Leibniz and Psychoanalysis

Leibniz held that every true proposition has the form “P is Q”. “P is Q” is true iff the concept (intension) of P contains Q. For instance, “Bachelors are men” is true because the concept of bachelor is the concept of man with the concept of unmarried added to it.

In set-theoretic terms, the hallmark of Leibnizian logic is that it uses only ⊆ and no ∈ (⟨man⟩ ⊆ ⟨bachelor⟩¹). This analysis, however, runs into the problem of distinguishing universal from singular judgments. On the traditional classification, “Bachelors are men” is a universal judgment, since it concerns all bachelors, while “Socrates is a man” is a singular judgment, since it concerns a single individual. In Leibnizian logic, however, the two propositions are analyzed as ⟨man⟩ ⊆ ⟨bachelor⟩ and ⟨man⟩ ⊆ ⟨Socrates⟩ respectively, and the distinction between universal and singular judgments collapses.

Is there a way to preserve this distinction within Leibnizian logic? One proposal is to draw it according to whether the subject is a final concept. Let us call a concept final if it is maximal with respect to ⊂. For instance, ⟨bachelor⟩ is not a final concept, since there exists an X such that ⟨bachelor⟩ ⊂ X (e.g. X = ⟨Newton⟩). ⟨Socrates⟩, by contrast, picks out a unique individual, and so appears to be a final concept.

However, this proposal soon meets a difficulty, for it is unclear whether the concept ⟨Socrates⟩, as we understand it, really is a final concept. Our ⟨Socrates⟩ amounts to something like “the Athenian philosopher who taught Plato and drank the hemlock”, but it does not settle whether he loved Plato. That is, the concept obtained by adding “loved Plato” to ⟨Socrates⟩ and the one obtained by adding “did not love Plato” are both consistent, so ⟨Socrates⟩ is not a final concept.² Moreover, if some predicates remain undetermined no matter how (finitely) many predicates we add, it follows that endless chains such as ⟨S⟩ ⊂ ⟨S′⟩ ⊂ ⟨S″⟩ ⊂ … exist. The individual concept of Socrates is given only as the limit of such a chain.

Indeed, Leibniz held that individual concepts (which correspond to what we have called “final concepts”) can be grasped only by an infinite intellect. Thus, according to Leibniz, we always grasp objects “dimly” — our concepts of individuals are never adequate. Only God can carry the analysis through to the end.

Yet despite Leibniz’s claim, there seems to be one concept that we grasp with the utmost certainty: the concept of the I. The ⟨I⟩ that grounds Descartes’s cogito, the ⟨I⟩ that represents and receives this world, is given to me immediately and indubitably. Then is not the concept ⟨I⟩, at least, an individual concept?

Leibniz could respond to this objection in two ways. The first is a moderate stance in which the concept of oneself is admitted as the sole exception. The second is a radical stance. Even ⟨I⟩ is not an individual concept, in the sense that I cannot grasp it adequately. The latter is Leibniz’s own position,³ and it rests on the distinction between certainty and adequacy. What the cogito provides is only the knowledge of my existence, not of what I am. I cannot doubt that I am, but I cannot analyze what I am to the end.

And we know the name of the discipline that concerns itself with this self-opacity, in which I do not grasp myself: psychoanalysis. In Leibniz’s metaphysics, the analysis of ⟨I⟩ is possible not by me, but only by God. In psychoanalysis, the analysis of the patient is possible not by the patient, but only by the analyst — modulo the difference that the analyst, not being God, never reaches the final analysis.⁴ Thus in Leibniz’s doctrine of individual concepts, we can glimpse the germ of psychoanalysis, which, by separating the object of analysis from the subject who performs it, probes relentlessly into the division and anxiety of the self.