Dani Park
Introduction
This is a short, experimental essay on the emergence of ideas, both as a source of critique and radical possibility necessary for a better world, both maddeningly elusive and within reach; experimental precisely due to the fact that, although I use mathematical formulae, they are not mathematical, in the traditional sense of the term. Rather, I utilize mathemes, first coined and popularized by the psychoanalyst Jacque Lacan,[1] in order to explain a theory of ideas and the subject. This essay is meant to entertain the importance of ideas in changing the world and, more importantly, that the decision to unleash the creative powers of ideas in the world is up to the very beings that can ultimately deny it.
The Theorem
Firstly, we cannot accept any ontological assumptions that are not fundamental. There exists a subject
(1) S
Within this subject exists harmony but also no possibility for a better future: the subject simply is and forever reasserts her own existence. What exists is a tautology of the most fundamental state
(2) S = S
This reassertion, although comforting and harmonious, also rejects any possibility of change in which the subject becomes something else
(3) S = S ≠ x
Given this, what is an idea if not the very possibility of change; something that is different from the subject and her self-assured certainty. An idea emerges due to the two incompatible and otherwise contradictory states of the world: the world as it is (∀n) and the world as it could be (∀f), for without it there would be no manner in which the two states could be reconciled
(4) ∀n=∀f, where ∀n≠∀f
The idea provides the necessary linkage that collapses the contradiction by positing a temporally linear relation rather than that of equivalency
(5) ∀n⇒∀f
It stems from a discontentment that arises from the inability of the subject tautology of (2) to remedy this.
Given this, however, the relation between the subject and idea is still unknown and uncertain. All that is known is that there exists some relation between the static subject and the possible idea, which can be a myriad of different things
(6) S ? i
Yet we do know that there exists a relation. For one, ideas exist, but they cannot be actualized without the subject. This seems to indicate that the idea depends on the subject
(7) S>i
Yet this relation is not unidirectional: the subject too depends on the idea for the idealized world she craves, which, due to the limitations of ontological self-assertion of (2)
(8) S⋄i
Alone, the two exist in symbiotic relation. Yet there exists an underlying tension due to the ontological separateness-from-the-world
(9) ∀n⋄((S)⋄(i))
The idea and subject are part of the current world, yet distinct from it as well. The world conditions each- distinguishes the boundaries of the subject and idea- but is in turn changed as well.
There exists a contradiction, for an idea cannot both be separate and distinct while also being derived from- a pure extension of- the subject. The relation between subject and idea becomes that of domination (ontological certainty defined by total equality), which is ultimately untenable due to this contradiction
(10) ∀n ((S)=(i)), where S≠i
The desire to maintain the world as it is is not at all arbitrary. By embracing the world of the future- that is, the world of the idea- the subject risks losing the very certainty of being granted by the tautology of (2). The subject, driven by the fear that she is not ontologically distinct from the world, subsequently attempts to remedy this through the subjugation of ideas and claiming that she is the source of all of them, and in the process claims (5) and denying the possibility of (6). This collapses the contradiction of separateness and reclaims a harmony of existence[2]
(11) S ≥ i
However, it also castrates ideas and makes them inoffensive and harmless by relegating them to the affirmation of the ontology of the subject; radicalism is an overt sign of the vitality of an idea. (Indeed, such radicalism precisely hints at an idea’s dissatisfaction with the current state of things.) The world as is fully encompasses and synthesizes the idea into the subject
(12) ∀n (i→S)
Yet note that an idea can never revert back to the state of (1). (9) is not equivalent to (1)! Ideas always contain the potential imbued in its separateness-from-the-world to actualize, independent of any individual subject. The idea can be saved through the social
(13) ∀n (i→S)⋄∀f= ±i
An axiomatic choice is the result: either the collective subjects constituting the aggregate social liberates the idea by actualizing the radical possibility inherent to it (12) or rejects the idea through inaction or indifference (13)
(14) +i⇒∞i
(15) -i⇒(S=S)
The former leads to the emergence-in-the-world of the idea and the change in the current state that necessarily entails it. The latter leads to the ontological affirmation of the subject, and with it loses the radical possibility of the idea (see fig. 1).
Appendix A
Figure 1: Structure on the emergence of idea
[1] See Jacques Lacan and Alan Sheridan, Écrits a Selection (London: Routledge, 1977): 208.
[2] Note that the functions (9) and (5) are not equivalent. (5) denotes a relation between the subject and idea open to the possibility of equality, whereas the subject dominates the idea in (9) and, in doing so, becomes incapable of such a state.