To Engels’s mind, there was nothing in math that was not already in nature; mathematics was simply a reflection and an explanation of the physical world. As a result, he attempted to crowbar all sorts of mathematical models into his system of dialectics. “Let us take an arbitrary algebraic magnitude, namely /a,” /begins one passage in /Dialectics of Nature. /“Let us negate it, then we have /-a /(minus /a). /Let us negate this negation by multiplying /-a /by /-a, /then we have /+a, /that is the original positive magnitude, but to a higher degree, namely to the second power.” As the Trotskyist scholar Jean van Heijenoort points out, this is all horribly confused: to take just one example, ‘’negation" in Engels’s usage can refer to any number of differing mathematical operations. Worse was to come as Engels, playing the reductive philistine, dismissed complex numbers and theoretical mathematics—those parts of theoretical science that went beyond a reflection of natural phenomena—as akin to quackery: “When one has once become accustomed to ascribe to the [square root of] -1 or to the fourth dimension some kind of reality outside of our own heads, it is not a matter of much importance if one goes a step further and also accepts the spirit world of the mediums.”

[C]ommon-sense deontological morality, standing between egoism and consequentialism, sometimes seems to be caught in a kind of normative squeeze, with its rationality challenged in parallel ways by (as it were) the maximizers of the right and of the left: those who think that one ought always to pursue one’s good, and those who are convinced that one should promote the good of all.

[A]nalytical Marxists do no think that Marxism possesses a distinctive and valuablemethod. Others believe that is has such a method, which they call ‘dialectical’. But we believe that, although theword ‘dialectical’ has not always been used without clear meaning, it has never been used with clear meaning to denote a method rival to the analytical one[.] […] I do not think that the following, to take a recent example, describes such a method: “This is precisely the first meaning we can give to the idea of dialectic: a logic or form of explanation specifically adapted to the determinant intervention of class struggle in the very fabric of history.” (Étienne Balibar,The Philosophy of Marx, p. 97.) If you read a sentence like that quickly, it can sound pretty good. The remedy is to read it more slowly.

Hegel n’a pas de problèmes à poser. Il n’a que la dialectique. M. Proudhon n’a de la dialectique de Hegel que le langage. Son mouvement dialectique, à lui, c’est la distinction dogmatique du bon et du mauvais. […] Ce qui constitue le mouvement dialectique, c’est la coexistence des deux côtés contradictoires, leur lutte et leur fusion en une catégorie nouvelle. Rien qu’à se poser le problème d’éliminer le mauvais côté, on coupe court au mouvement dialectique.

Hegel’s system of dialectical logic has never won acceptance outside an isolated and dwindling group of incorrigible enthusiasts.