[Laruelle’s book on Non-Marxism has not yet been published, however, Katerina Kolozova in essay “The Project of Non-Marxism: Arguing for ‘Monstrously’ Radical Concepts” is a fairly comprehensive overview of Laruelle’s project and contains several key insights into his overall argument. One aspect of the project of non-Marxism is the “underdetermination” which in science and the philosophy of science (Quine) is a somewhat more complicated manner but here I take to be the reverse of Althusser’s “overdetermination” which non-philosophically can be defined as a term according to its “determination-in-the-last-instance” (DLI). The non-philosophical usage of the DLI is difficult to summarize. However, in the Principles of Non-Philosophy it is defined as a reduction of the fractional matrix representing the philosophical decision which is comprised of three terms:
[The matrix of the philosophical decision] seems to contain three terms: a real or indivisible identity—the Real one; a term = X, strictly speaking, received from transcendence and which is thus not immanent; and thirdly a term called “Transcendental Identity”, a true clone of the One which the term X extracts from the Real. In reality, the One is not a “term”, not being identifiable in transcendence and being nothing but an identity-without-synthesis; the term X, “added” to the Real, does not form a dyad and fails to form a dyad with the One which refuses to be counted in the structure. On the other hand, it resolves its desire in extracting from the One an image-(of)-the One where the One does not alienate itself; thus a purely transcendental image, but with which it forms a duality or a dual wherein the transcendental is only counted from the point of view of X: a duality called “unilateral” for this reason. This transcendental cloning of the Real represents a simplification and a radical minimalization to the “naturals” of the matrix of Philosophical Decision. (p. 6)
This syntax has received a name in the history of philosophy; a surprising name but of which we believe—though this is not important—that it is indeed this very logic that it designates; logic that is not philosophical, but is nonetheless still interior to philosophy. This name is that of “Determination-in-the-Last-Instance” whose sense the philosophers have barely been able to grasp as a result of their desire to re-dialecticize this form of causality. (ibid.)
Thus, the determination-in-the-last-instance is a decomposed philosophical decision which indicates the immanent causality of the Real, i.e., a philosophical decision in the mode of a “letting” rather than a “forcing” which implies an occasional causality deprived of any philosophical authority. The determination-in-the-last-instance, then, cannot really be defined except in an extremely provisional or contextual sense: it is a syntax, which we can take by its dictionary definition as a “well formed language” of the Real or “degree zero” writing, that concretizes the causality of the real-One as a “transcendental organon,” a kind of (non-)philosophical prosthetic that accords, abides, or adequates-without-correspondence to the Real. More specifically, the “organon” that Laruelle mentions which both comprises the DLI and is its essential function is “force-(of)-thought,” the noetic or transcendental component of the DLI which, “accords radical primacy of the Real over thought with the relative autonomy of thought” (p. 22). Thus, the DLI indicates an instance of the essence of the One (its force-(of)-thought, its minimally transcendental or aproiristic properties) in a manner which, according to the entry in the Dictionary of Non-Philosophy, does not add or subtract anything to the Real itself yet can “enact or possess a causality without being alienated in the material of its action.” The example provided is the Marxist concept of “labor power” or “labor force” (force du travail):
This is an energetic concept of human energy which only exists in the personality of the worker and which is irreducible to his functions or operations, to work output or expended. This concept is necessary so as to transform the object of work into exchange value and is thus creative of value. According to the plan of the Marxist systematic, it articulates the Marxian ontology of the individual and the theory of capitalism. Nietzsche and Deleuze propose an idea of thought as a symptom of forces, establishing its cause in a differential play of multiple forces rather than in a Real-of-the-last-instance. (Dictionary of Non-Philosophy, p. 19)
