In previous posts I extended my proposed matheme of noesis up to eleven stages, I have now added some supplementary steps and reworked a few, bringing the mapping up to fourteen elements. From naive philosophy to the drive to conceptual creation.
Extended Matheme of Noesis:
I(A) Δ $ → S($) → m/i(a) → s(A) → S(A) → S◊A → ($→a) → $◊A → $◊a → S(Ⱥ) → $(Ⱥ) → $◊Ⱥ → $◊Ð → a◊J
Glossary of Terms and Stages (I have taken the symbols from Lacan’s « Graph of Desire » that I reconstrue as a map of noesis
PHASE 1: AWAKENING TO THE CONCEPT
The starting point of noesis is double: I(A) Δ $
I(A)
Imaginary relation to the philosophical Other.
An initial, naive coherence where the Other is experienced as a stable presence. This corresponds to the early formation of thought and worldview, where the noetic subject feels an affinity with the concept, is « split » by the concept, but is still caught in images of wholeness.
Δ
The structural impossibility separating I(A) and $.
Contrary to the diamond-punch, this delta is not an emergence operator, but a mark of the irreducible gap between imaginary coherence and the symbolic split of the subject. It is the structural impossibility that ensures that no relation between the subject and the Other is ever complete. This impossibility is foundational to noesis itself, i.e. this impossibility, rather than blocking thought, is what compels the movement forward, from naive relation to philosophical subjectivity. The absence of a direct path is what forces conceptual articulation and initiates the noetic ascent.
$
The barred subject.
The noetic subject emerges as split, marked by lack of understanding and division by the concept from the outset. Thought is not whole but structured around an absence.
S($)
The signifier of the barred subject.
The first symbolic attempt to stabilize this division: the creation of minimal formal marks that represent the subject in the field of the Other, as a subject that « thinks ».
(Comment 1: The ascent starts from « naive » thought, where the subject, $, observes that it has a singular affinity with thinking perceived and imagined as a social activity, practised by exemplary role models, I(A). It identifies as a thinking being. This is expressed by the formula I(A) Δ $, which figures the base of the graph, where there is no direct path between I(A) and $.)
I put “naive” in scare-quotes, because even this lowest level is under the sway of the signifier. This is why I add a supplementary term S($), the signifier of the subject assuming its split by the concept.
PHASE 2: OPINION, WORLDVIEW, SYSTEM
m/i(a)
Imaginary identification (mirror stage) with the ideal other a.
At this stage, the subject organizes itself around imaginary identifications and ideal images — the “me” is formed by aligning with a projected wholeness (a), masking structural lack.
s(A)
Worldview.
A signified-oriented structure of naive thought, in which coherence and stability seem given. It is the natural resting point of thought before it encounters conceptual instability.
S(A)
Philosophical system.
A systematized, signifier-oriented construction built from the worldview. Philosophy at this stage seeks coherence, stability, and completeness.
(Comment 2: We next move to opinion, m-i(a), where the subject self-identifies as a thinker, i.e. it reflexively identifies with an idealised version of its thinking self and of its thoughts, and then moves by way of the treasure trove of philosophical views (A) to the formulation of the subject’s convictions s(A) that serve as the basic principles for an articulated worldview, S(A), where the subject’s opinions are informed, organised, debated, and reasoned.
This move s(A)→S(A) is not discussed by Lacan. I add the formula S(A) to express the move whereby the subject by means of its “quilted” convictions” goes on to envision the whole of the symbolic (A) through their organising perspective.)
PHASE 3: NOETIC DESIRE
S◊A
System–worldview punch.
The moment where the philosophical system collides with the worldview it formalizes. This stage introduces instability: the recognition that the worldview and system cannot perfectly align.
($→a)
Noetic desire articulated as a relation between the subject and the object cause (a) of conceptual desire.
At this point, thought recognizes its movement toward an object that structures its lack in understanding. This object cause, and the resulting desire, begin to destabilize the system, i.e. this desire no longer seeks total completeness but the repetitive partial closure of conceptual gaps.
