The Many Logics of Negation
Unconscious Negation: Freud
In his Clinical Introduction to Freud, Bruce Finks makes the strange claim that, for Freud, the unconscious is the exact opposite of the conscious. This opposition immediately suggests negation. The thesis (consciousness) is negated in the antithesis (unconsciousness). They exist contemporaneously, sometimes harmoniously and sometimes painfully, alongside one another, one two separate ‘tracks’ of the mind. So, the story goes for those in the Freudo-Lacanian camp.
For Freud (and Lacan, following Freud, which we will discuss later), the unconscious is, as Fink says, the exact opposite of consciousness. We need to spend some time picking this apart.
For one thing, we cannot say that the unconscious is underneath or behind consciousness. That would give it a more thing-like positioning within psychic life. Rather, we must try to conceive of the unconscious without reifying it. One way to do this is through the idea that the unconscious is that which is the negating factor within consciousness. So, in this theory, we aren’t conscious and unconscious — we are always both, and it’s strictly impossible to separate the two. But what kind of negation does psychoanalysis make with the concept of the un-conscious? To really make sense of how the negation of the Freudian unconscious operates, we must take a detour through logic.
The Logic of Negation: Badiou[1]
In traditional logic, something is either P or not-P. But how and why is P “not equal” to not-P? Or, as Alain Badiou puts it, regarding political enemies, “the difficult question is the relationship between the two, particularly when the relationship is clear” (2008). Another way to frame this question, a way that is more aligned to our overarching project of nothingness is: what is true or necessary of P that it cannot be not-P, and that’s the relationship between the two — and there’s a host of possible solutions to this problem.
In a 2008 address to a symposium on law, Alain Badiou gave what is known as the “Three Negations”. In it, he proposes three forms that negation can take, depending on the logical framework one is leaning on.
First, there is the classical logic of Aristotle. Classical logic relies on two basic rules: the law of non-contradiction (LNC) and the law of excluded middle (LEM). In LNC, the basic negation of P is not-P (e.g., this thing is either blue or it’s not blue). So, we can say that not-P is a negation of P, and vice versa. In other words, things are self-identical, and they have a differential relationship with other things. In LEM, there is no ‘between’ or ‘third option’ to P and not-P. At the most minute levels of measurement, there is no fluidity between two things (we will see later how important this is for Sartre), and in every proposition either P or not-P is true. An example of classical logic would be war, in which the success of one entity or nation is the direct negation of the other’s success. In other words, “When both LNC and LEM hold, the negation is total; there are no stray elements of P in non-P” (Vartabedian, 2018).
Next, we have intuitionist logic, which does follow LNC but does not follow LEM: meaning that there can be an indeterminate number of multiples. In classical logic, the quantity and quality of things in any given set or group is limited by the fact that (a) objects cannot contradict, and (b) that there is no ‘in-between’, or gradient. Theoretically, under classical logic, we as humans could give a name and measure everything that exists because there is no slippage of things. Thus, negation would look different in an intuitionist program. Instead of the absolute/binary negation in classical logic, we find the requirement to always qualify P or not-P. For instance, in the field of law, Badiou holds that we don’t have just “innocent” and “guilty” as possible truths of a given proposition. Instead, we could have “innocent because certainly guilty, but without sufficient proof” or “guilty but then later turns out to be innocent” — the possible truths are almost infinite. As we can see, negation within intuitionist logic is much closer to the kind of negation we might experience in our ‘regular’ or ‘everyday’ life: yes, there is truth and falsehood, but things in the middle are always messy. Importantly, for intuitionist logic, there needs to be absence of proof in order to claim something is true or false, positive or negative. So, the conclusion to a line of argumentation might very well be not-P, but it is incumbent upon the thinking subject to show exactly how and why it therefore cannot be P. What this does to negation and nothingness is move it to the domain of dynamism and openness, rather than the closed absolutism of classical logic.
So far, we have logical systems which hold to the notion that both P and not-P cannot be true — up until this point, the Law of Noncontradiction, first formulated by Aristotle, reigns supreme. But this is suspended in the third and final logical system Badiou investigates in “The Three Negations”: paraconsistent logic. In a paraconsistent system, the Law of the Excluded Middle becomes the arbiter of truth, while LNC is suspended. In a paraconsistent system, there is the possibility that both P and not-P are true, but only insofar as our mode of knowing the truth or falsity may be the thing that’s in the wrong. So, paraconsistent logic doesn’t throw away the problem of contradiction altogether, it only “demands attention to the context(s) in which these competing claims are asserted” (Vartabedian, 2018). For instance, take the assumption that “it is raining”. To the classical logician this is either true or not — either “it is raining” or “it is not raining”. But also suppose you’re in an environment with microclimates, like the city where it rains on one side of the street and not the other. Considering the larger context, it is both true that in this city “it is raining” and “it is not raining”. However, if we narrow our focus on blocks, we cannot say the same thing. Instead, we must say that on this block “it is raining” or “it is not raining”. Negation, in paraconsistent logic, is thus open to the interpretation of the person examining the proposition.
Badiou assigns these negative logics to his ontology, which is useful for us to an extent:
1. The ontology of being, which is the theory of things in the world at a fundamental level of multiplicity, is governed by classical logic. In being, either a thing is this or its that, but it’s not both, and there’s no third option. Badiou calls this a strong negation.
2. The ontology of appearance and existence operates according to intuitionist negation. In appearance/existence, a thing is either this or that, or else may other things, but these things can’t possible contradict one another. In this, we find a weaker negation (it isn’t so absolute).
