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Kant, Strawson, and Conditionals

P. F. Strawson is not one of Kant's more sympathetic interpreters: Kant's faculty psychology, he thinks, is no more than a historical curiosity. The account of logic is likewise a mess. Above all, transcendental idealism is sheer nonsense. Also, of course, Kant's arguments notoriously rely on the claim that Euclidean geometry is known a priori to be the geometry of the sensible world, whereas we now know that this claim is not only not known a priori, but is actually false. (James Van Cleve has argued, however, that Kant needs only the existence of some a priori geometrical knowledge, and not the whole of Euclidean geometry.)

In the section of the Critique of Pure Reason known as the "Transcendental Analytic," Kant lays out an account of the possible forms of judgment, and argues that these forms of judgment presuppose certain 'pure concepts of the understanding' which must be imposed by the understanding on the raw matter of sense perception (the notorious 'unsynthesized manifold') in order for ordinary perceptual experience to be possible. Strawson believes that Kant's account here is infected by his antiquated logic.

According to Kant, every judgment can be "brought under four titles, each of which contains under itself three moments" (A70/B95, tr. Guyer and Wood). That is, Kant thinks there are four different questions we can ask about a judgment, and each question has three possible answers. One question is what relation is involved in the judgment, and here the possible answers are categorical, hypothetical, and disjunctive. These are supposed to be the fundamental forms that judgments can take: they are not supposed to be definable in terms of deeper primitives. Strawson complains, however, that Kant's "list includes the hypothetical and disjunctive forms which in modern logic are interdefinable with the help of negation" (The Bounds of Sense, p. 80).

Today, it is Strawson's logic that is antiquated. (Strawson's book was first published in 1966.) Here is what Kant actually says:

The hypothetical proposition "If there is perfect justice, then obstinate evil will be punished" really contains the relation of two propositions, "There is perfect justice" and "Obstinate evil is punished." Whether both of these propositions in themselves are true remains unsettled here. It is only the implication that is thought by means of this judgment. Finally, the disjunctive judgment contains the relations of two or more propositions to one another, though not the relation of sequence, but rather that of logical opposition insofar as the sphere of one judgment excludes that of the other, yet at the same time the relation of community insofar as the judgments together exhaust the sphere of cognition proper; it is therefore a relation of the parts of the sphere of a cognition where the sphere of each part is the complement of htat of the others in the sum total of the divided cognition, e.g., "The world exists either through blind change, or through inner necessity, or through an external cause." Each of these propositions occupies one part of the sphere of the possible cognition about the existence of a world in general, and together they occupy the entire sphere. To remove the cognition from one of these spheres means to place it in one of the others, and to place it in one sphere, on the contrary, means to remove it from the others. In a disjunctive judgment there is therefore a certain community of cognitions, consisting in the fact that they mutually exclude each other, yet thereby determine the true cognition in its entirety, since taken together they constitute the entire content of a particular given cognition. (A73/B98-A74/B99)

It is true, as Strawson points out, that with the help of negation the material conditional and the simple truth-functional disjunction are inter-definable, but the two forms of judgment Kant here describes are not truth-functional. Kant's hypothetical involves an implication, and thus is probably the subjunctive conditional, though it could be the indicative conditional on some modern views. (For an opinionated summary of the recent literature on indicative conditionals, see the first half of Bennett's A Philosophical Guide to Conditionals.) Kant's disjunctive relates a list of propositions which are mutually exclusive and jointly exhaustive. In Strawson's day, it was thought that if we were to give any sense to these sorts of non-truth-functional operators, we needed to reduce them to the truth-functional ones. Today I think many philosophers have given up on the prospects for this task. In other words, while there are clearly advantages to modern symbolic logic, Kant's logic captures much more of the sophisticated machinery of natural language than Strawson's purely truth-functional approach. Today, we should not, I think, be as quick as Strawson to dismiss Kant's general logic.

Posted by Kenny at October 5, 2010 1:15 PM