$◊A
The subject’s critical engagement with the worldview.
An intermediate stage where the subject begins to question and reconfigure the worldview itself, propelled by desire and structural doubt.
(Comment 3: from S(A) the subject moves to an objective overview of its conceptual field, S◊A, and then to ($→a), discovering its desire to structure and stabilize its incomplete understanding, driven by the fundamental gap in understanding that a represents, and from there moves on to its own subjective philosophical synthesis $◊A. These last four are intermediary moves that are not formulated by Lacan, who does not use the formulae S(A), ($→a), S◊A or $◊A.)
PHASE 4: DOUBLE CRISIS
$◊a
Traditional philosophy as fundamental fantasy, actual impasse and potential breach.
The grand philosophical project: the edification of a conceptual edifice sustained by the object-cause of desire. Philosophy here is a structure of fantasy, striving for completeness but harbouring structural cracks.It is in these cracks that there resides the potential breach: $◊a is both the fantasy impasse and the tension point through which thought can rupture and reconfigure.
S(Ⱥ)
Symbolic crisis.
The philosophical system now confronts its own impossibility: the barred Other. This is the stage of double impasse, where the system wavers between forced differentiation and in-differentiation, unable to ground itself.
$(Ⱥ)
Double crisis (subjective destitution and symbolic crisis combined).
The subject accepts both the incompleteness of the symbolic order and its own structural lack. This stage marks the threshold of barred philosophy, where traditional philosophical structures dissolve.
(Comment 4: this active synthesis, $◊A, leads to the creation of a new philosophical system, $◊a, where the subject has a worked out, singular, fundamental conceptual paradigm or noetic fantasy, and from there to a research practice, aware of the open and incomplete nature of its system of thought, S(Ⱥ), where the subject is capable of trouble-shooting the system (puzzle-solving and theory-adaptation), and then to the subject’s personal confrontation with this incompleteness and self-inclusion within it, $(Ⱥ), Note: this is another formula not explicitly considered by Lacan).
PHASE 5: NOETIC DRIVE
$◊Ⱥ
Barred philosophy (p̶h̶i̶l̶o̶s̶o̶p̶h̶y̶).
Thought singularly pursued beyond fantasy, propelled by drive, constantly reconfiguring its conceptual apparatus in relation to an incomplete Real. This is structuralism-2.0, what Lacan calls the seriousness of thought: subjective fidelity to the absence of objective totality.
$◊Ð
Noetic destruction.
The act of conceptual demolition: cutting through fantasy supports and system remnants. Thought encounters the impossibility of closure and confronts the void without fear.
a◊J
Conceptual creation driven by the pure drive of noesis.
At the end of the journey, what remains is a — the conceptual fragment, the minimal residue of the Real — punched into J, structural jouissance. This articulation produces the site of conceptual invention: not completion, but the point where thought, impossibility, and drive generate new concepts in fidelity to an incomplete Real.
(Comment 5: finally we come to the level of noetic drive, pushing us to an open, complex, incomplete dialogue with the real outside imposed mono-frameworks. The formula $◊Ⱥ does not figure in the list of mathemes actually used by Lacan, but it makes sense on the analogy of the formula $◊a, which Lacan does use to formalise the matheme of the fundamental fantasy. In the context of noetic ascent $◊Ⱥ is the matheme for what I am calling “barred philosophy”, the mode of thought arising from the subjective assumption of, and inclusion in, the incompleteness of the Other.
The philosophical subject, split and marked by the concept, assuming the inherent incompleteness of philosophical systems, traverses the demand for philosophising to its vanishing point $◊Ð, perpetually orbits the concept petit a, ceaselessly striving to express it without capture, driven to explore concepts outside the bounds of established frameworks, thereby liberating itself from its paradigm and able to effectuate fundamental conceptual change, a◊J, and propel an endless cycle of reinvention.)