
Now it must be evident that in general, it is possible to infer from a given set of premisses which includes a principle of deduction, other propositions not contained in this set.² In the system we are discussing, the Laws of Logic are included in the premisses and yet Prof. Saunders takes exception to the fact that other propositions are asserted, apparently merely because they are different from the premises. […] Since the Laws of Logic are included in this body [of certain propositions], all logical deductions from the premisses can be justifiably asserted in his system. This class of propositions will, I think, cover all Mr. Russell’s statements “constituting his position as such, statements about it, and statements about other philosophies”. (Wrinch 1917: 449)
Ouch. But that was not the shade that inspired this post. It is this little footnote 2, which reads:
Cf. Principia Mathematica in which three volumes of propositions are inferred from a very small number of primitive propositions.
That is a hilarious rejoinder, indeed. “You think that if the laws of logic and facts about sense-data are certain, then nothing else is? Have you even read Principia?”