3. The ontology of event or truth, which arises when the law or order is transgressed, opening up the possibility of a new order. The event can actually take place in any of the three logical contexts with different effects. In classical logic, it is revolutionary and truly subversive, because it entirely negates the previous order; in intuitionist logic, the negation is softer and is the emergent truth is subsumed or substituted; in a paraconsistent system, the event loses all of its potentiality, as everything is potentially identical to everything else.
Little Pools of Negativity: Sartre
We established in the previous session that in Being and Nothingness, Sartre does not give an ontological or fundamental account of nothingness in the sense of it coming from somewhere outside of the human subject. Nothingness, for Sartre, is born from and through subjectivity — and particularly the freedom of the human subject. That is, we encounter negation in the world because the consciousness of the human subject is marked by a structure of non-being, of absence.
We encounter negatities, which Sarah Richmond identifies as ‘little pools of negativity’ in the world. These little pools of negativity that we encounter — feeling the presence of a lost loved one, alienation, the present moment, and so on — are possible because of the non-being of the subject.
But how exactly does our non-being produce these little pools of negativity, these moments of lack? Sartre also develops his own theory of logic and negation which we can look at with fresh eyes following Badiou’s “The Three Negations”. Sartre identifies internal negation and external negation as the mechanisms which govern the relationship between objects and subjects.
An external negation is very simple: this is not that; or, something is P or not-P. It doesn’t take much to see the debt Sartre owes to classical logic for this form of negation. External negation is an absolute negation of fixed things in the world, and is used to examine the relationship between an in-itself and another in-itself. So, we could say that this car is not that dog (comparing a particular thing to a particular thing). We could also say that dogs aren’t cats (comparing two universal things), or even that this watch is not a car (comparing a particular and a universal thing). No matter the quantity or quality of what is positive and what is negative, for Sartre, external negation uses classical logic. Importantly, in external negation, the connection is “an ideal and categorical connection that I [as witness] establish between them, without modifying them in any respect, without enriching or impoverishing them with the slightest quality” (B&N 249). The essences of the two, in their relation to each other, remain undisturbed.
Internal negation is more slippery, because it comes into play when we introduce subjectivity. Subjectivity, as we know, Sartre calls the for-itself and it is radically different from the category of the in-itself. (We might even say that this very categorization of the absolute difference is something of a classical logic, P or not-P, which earns Sartre the shameful title “dualist” from many other philosophers.) When it comes to negation, the distinguishing factor between the for-itself and the in-itself is that while the latter has negation built into it (the difference between dog and cat are measurable and observable), consciousness is negation itself, and so must do the work of negating things which it is not. Properly speaking, consciousness is nothing, so it can’t be directly compared to one thing or another, as each category is operating in a different field: each, to use our earlier vocabulary, has a different logical system. The for-itself, or consciousness, is always in the process of saying “No, I am not that” but is never able to arrive at a final identity which it can definitely say it is. This is essence of Sartre’s highly dynamic view of consciousness. It can never be pinned down, isolated, and compared in some final sense. Consciousness is always uneasy, never at home with itself or in the world. It is the very act of this constant negating which both gives consciousness its unique character among entities in the world.
Additionally, an internal negation produces something positive about the subject. If I say “I am not wealthy,” I might say it with a certain melancholy, or I am imply that I am instead financially middle class or poor. With external negation, we don’t really have negation proper: we have two assertions of positivity and difference. In internal negation — which is introduced only qua subjectivity — we get real negation. “The fruit is rotten” or “My uncle is a grinch” introduces nothingness into those beings. The being can’t help but be altered by negation.
Badiou and Sartre, and the Unconscious
To return to our question at the beginning of this essay: what does it mean to say that the unconscious is the negation of consciousness, or that it is the exact opposite of consciousness?
The Badiouan response would be that the unconscious is a kind of classical negation. It is an absolute negation of some positive entity. There is no in-between (unless we account for Freud’s early conception of the ‘preconscious’, which most contemporary scholars don’t much care for) and there is no third option, some kind of supra-conscious or spiritual-consciousness. A thought is either conscious or it is unconscious.
However, there are many moments in psychoanalytic theory and practice which reveal something more slippery and transitional than what Fink portrays as the unconscious. For instance, the bisexuality of all people (Freud), the transitional object (Winnicott), the co-existence of love and hate (Klein). These ideas are all situated more comfortably within intuitionist logic, which allows for a negation (all of these are un-conscious) but which also makes room for gray areas.
These ideas and their logical structure will be explored in more detail in the coming essays.
But something must be said about the Freudian divided psyche: the unconscious co-exists with the conscious and has effects on it. We know that we forget the name of a person or that a joke contains something distasteful. We know that, during analysis, we sometimes encounter an impasse in our speech but can’t account for why. We might say that the relation is a kind of internal negation, wherein the negation of the one actively changes the nature of the other.
Consciousness and the unconscious are dependent upon each other for Freud and psychoanalysis. You cannot have one without the other, and this is especially important when considering the singularity of a specific case.
What this also means is that we need to account for the kind of relationship that consciousness has to the unconscious, it’s direct and influential negation, and for this we need to think about repression, displacement, disavowal, and other mechanisms of psychic negation.
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[1] I am indebted to a talk that Sawyer Macres gave in Denver at a psychoanalytic seminar for pointing to the connections between Aristotle, Badiou, and psychoanalysis.
References
A. Badiou, “Three Negations” (2008)
B. Fink, Clinical Introduction to Freud (2017)
B. Vartabedian, “Negation, Structure, and Transformation: Alain Badiou and the New Metaphysics” (2018)
J. P. Sartre, Being and Nothingness (1943) (abbreviated ‘B&N’)
