I found an essay by a fellow Jonathan Webber that explains Sartre’s use of “non-thetic awareness” in Being and Nonthingness and a number of other terms that have made their way into non-philosophical parlance by way of existentialism and phenomenology. The essay is also useful in that it makes strong correlations between this terminology and the terms “conceptual” and “non-conceptual” as they are understood in contemporary anglophone philosophy of mind. Some of this is already implicit in Laruelle’s writing but for those of us who would like to know where these terms come from this essay is quite practical and gives a straight forward presentation.
He states his thesis plainly: “I am going to argue that Sartre’s distinction between thetic and non-thetic awareness should be understood as a distinction not between representational and non-representational forms of awareness, but between conceptual and non-conceptual representational awareness if it is to play the role in bad faith that Sartre ascribes to it” (p. 6). Putting this bad faith business aside briefly to get at the definitions that interest us, Webber describes Sartre’s phenomenological account of “position” in a fashion that discloses its transcendental hangover which is preserved at the level of intentionality and thought:
To call a consciousness ‘positional’, for Sartre, is to say that ‘it transcends itself in order to reach an object’ (B&N: xxvii). The object posited in an experience is the object singled out, to which I ‘direct my attention’ (B&N: 95). Looking at a photograph of my friend Peter, for example, I may inspect the shapes and colours on the card, or I may see it as an image of Peter. Only in the former case, according to Sartre, am I seeing the photograph: it is the object posited. In the latter case I am imagining Peter: he is the object posited (PI: 17-8). The positional character of experience, for Sartre, then, is its direction on or towards some particular object, the object posited. (p. 2)
In other words. To take a “position” is to invest a level of conceptual attention/intention that recognizes objects in their identity rather than as a aggregate of parts or qualities. The term “thetic,” is meant to elaborate this conscious position-taking and recognition by including a moment of cognition in the recognition of an identity of an object or thing. Things become a little muddled here for Webber when he compares the more specific concept of “positing” as an act of classification or evaluation in Husserlian phenomenology to Sartre’s more propositional concept of positing as forming a thesis about an object. But this comparison is meant to disclose that their remains a “thetic” component in “positing” or phenomenological position. He states relatively clearly:
The thetic component of an act of consciousness, for Sartre, consists in a thesis or proposition (thèse) classifying the object posited (see B&N: 90); it is the set of ways in which the object is understood. For example: ‘In the case of the perception of the chair, there is a thesis — that is, the apprehension and affirmation of the chair as the in-itself which consciousness is not’ (B&N: 140). (ibid.)
Sartre calls the components of the thetic component of awareness ‘determinations’: determinations are the category headings that the thetic component of a consciousness classifies its object under; they are the way the object is intended. The thetic component of perceptual experience, according to Sartre, ascribes the determinations ‘present’ and ‘existent’ to its object. But the thetic character of perceptual experience is by no means restricted to this. There are, for Sartre, two further varieties of determination that can be involved in the thetic component of a perceptual experience. (p. 3)
More simply: “Perception involves, for Sartre, positing the seen object as present and existing; the thetic component of perception, that is, represents the object posited as present and existing” (p. 3). The crux of this argument that makes it interesting non-philosophically is not when he proposes that bad faith (which stems from non-thetic awareness) is the equivalent to non-conceptual thinking, this lands us back in philosophy proper, but when he proposes that non-thetic awareness and non-conceptual thinking are the same. That is to say, if we extract Sartre’s value judgment, we can begin to see something resembling Laruelle’s non-philosophical usage of non-thetic in his term “non-thetic position” (NTP).
