When I speak about anti-scientific and anti-rationalist tradition, I don't imply that we may be "pro-science" or a-critic about "science", and dogmatic "pure rationalists" but mostly that the tradition is specific to far-right. But I think that what I say is more revelent concerning the french or european contexts I'm living in.
I think that from bakunin to feyerabend, a lot of valuable critics have been made concerning the logic of science, and the way any kind of power use the idea of science so as a new god. (a good sum up of this to me is this book :
https://libcom.org/library/review-science-capital-radical-essays-science-technology-various).
But, for example, as far as I'm concerned, as anarchists we may subscribe to the principle of "reasonable doubt". By that I mean that it should be a good start to considere that people who deny simple and basic inter-subjective realities (as "2+2=4", to take back the famous point of Orwell) should be regarded with skepticism.
On the contrary, most of far right "intellectuals" right here reject this idea of reasonable doubt by asserting things without any evidences, just arguing that "the actual power is trying to hide everything from us". Here it's very linked to the anti-communist intellectual tradition, as if so-called communist regimes were the only ones that used methods of falsification of history, mass propaganda, etc.
I also disagree on the idea that conspirationnist give evidences of their claims. Most of them on the contrary give a lot of ultra-skeptic arguments, and then ask you to give evidences that what they say is wrong.
This method is very close to the religious rhetorical methods of fallacious argument.
I give you an example : I say that god exist, and that it's a big electron floating in space looking at us. Prove me I'm wrong. You can't ? Then maybe I'm right. This this type of argumentative method is essentially based on false inferences rather than logical deductions .
This reject of reasonable doubt and ultra-skepticism (but always partisan and always negating certain aspects of reality -be it the principle of oppression, or the violence of the state, or historical facts, or even the existence of the moon...) is always used to bypass any contradiction or even facts that enter in conflict with their political theories and authoritarian perspectives.
To me, it seems that anarchism, as a set of methods of struggle and analyse, tends to base itself on practice and try to accept the facts (be it always again established on inter-subjective consensus about "reality") even when they go against some of our own ideas, theories or principles.
To be more specific, it's not a coincidence to me if the vast majority of people who deny the existence of the nazi genocide are far-rightists or neo-fascists, as it's no coincidence if most of the creationists are actually are religious bigots and theocratic charlatans. It's linked to their ideologies and their paradigms. When we can't think about the deep causes or real aims of such theories, we shall take look at who broadcast it, and their immediate consequences.
Then, about new age shit conspiracy theories ("ancient aliens", illuminati stuff, reptilians, etc), I would say -if I didn't say it before already- that most of it should be called something like a form of modern mythology intended to confuse the brain of the exploited, dominated and/or excluded people.
In fact, I would say that the new-age conspiracy theories are a sounding board for ultra-authoritarians to cover their shit, and especially (but not exclusively, stalinists and some other leftists are to include) neo-fascists and far right theories and analyses of society.
Antisemitism (or other forms of systemic racism) fulfills some of the same features, including diverting possible social anger and rage against power towards invisible enemies or scapegoats.
You would quickly remark, if you read a bit about it, the dazzling similarity between the old conspiracy theory designating the Jews (or "the zionists") as an "organized community " or a " secret society "aiming to dominate the world (or already controlling it) and the rest of the modern conspiracy theories involving a secret plot for world domination, and a pyramidal structure.
The other big problem with this idea is that it doesn't analyse society as the result of contradictions, movements, and antagonisms, or as a set of oppressive and coercive systems or institutions, or even as a complex web of social relationship, but only as the product of an "invisible hand" that would have created it all.
I partly agree with the idea of anok that conspirationnists share with anarchists a trend to be very critical concerning any kind of official truth, but the big difference that make the seperates them from "us" is that anarchists designate themselves (simply by calling themselves anarchists) as advocates of a certain ethic, implying to me what I call reasonable doubt.
This raises two questions : should we doubt everything ? And can we really reasonably doubt everything ?
On the principle, I would say yes to the first question, without any doubt. To the other, I doubt that it should be possible. ;-)
edited to make a comment