Kropotkin on the dialectic

I was reading some of Kropotkin's revolutionary pamphlets recently, and I was particularly struck by "Modern Science and Anarchism," which seeks to defend actual science as the only way to advance the ideas of anarchism, in opposition to more philosophical approaches. Regarding the dialectic in particular, K. says:

"We have heard much of late about "the dialectic method," which was recommended for formulating the socialist ideal. Such a method we do not recognize, neither would the modern natural sciences have anything to do with it. "The dialectic method" reminds the modern naturalist of something long since passed - of something outlived and now happily forgotten by science. The discoveries of the nineteenth century in mechanics, physics, chemistry, biology, physical psychology, anthropology, psychology of nations, etc., were made - not by the dialectic method, but by the natural-scientific method, the method of introduction and deduction. And since man is part of nature, and since the life of his "spirit", personal as well as social, is just as much a phenomenon of nature as is the growth of a flower or the evolution of social life amongst the ants and the bees, there is no cause for suddenly changing our method of investigation when we pass from the flower to man, or from a settlement of beavers to a human town.

The inductive method has proved its merits so well, that the nineteenth century, which as applied to it, has caused science to advance more in a hundred years than it had advanced during the two thousand years that went before. And when in the second half of the century this method began to be applied to the investigation of human society, no point was ever reached where it was found necessary to abandon it and again adopt medieval scholasticism. Besides, when philistine naturalists, seemingly basing their arguments on "Darwinism," began to teach, "Crush whoever is weaker than yourself, such is the law of nature," it was easy for us to prove first, that this was not Darwin's conclusion, and by the same scientific method to show that these scientists were on the wrong path; that no such law exists: that the life of animals teaches us something entirely different, and that their conclusions were absolutely unscientific. They were just as unscientific as for instance the assertion that the inequality of wealth is a law of nature, or that capitalism is the most advantageous form of social life calculated to promote progress. Precisely this natural-scientific method applied to economic facts, enables us to prove that the so-called "laws" of middle-class sociology, including also their political economy, are not laws at all, but simply guesses, or mere assertions which have never been verified at all."

I tend to agree with Kropotkin here, although I think his criticism is a bit too harsh, and perhaps not totally unrelated to his great dislike of Marx in general. The Marxist dialectic after all does not contradict scientific experimentation, although it does potentially come into conflict with a hard positivist perspective that sees science as independent of social causes and completely transcultural. But this is not K's position; he does afterall point out that scientists can be in the service of capitalism, cooking up bogus social darwinist theories for example.

So what do people here think? Is there a conflict between Marxist dialectics and the scientific method? And if so, which one is more useful to advancing anarchist ideas?