Philosophically speaking, a concept like labor force allows for certain generalizations, what we will call a signifying infrastructure, which adequates-without-correspondence to the Real. One can certainly apply scientific metrics to the term, e.g. as a term that more comprehensively describes multifactor productivity: the exhaustion of calories as a measurement of the “force” exerted in the act of production relative to the average cost of food per calorie (energy per unit of production) or the usual measurement of worker productivity as the speed and quantity of their economic output (the number of commodities they produce per hour) relative to the price of the commodity they are producing and the firm’s profit, etc.) and, as Kolozova will argue, it describes an element of the “lived experience” of the worker. However, Marxism, I’m sure Laruelle will argue, has both misunderstood and exploited this aspect of their theory (it has certainly been used more for the sake of political persuasion than science and Marxists have gained an unfair amount of mileage with the term even though it was never rigorously defined by Marx). Laruelle says explicitly in Principles that Marxist theorists kept integrating the term into their dialectics of contradiction to the overall detriment of the field, a degenerative tendency of the otherwise relatively scientific field which resulted from its philosophical hangover with Hegel. “Labor force,” defined by Kolozova, however, is much more potent than all that:]
[It] is already a concept, but a radical one, correlating with the Real of the condition of the “Proletariat” as labor force that is non-reflected, lived, experienced. Even the linguistic construct itself, the concept of “labor force,” is merely descriptive of a real condition, consisting of a minimum of transcendence. And it is precisely the method or style of descriptiveness that Laruelle invokes as the non-Marxist and non-philosophical approach par excellence. The minimally descriptive concept, the radical concept, the one in which the Real has “cloned itself,” is the causality in the last instance of a certain theory—it’s Determination-in-the-last-instance (DDI). (“The Project of Non-Marxism,” p. 10)
[Thus, if Kolozova’s article and analysis is to be followed], non-Marxism is a conceptual contraction of Marxism’s terms using non-philosophical methods: it dually exploits the différance implicit in all theoretical terms (that is to say, their explosive syntagmatic and diachronic movement) and their ability to become algebraic constants or “bound variables” that specify their meaning to the extent that this differential movement is confined to the conceptual boundary conditions implied by its referent. In other words, theoretical terms conceptually knot “mixtures” of thetic (transcendent) and empirical (immanent) content. However, the term itself is subject to movement (slippage) on both sides which thereby produces a dynamically expanding but finite index or topologically localized neighborhood of meaning—a “signifying infrastructure” relative either to the “One” (the thetic-linguistic content of the term) or the “Real” (the referent or the thing the term describes—the immanent content of the term).
[It is important, however, to recall that the One and the Real remain sufficient and co-determinate in non-philosophy without being equivalent: the One appears to us from its philosophical description as that which eludes every philosophical while still determining them. However, we must recall that the One is not the result of a process of philosophical “scission” or in any way an “indivisible remainder” of a symbolic process (description). These semiotic and psychoanalytic descriptions (can easily) imply that language is in someway constitutive of the Real. This division between the Real and the One is meant to imply the directionality of their determination-in-the-last-instance. The One “strikes” from the side of language since, for Laruelle, it is indicated and eluded by its philosophical description. The Real strikes not as a result of language’s “ontological capture” of the Real via a referent but by its radical foreclosure to language and thought. The way in which philosophical terminology presents itself as material to non-philosophy is as Real in itself and as an element of the One in itself.
None of this is meant to imply that language or philosophy provides “assistance” to the One or that terminology “Distances” itself from the One by its description of it. The “composition of the sign” traditionally provided an entry way for a kind of semiotic idealism which separated ideas or concepts from signifiers while recognizing the “empirical” fact that the two were co-determined (the structuralist claim that you cannot have thought without language). Non-philosophy treats the conclusion that the sign is arbitrary as arbitrary in itself and sufficiently expresses the property of a philosophical decision (despite its anti-philosophical insinuations) to offer itself as material. Laruelle, however, exploits this philosophical material at an aesthetic level: as that which produces “a/effectuations” in a generalized sense, i.e., insofar as their significations, their effectuations, and so forth are determined-in-the-last-instance by the One or are accomplished according-to-the-One. In this sense, any thetic, transcendental or conceptual content, any philosophical term is already radically autonomous and radically immanent, i.e., in-One, Seen-in-One, or Real. Non-philosophy arrives on the scene to announce this and inoperatize or disactivate their philosophical function so that they might “accord” to their immanent or demotic signification by the One.]