In order to bridge the gap between Sartre’s phenomenology and anglophone philosophy of mind, Webber needs to placate Sartre’s critique of representation and demonstrate that the latter construes representation in a way that is already amenable to Sartre’s phenomenology, i.e., in a way that accounts for representation such that it includes a moment of intentionality: “To say that a mental state or event has representational content, these days, is just to say that it picks out an object or state of affairs and presents it in some way or other” (p. 6). Thus, Webber defines a concept as the following:
Anglophone philosophers distinguish two kinds of representational content: those that are composed of concepts and those that are not. A concept is an inferentially relevant constituent of a representation, and possessing a concept consists in having a set of inferentially related representations with a common constituent. Possessing the concept ‘cat’, for example, consists in possessing a set of inferentially related representations concerned with cats, such as the beliefs that cats are domestic pets, are tame, and are smaller than houses. A representation is conceptual, then, only if it is composed of concepts, which means that it stands in inferential relations to a set of other representations possessed by the same organism. A nonconceptual representation, on the other hand, does not stand in inferential relations. It can be possessed by an organism that does not possess the concepts required to express that representation. A nonconceptual representation is a representation: it specifies a possible state of affairs. But it is independent of what Wilfrid Sellars called ‘the logical space of reasons’: it cannot be inferred from other mental representations, other mental representations cannot be inferred from it, and it cannot be linguistically articulated, say in response to a question. An intention, for example, would consist in a nonconceptual representation if it consisted in a state of the brain or mind that specified a possible future state of affairs as something to be aimed for, but was independent of the logical space of reasons. (p. 6)
In other words, there cannot really such a thing as “non-representations” so the opposition non-representational/representational forms of awareness is either moot or a matter of semantic: the mind cogitates representations one way or another, but whether or not it conceptualizes them is something else. Thus when he begins to define “non-thetic awareness” as something that concerns non-conceptual knowledge we actually have something very interesting, non-conceptual or non-thetic awareness as a form of knowledge (similar to the psychoanalytic notion of savoir or non-knowledge, see also Bataille’s original conception of non-knowledge) rather than ignorance (what is starting to be called agnotology):
Why is it that non-thetic awareness allows one to report current activities but not how they are carried out? If non-thetic awareness is understood as involving nonconceptual content, then this seeming contradiction can be resolved. The awareness does not stand in the space of reasons, so one cannot form linguistically articulable beliefs on the basis of it: it allows one to be aware of what one is doing without being able to explain how it is happening. But also, nonconceptual awareness may be responsible for an action feeling appropriate or inappropriate to a conceptually formed intention: if I conceptually intend to count cigarettes, then proceed to do so, the non-thetic awareness of my activity may be an awareness of the appropriateness of my activity given the initial intention. If the initial intention is not itself conceptually structured, of course, then no linguistically articulable belief about it can be formed. (p. 7)
What this implies is a form of action and awareness (even intelligence and knowledge) that is, strictly speaking, not philosophizable because it is not given to conceptualization or language. One can count cigarettes but the act of counting is an automatic or mechanical process separate from conceptual thought: it is more at the level of an action and is thus a technical matter of how? (enumeration or identifying objects in a ordered list that are countable and using a symbolic counter to indicate every unite in the set) rather than why? while the question what? (what is counting?) is a description at worst and a complex explanation at best can never grasp or transfer the knowledge qua competence, skill or savoir faire of counting. Divorced from Sartre’s philosophical prejudices which denounce non-thetic awareness as bad faith, non-thetic awareness is an essential component of any field that grounds itself by a positive practice.
