Let’s discuss Nietzsche’s explicit hatred of the syllogism and its enduring relevance to reactionary politics more generally. According to him, “the knife-thrust of the syllogism” is how “Greek taste undergoes a change in favour of dialectics,” how “the rabble gets on top.” “That is why the Jews were dialecticians,” he added.
To give context to the following elaboration, let me quote at some length what I wrote in “Really Existing Fascism” a few years ago:
As Losurdo demonstrates in Nietzsche, the Aristocratic Rebel, Nietzsche tenaciously pursued, through various experimental phases, a consistent project of understanding the true source of the “historical sickness” of modernity and its tendency towards — and Nietzsche was not alone in thinking so — a mediocre egalitarianism. Nietzsche, like Marx and Engels, treated liberal hypocrisy and its pseudo-scientific rationalization with disdain. However, he stood at the opposite end of that contradiction. Unlike the forward-looking Marx and Engels, he identified the heights of human civilization in an idealized version of Ancient Greece, and was horrified by both the French Revolution and the Paris Commune. Nietzsche went so far as to identify “the knife-thrust of the [Socratic] syllogism” as the beginning of the end, the first gesture of the resentful slaves’ rebellion against their betters.
Socrates belonged, in his origins, to the lowest orders: Socrates was rabble. One knows, one sees for oneself, how ugly he was. […] With Socrates Greek taste undergoes a change in favour of dialectics: what is really happening when that happens? It is above all the defeat of a nobler taste; with dialectics the rabble gets on top.
Marxists around the world would do the exact opposite: they would look optimistically ahead, dialectically treating time and change as an ally rather than a threat. 
Talking with some friends the matter came up that perhaps more work could be done to explain what the syllogism actually is. It’s very simple. It’s almost hard to explain because it’s like giving a stilted, arcane word to something everyone already knows. The syllogism is just basic logic:
The Law of Syllogism
A form of reasoning in which a conclusion is drawn from two given or assumed propositions.
Statement 1: If p then q.
Statement 2: If q then r.
Conclusion: If p then r.
Nietzsche’s narrative goes like this: before “logic” things just “were.” Nobody had to “justify” themselves before anything or anyone: Masters were masters, slaves were slaves. Here’s the men, there’s the women. Every hierarchy was to be accepted “as it is,” unquestioningly, categorically, naturally, without any pesky “logic” causing any trouble. And Nietzsche presented this as the happiest era for humanity, where slaves were spared painful hope and the idle rich were able to fully dedicate themselves to art.
Logic in this narrative is the dissolving and reconstructing agent that causes change. This is why he preached a more “impressionistic” way of living, always spurning any social pressure to deliver justifications for one’s actions. This is why he is today something of a patron saint for the bourgeois artist, whose credo remains “Art for art’s sake.”
But Nietzsche appeals to more than just artists. Rebels of all kinds, more or less indifferent to art, find immense appeal in the acid way Nietzsche rejected anyone’s efforts to impose any truths whatsoever upon himself: “I was the first to discover truth, and for the simple reason that I was the first who became conscious of falsehood as falsehood. That is to say, I smelt it as such.” Nietzsche’s genius was that he realized by presenting himself as a so-called “skeptic” of all institutions and all morality, by forever refusing the “shackles” of logic, he could find a very roundabout way of getting back to the barbaric “might makes right” political position. What he really discovered was that ruthless ruling class theories of “survival of the fittest,” social Darwnism, eugenics, and slavery could all in fact be dressed in very regal garb, thus opposing Hegel’s progressive modernism.
See, Hegel characterizes humanity itself as driving towards resolution and understanding:
Since the man of common sense makes his appeal to feeling, to an oracle within his breast, he is finished and done with anyone who does not agree; he only has to explain that he has nothing more to say to anyone who does not find and feel the same in himself. In other words, he tramples underfoot the roots of humanity. For it is in the nature of humanity to press onward to agreement with others; human nature only really exists in an achieved community of minds.
Nietzsche, meanwhile, denounces even the study of natural science as a sly way to shackle aristocrats — if they submit to the laws of physics, they’ll soon be submitting to any spurious “humanity”:
“Nature’s conformity to law,” of which you physicists talk so proudly […] is no matter of fact, no “text,” but rather just a naively humanitarian adjustment and perversion of meaning, with which you make abundant concessions to the democratic instincts of the modern soul! “Everywhere equality before the law — Nature is not different in that respect, nor better than we”: a fine instance of secret motive, in which the vulgar antagonism to everything privileged and autocratic — likewise a second and more refined atheism — is once more disguised.
