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From just the Wikipedia article and a few stray references here and there, I don't understand what Laruelle's "non-philosophy" is and how it can by aptly be described by its title.

The link above quotes Ray Brassier, who

defines non-philosophy as the "theoretical practice of philosophy proceeding by way of transcendental axioms and producing theorems which are philosophically uninterpretable"

What does 'philosophically uninterpretable' mean? If a statement is uninterpretable, doesn't that make it meaningless? If it isn't meaningless, than I can discuss/ponder it's meaning or relevance, and that already lands us into philosophy. The comparison to Euclid and non-Euclidean geometry seems unfair, as we wouldn't call non-Euclidean geometry "non-geometry" because it still concerts shapes and their mathematical properties. Similarly, isn't Laruelle still attempted to deal with the questions or topics of philosophy?

Furthermore, non-philosophy is a critique of philosophy for its dialectical splitting, which is never justified.

First of all, not all philosophers engage in making distinctions, and secondly, justification for their distinctions has indeed been a great concern for many of these philosophers and is often the subject of much ongoing discussion. Should we call such discussions 'non-philosophical', because it questions the legitimacy of earlier philosophers? And what of those 'dialectal splittings' that do appear to makes sense, or seem to be correctly induced from the state of things as we perceive them? Should they be any less justified than any claim made by Laruelle?

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A quick qualification: Laruelle's decades-spanning project is going to be something very difficult to convey accurately in a few paragraphs, especially when trying to field the supplemental questions you pose here. It might make sense to try to approach all this a bit more straightforwardly, slowly, incrementally -- if a careful, pedagogical explanation of the material is actually what you're after :)

Another qualification: while I am not really an expert on Laruelle, I have attempted to read it in good faith, and have plugged through a lot of his work that's available in English. Finally, I do find myself quite sympathetic to his project.

More or less the basis of my own interest in Laruelle, and at the very least a key reference, is Deleuze and Guattari who at the end of What is Philosophy? talk about nonart, nonscience, and nonphilosophy as "outsides" of art, science, philosophy. These negations form part of a shadow which renders art/science/philosophy indiscernible; the shadow of a future people, a people to come, capable of advancing beyond the arbitrary/neurotic/anthropoid divisions between these creational practices (towards a reunified/indivisible art-science-philosophy, something like what Nietzsche talks about with his joyful wisdom which would reunite art and science once they have sufficiently "matured".) Philosophy needs a nonphilosophy to comprehend it, D+G say. It is definitely a nod to Laruelle and they mention him as one of the most interesting working contemporary French philosophers in a footnote (note this was some 20 years ago.)

Okay. So let's start thinking about decisions, or as you emphasize distinctions or "dialectical splittings". This may seem odd, but Laruelle's point that all philosophies are structured around a prior decision is not an "axiom" for him; rather it is the axiomatic character of philosophy that is here captured in a kind of non-axiomatic way. The decisional structure of philosophy demands not an analysis based on assumptions; but as he says a kind of "dualysis"...

Laruelle identifies something like a Godel-effect operating over the informal-abstract conceptual phase-spaces through which philosophy traces its cognitive trajectories, constructs its planes of reference, effracts new conceptual schema, etc. There is a hole in every philosophical plane of thetic organization. Concepts or system of concepts which populate these planes, and the discourses disclosing them, cannot avoid these vortices. Philosophy inevitably relies on obscure distinctions (confused decisions) that cannot be grasped by that philosophy in itself, or rather that require new concepts ad infinitum. I am tempted here to talk about the fractality of sense or thought, the fragmentation of philosophical "dimensionality". But again this is really endemic to an image of thought called "philosophy" (Aristotle says Zeno invented the dialectic with his paradoxes of motion.)

One key to my mind is the "non-Marxism" of Laruelle; as Deleuze says, for most of history, philosophy amounts to an image of thought that enforces stupidity, that actuallys stops people from thinking. Laruelle says something to the effect that future generations may not show the same gratitude towards philosophy -- and its repressive, neurotic, stunting effect on human thought and ultimately life on the planet -- that we are still hypnotized into showing today. Nonphilosophy is a kind of generalization of Marxism, at its humanist core a project about improving the condition of humanity in the world. For Laruelle, radical immanence is "humanity in person".

So Laruelle posits the "transcendental" equivalence of all philosophical positions: a kind of "suspension" of certain philosophical axioms in order to open up a space for thought, experimentation, learning, creation, etc., outside the (regressive, exploitative, philosophical) image of thinking, knowing, creating; making use of philosophical materials in new ways...

Hopefully this represents some starting points and helps give a sense of the spirit of the work. Apologies for the obscurity/sparseness of this presentation (it is going to be difficult to summarize his project briefly, and it may be more constructive to approach the subject a bit more iteratively; please consider asking further questions here!) Laruelle's work is definitely difficult, but can also be incredibly rewarding; I would definitely recommend looking at Philosophy and Non-Philosophy and Principles of Non-Philosophy, both of which should now be available in English translation.

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What does 'philosophically uninterpretable' mean? If a statement is uninterpretable, doesn't that make it meaningless?

well if the wikipedia article is reliable, the author is probably talking about ways of thinking that A) are not translatable into a specific [traditionally philosophical] vocabulary, and B) cannot be answered in those terms.

perhaps this can seen to be possible through examples.

Newtonian physics cannot explain the Planck effect, and those empirical results cannot be interpreted in classical mechanics; in classical mechanics there are A) no quanta, and B) no explanation of quanta

https://physics.stackexchange.com/questions/57771/newtonian-mechanics-and-quantum-mechanics

Commensurability is a concept, in philosophy of science, whereby scientific theories are commensurable if scientists can discuss them in terms permitting direct comparison of theories to determine which theory is truer.

from wikipedia ^^. similarly vitalists cannot tell you why electrons have negative charge.

more generally, it would be wrong to say that all truth or even thought is "philosophical". i doubt that l. is claiming that philosophical tools of thought must all be abandoned, only urging philosophers to create a new vocabulary, questions etc. that may have surprising successes.

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