[Disclaimer: the rest of this is relatively hermeneutic and “history of philosophy-ish” so non-philosophy diehards against citation might find it somewhat against the “spirit” of non-philosophy.] Laruelle himself abandons his notion of non-thetic reflection or non-thetic position (developed in Philosophy II) in his Principles of Non-Philosophy (where he claims that it has reached its more adequate form as “transcendental cloning”). However, in Philosophy and Non-Philosophy, he considers non-thetic position or reflection to be comprised in the matrix of the philosophical decision: it is an a proiri in the quartet that comprises the initial material that offers itself to philosophical decision or chora and then the respective positions taken to it in Philosophy II:
As for the types and total numbers of a prioris, they are deduced from the number of dimensions of the philosophical decision of which they are the a prioris [this is extremely unclear]. There are four of these dimensions–there will therefore be four non-thetic a prioris, including the chora which “corresponds” on its side with decision’s auto-position or auto-givenness. In philosophy, this auto-position is there from the start. Afterwards, there is scission or decision, or even transcendence or exteriority. Then there is the dimension of position as “base,” “generality,” or even as “attribute,” dimension of position-as-universality or of being. Lastly, there is Unity, internal or external to the dyad of the preceding, the mixture itself as Unity, These invariants of philosophical decision correspond with the four a prioris deprived of the form of their philosophical unity of blend, of their entanglement in a mixture. (Philosophy and Non-Philosophy, p. 64)
He continues: “The chora first of all; then a non-thetic or non-mixed Transcendence (without scission and without an accompanying position); a non-thetic or non-mixed Position (without the position stemming from a scission or decision; absolutely indivisible and globally given); lastly, a non-thetic or non-mixed Unity (respectively: NTT, NTP, NTU)” (ibid. p. 64-5). We can consider these positions and the philosophical “chora” to be strategies that authorize the philosophical decision (the false need to “decide” the undifferentiated and chaotic real and lend coherence to reality). The presentation of the One as chora that philosophy needs to rescue itself from has mandated much of the heroic philosophizing of figures like Badiou and Zizek. The best way to recover this quartet from Philosophy II is to consider the quartet as the mode of presentation of the One according to (the) philosophy’s Vision-in-One or its falsely asserted realism. Here “non-thetic” can be read as “actual” rather than “non-conceptual” according to philosophy’s basic persuasive procedures. The philosophical assertion of the non-thetic should be non-philosophically coded as the opposite and comprised in this quartet or the fractional matrix of the philosophical decision. The creation or indication that something is “non-thetic” in non-philosophical terms is a result of the cloning or dualysis of philosophical material, i.e., reduced to demotic language deprived of its philosophical property referring to a “given” in-itself, providing a “clearing” for the One (Being), or corresponding to a “given” element of the Real so that it is given-without-givenness; reduced to its determination-in-the-last-instance; and given a signifying infrastructure, force-(of)-thought, or non-philosophical syntax that refers to the immanent causality of the real-One.
From the standpoint of non-philosophy non-thetic reflection, position or non-thetic awareness are (im)possible: they can only be indicated by language since every description fails it and they are foreclosed to all forms of thought besides their own form of autonomous thinking even while they function as an in-Real practice undertaken as the “industry trade,” “discipline,” “art,” or even “profession” of a myriad of domains of human activity. Non-philosophy is obliged to bring out this human element of the Real-One as practicity and defend it against its auto-positional appropriation by philosophy (auto-encompassing) whereby it assists philosophy by authorizing and soliciting it and serves it as an legitimizing “auto-factualizing” auxiliary practice (whereby Badiou is a mathematician who happens to philosophize or Popper is a scientist who happens to do the same or Sartre is a revolutionary… Kristeva is a psychoanalyst… and so on and so forth). Thus, outside the diectic center of philosophy and non-philosophy and their quarrels, what presents itself as “non-thetic” or announces it as such is this savoir faire or technical competence we mentioned before: a form of skilled non-knowledge that is non-conceptual and not adequately describable in language. It is an element of the One or “in-One” and shares certain similarities with it insofar as every description of non-thetic knowledge.
 “Sense (of) identity of supposedly Real philosophical faith when the vision-in-One transforms it into its correlate (unilate) or gives it its sense (of) identity. The chora is the site through unilateralization that philosophy has become (as identity) by wanting to be equal to the Real (still not as transcendental unity). It is the phenomenon or given-without-givenness (of) this real hallucination. Chora designates the spatial emplacement, or better yet the receptacle, indeed the prima materia through which it ends up being confused with Chaos, thus generating the dialectic of the One and the Multiple developed from that of the One and Being. Chora is the site of a pure multiplication: after its idealist reduction, when chaos becomes sensible diversity, the chora becomes its transcendental condition as spatiality, indeed, for certain philosophers, a name for a particular mixture of the transcendental and empirical, the…feminine” (The Dictionary of Non-Philosophy, p. 6).