Hegel, Marx, Engels, Lenin, etc. clearly understood that this aristocratic impulse never redounds to the enduring benefit of the masses.
This brings us to the relevance of these considerations. One of the problems with left-wing Americans today is that as a political bloc they haven’t decided whether they’re for or against the syllogism. When it benefits them, they want logic to win. But if making a logical argument is hard, they want “basic humanity” (or something else, like “common decency”) to win out.
Despite internal poverty and inequality, America is constituted as a “ruling country” from top to bottom, where most everyone acts like a barbarian who finds logic stifling. This is why in American political discourse there’s no logic, why Russian President Vladimir Putin appears as an erudite and logical genius by comparison — in reality, as Kit Klarenberg points out, he’s doling out “pretty standard dinner table discussion” (for Serbian standards).
In America it’s impolite for anyone to grill anyone else’s
A > B > C… chains of logic.
The norm is impressionistic, everyone just announces what they stand for and must be either taken at their word or denounced, but nothing is meant or expected to be worked through.
And it’s not just a “ruling class” conceit — perhaps because the whole country is constituted as such a ruling class vis-à-vis the rest of the world, the attitude penetrates from top to bottom, and all the way to the left.
Factors like the tribal loyalty of a fandom, or the stubbornness of hurt ego, or just a simple bribe, are all universally understood to stand higher than logic.
That is America.
And in the style I write (with apology), America refers to more than just a continental landmass. At least a fifth of the planet is now Americanized, in spirit if not by nationality. As B. B. points out, these considerations even apply to superstitious India, whose superficially rabid Hindu-nationalism really betrays quite an international-Americanist character:
A society where logic isn’t placed higher than might or sentimentality is simply a society where the irrational violence of the powerful is so disproportionate and total that it isn’t threatened by the existence of rational oppressed actors. 
But how do we escape this? After all, liberals are nothing if not fond of describing the hapless pleading of leftists as “illogical” and “impractical.” Here is where the Marxist tradition is most distant from the Christian-socialist and anarchist traditions with which it’s so often lumped together in marginality. Consider the following categorization of arguments in light of the preceding discussion of the syllogism:
- Illogical rhetoric. No syllogisms, just aphorisms (whether affirming or decrying the status quo).
- Logical argumentation. Syllogisms are present, perhaps mixed in with some aphorisms to glue things together.
- Dialectics. Logic not only predominates, but is also applied to competing logics. Meta-syllogisms are used to sort out contradictions arising from conflicts between locally-valid syllogisms. 
Let’s look at a concrete example. Liberals often argue, in so many more words, “The corporation has to kill people to survive.” We should resist the temptation to respond to them with something like “Feelings and compassion should prevail over cold logic!” They will not! But Marxists know that we can do better: at the level of core Marxist theorizing (even if not yet at the level of mass rhetoric), higher and more universal global logic has to completely override the petty parochial logic of the bean-counting corporation.
In other words, we can defeat liberal cultists, we don’t have to bow and scrape for their mercy. Indeed, this is the only way out for the working classes. As Marx himself wrote in The German Ideology:
[E]ach new class which puts itself in the place of the one ruling before it […] must represent its interest as the common interest of all members of society […] it has to give its ideas the form of universality, and represent them as the only rational, universally valid ones.
This is the responsibility that falls upon the working classes, and especially upon communists — who historically have never all been themselves of the working class. No matter where they hail from, the most daring and far-out revolutionaries can answer affirmatively and convincingly what’s in it for them and for everybody. This might sound today like “Peace and bullet trains,” or maybe something else entirely. But it has to be argued for and fought for in this way.
Very influenced by Losurdo’s work, I’ve long come to the conclusion that I despise Nietzsche. But I also think of him with a great deal of respect. He was the most intelligent reactionary. He was so adept at his project that many people today under his aegis can be reactionary while portraying themselves as playful and even progressive! If we are to survive what is coming next, we’ll need to leave his decadence behind, and learn to treat the syllogism as our ally once again.
 Nia Frome once sent me these corresponding diagrams in the form of a text message, comparing thoughts and connections between them as nodes and edges, with void spaces between them. It really stuck with me: (1)
o——o o––o, (3)
o–––––o. — R. D.