For example, when I write the phrase “eco-Marxianism” or “Marxist radicalism,” even though these are not well-established or meaningfully—in the sense of actually—occupied political positions we can still imagine what a corpus of eco-Marxian texts might look like and that “Marxist radicalism” would likely be a “Left” tendency relative to orthodox Marxism, if we agglutinate the terms and produce “eco-Marxian radicalism” than we actually manage to produce more sense and specificity even as it loses any and all correspondence to reality and fails to describe anything “real.” However, this term gains significance in and according-to-the-One.
This kind of non-philosophical “disinterpretation” and “underdetermination” of a term like “labor force” is an anti-hermeneutic procedure which aims at efficiency and impact at the level of the One (rather than persuasive efficacy at the level of the “thought-world”) and immanence to the Real by exploiting a term’s “unilateral duality” or “determination-in-the-last-instance.” This non-philosophical usage of philosophical material “frees up” a term’s (philosophically) imputed univocal correspondence to the One so that it accords to its manifest or contextual signification (its determination in this—from the immanent position of the reader, the last—instance) rather than the arbitrary or decisional definition of the term.
Philosophy is aware of this movement or the “play of the signifier,” however, it exploits this ambiguity by both controlling the context and means of its play by assigning multiple definitions to a term in the form of its continual explanation. This embroils the reader in endless hermeneutics and leaves them in the precarious care of the philosopher to provide definitions and explanations of the term, i.e., control the conceptual stricture and limit the general sense of a term, as they purposefully complicate and multiply the significations of a term to suite their argument. The classic example of this in Marxism—which G. A. Cohen tries to fix in Marx’s Theory of History and is shamelessly exploited by Althusser—is the ambiguous and even downright manipulative usage of the terms like “forces of production,” “relations of production,” and even “capitalism” in general for the sake of persuasive argument. Suffice it to say, such a usage of philosophical terminology invariably decides the One according to a contingent (in this case ideological) Vision-in-One rather than the One itself.
The non-philosophical reclamation of philosophical terminology, its reduction to material through dualysis and cloning finds philosophical terms that are in the form of a “axiomized abstractions.” Laruelle states in the glossary of Future Christ.
[Axiomized abstraction] proceeds by way of operators from names (like One, Identity or Man), from adjectives like radical (radical identity, etc.), from prepositions like in- (One-in-One, etc.), without (without-consistency, without-world, etc.), non- (non-conceptual, non-definitional, etc.), in person (Man-in-person, One-in-Person, etc.) These operators are the expression and effects of the Real, which are inseparable from its radical immanence. (Future Christ, p. xxvi)
 The examples could go on: micro-Marxism, Marxist individualism, Marxo-Levinasianism, Marxist Sikhism, Afro-Caribbean Marxism, Marxism with indigenous characteristics, neuro-Marxism. They could even border on the absurd and contradictory (e.g. Marxist-Capitalism, Marxist anti-workerism) or redundancy (e.g. Marxist historical dialecticism, neo-Marxian materialism). The effects vary from producing unlikely but viable “Marxisms” to sounding like one has never studied Marx but seems to sort of know what they are talking about. (Neologisms are also a possibility: Marxiarity, Marxineity, Marxisminism.) The reason this “works” is because these terms have a generic or reduced signification that implies some sort of thetic content that is conjugated or reciprocally redefined by the previous or next term. Within the conceptual framework provided by non-philosophy, these terms are dualyized or cloned so that they produce meaning “according-to” the Real or the One respectively. However, if we frame this in terms of an “aesthetics” of non-philosophy, we have an instance of the production of “rigorous” fictions that poetically exploit the thetic or transcendental content implicit in these terms that produce aesthesis, a “real” effect or sensation at the level of or in the form of thought. Consider also Laruelle’s use of mixing proper names in Philosophy and Non-Philosophy, an amusing habit he has unfortunately abandoned in his recent works: by this procedure he imagines fake philosophers like “Laceuze” and “Derritard”—again, it is not impossible to imagine the books these figures might write and their specific politics. Lyotard deploys this strategy when he imagines in Libidinal Economy a “little girl Marx” a “big fat Marx,” an “old man Marx,” and a “beardless Marx.” See, Lyotard, Jean-François. Libidinal Economy. Bloomington: Indiana UP, 1993, pp. 94-154.