Is formal logic an instrument of male supremacy?

During the 1970s many embraced the idea that “everything is political.” This statement is clearly too categorical, though there may be something to be said for the notion that many things are either tinged with politics, or are capable of such tincture.

A particular application of this notion is the idea that mathematics and formal logic, at least as we have known them in the West, are instruments of male supremacy. This is the central thesis of the magnum opus of the late Arthur Evans, “Critique of Patriarchal Reason” (1997).

Evans, who did graduate work in philosophy at Columbia University, seeks to trace the evolution of what he terms “the Parmenidean myth” from the fifth century BCE to the present. The sole surviving writing of Parmenides is a poem,,“On Nature.” There the Pre-Socratic thinker sets forth two views of reality. In "the way of truth" section of the work, he argues that reality (described as "what-is") is unitary, change is impossible, and existence is timeless, uniform, necessary, and unchanging. In the contrasting "way of opinion," he explains the world of appearances, in which one's sensory faculties lead to conceptions that are false and deceitful.

Evans pays little heed to Parmenides’ eccentric, counterintuitive view that change cannot occur. Yet he is much taken with the implications of the binary contrast, a principle that he calls “bivalance.” This point recalls Jacques Derrida’s postmodernist denunciations of binarism. Evans does not mention Derrida, but it seems that the idea was in the air at the time Evans conceived his book.

To the principle of bivalence, Evans adds to the purported Parmenidean heritage “the universal force of logical necessity” and “the inherent superiority of an impersonal static model of lnoledge and reality” (p. 94). Reverberating down the centuries, as seen in such figures as Leibniz, Frege, and Bertrand Russell, this malign triad has served as the preeminent support of male supremacy. Why should this be so? Surely it cannot simply be that “the Parmenidean myth” has been mainly espoused by men. This would be a rather transparent instance of guilt by association, one that would backfire since Evans is a man. If the adoption of a view by a man or men is sufficient to taint it, then the “Critique of Patriarchal Reason” must be rejected, together with the writings of all those other Western Civ icons.

Evans offers a familiar argument to the effect that absolute objectivity is rarely, if ever achieved. Just so, but we can strive to reduce the subjective element in accordance with striving for truth--something that does actually exist. Much of this subjectivity derives, to be sure, from one's gender, nationality, and social status. In this sense, all knowledge is situated knowledge.

Evans points out, persuasively in my view, that the homosexuality of Ludwig Wittgenstein affected his approach to philosophical problems. By contrast his mentor, Bertrand Russell, thought that homosexuality was the result of bad parenting, and was dismayed when his gay son John came out to him. How did Russell's orientation affect his views? Evans fails to explore this possibility. He is, however, admirably clear about the way the Wittgenstein establishment, fearing that the truth about the Austrian thinker's sexual orientation would damage his standing as a philosopher, attempted to squelch any discussion of the matter.

Evans seems particularly troubled by the either-or aspect of the principle of bivalence. It has, he believes, inflicted on us such pairs as male vs. female and heterosexual vs. homosexual. In these contrasts one pole tends to be viewed as superior to the other. However, if patriarchy is as pervasive as Evans believes, surely it is wily enough to survive without such props, It can find other rationales.

Moreover, a moment's reflection will show that even in ordinary thinking we are not hobbled by any such absolute principle of bivalence. Consider the binary “hot” vs. “cold.” Every sensible person recognizes that there is a spectrum of such thermic states: ice cold is different from cool and warm is not the same as hot.

Still Evans labors on. He thinks that we will be able to shed the sexist shackles of Parmenideanism if we adopt something he calls "gradient logic." This approach (sometimes unfortunately termed Fuzzy Logic) permits one to detect more than two points in a continuum. Yet this ploy has always been available, even to those who have not benefited from a college education, as the sequence cold-cool-warm-hot demonstrates.

Arthur Evans says that it took him nine years to write the book. Since it was published in 1996, the inception would go back to 1987, an interesting point in intellectual history.

Let us turn first to the feminist writer Sandra Harding’s “The Science Question in Feminism” (1986). In the following passage she begins with an interesting observation on a type of metaphor that occurs in some authors of the early modern period. But then she takes us on a wild ride.

“One phenomenon feminist historians have focused on is the rape and torture metaphors in the writings of Sir Francis Bacon and others (e.g. Machiavelli) enthusiastic about the new scientific method. Traditional historians and philosophers have said that these metaphors are irrelevant to the real meanings and referents of scientific concepts held by those who used them and by the public for whom they wrote. But when it comes to regarding nature as a machine, they have quite a different analysis: here, we are told, the metaphor provides the interpretations of Newton's mathematical laws: it directs inquirers to fruitful ways to apply his theory and suggests the appropriate methods of inquiry and the kind of metaphysics the new theory supports. But if we are to believe that mechanistic metaphors were a fundamental component of the explanations the new science provided, why should we believe that the gender metaphors were not? A consistent analysis would lead to the conclusion that understanding nature as a woman indifferent to or even welcoming rape was equally fundamental to the interpretations of these new conceptions of nature and inquiry. Presumably these metaphors, too, had fruitful pragmatic, methodological, and metaphysical consequences for science. In that case, why is it not as illuminating and honest to refer to Newton's laws as "Newton's rape manual" as it is to call them "Newton's mechanics"?”

Another example comes from the Belgian Francophone writer Luce Irigaray (“Parler n’est jamais neutre,” 1985).

“Is e=mc2 a sexed equation? Perhaps it is. Let us make the hypothesis that it is insofar as it privileges the speed of light over other speeds that are vitally necessary to us. What seems to me to indicate the possible sexed nature of the equation is not directly its uses by nuclear weapons, rather it is having privileged what goes the fastest.”

Now that a quarter of century has passed, these effusions have come to seem quaint. Lengthy as it is (376 double-column pages), Evans' argument emerges as simply a gay-liberation counterpart of these extravagant feminist indictments.

POSTSCRIPT. In fairness I should note that, for a philosophy book, Evans' "Critique" is quite well written. It also contains useful analyses of the achievements of such figures as Gottlob Frege, Willard Van Orman Quine, and Ludwig Wittgenstein. Dare one call them seminal? Oh, well.