Here are some brief notes I wrote up when trying to make sense of the analytic synthetic distinction. They might be helpful to those of you reading Kant on your own, or taking Daniel Warren’s Kant course. Anyway, thought I’d share.

The analytic/synthetic distinction, for Kant, is a logical distinction, which applies to judgments (one could also say that it applies to propositions, since this is what judgments express). Before deviling into the details of the distinction, its useful to look at an example to unearth some of the intuitions which might motivate the distinction or make it plausible. Here are some examples of judgments:

(A1) A triangle is a three sided figure

(S1) All my friends are jobless

It should strike the reader that there is a difference in kind between these two judgments. For instance, A1 seems trivial, while S1 seems like an unfortunate, but substantial, extension of the reader’s knowledge about my friends. It would make no sense to ask in ordinary life “well, how do you know a triangle is a three sided figure.” Anyone who competently speaks the English language will know this fact, and knowing that fact does not require looking at a bunch of triangles. It merely requires knowing what the concept triangle means. With regards to S1, the challenge “are you sure…” would make perfect sense. In order to know the unfortunate situation of my friends I claim to know, I would have to make some pretty substantial empirical inquiries, inquiries in which I may have erred. Another difference comes when looking at denials of these statements: while someone who said “all your friends are not jobless” may have perfectly good grounds, someone who says “a triangle is not a three sided figure” would be asked to repeat preschool geometry. That is to say, the denial of S2 is perfectly conceivable, while the denial of A1 sense inherently contradictory. While I don’t want to discuss the entire scope of this distinction, I hope this example brings something out about judgments like A1. I will now discuss the notion of an analytic judgment (or analyticity) in more detail.

Analytic judgments, of the simple subject-predicate form, are analytic in virtue of a particular connection between the subject concept and the predicate concept in the judgment. Kant calls this relationship is one of ‘containment,’ and notes that the predicate concept is somehow contained in the subject concept of the judgment. The notion of containment, however, is in some respect metaphorical. Since Kant is trying to get at something more than a picture of concepts as buckets full of other concepts, it is important to try spell out just what lies behind this containment metaphor. For Kant, what a concept contains must be understood in terms of what we can know simply by making the clarity and distinctness. These terms too stand in need of determination as to their sense.

Before proceeding further with analyticity, it is therefore necessary to take a brief excursion through Kant’s conception of logic. Kant’s conception of logic is markedly different than our now standard sense of the term. In the now standard account, logic is formal. That is to say, it is not concerned with the content of statements, but just what is true of them in virtue of their form. The logical form of a statement can be best shown by substitution. Any given statement can be transcribed into a more formal language, consisting of logical and a non-logical vocabulary. What is left over once all the non-logical vocabulary is substituted for names and variables is the logical form of the statement. So in asking about logically validity in virtue of a statements form, we are asking whether a statement preserves its truth value under all possible substitutions.

For Kant, logic is formal, in that it concerns the formal rules of all thought. But what Kant means by formal is markedly different. In logic, understood in the Kantian manner, we are concerned solely with the form of a thought’s expression. When Kant looks at logic, he is looking at the propositions in questions as the thoughts of a single subject. So Kant’s concern with logic is about how we cognize, and he means ‘rules of thought’ quite literally: the laws of what it is actually possible to think, given the form our thought must take. So, for Kant, logic is normative, but not merely in the sense that we should think in accord with it. The normative of logic for Kant runs deeper.

Kant thinks that logical principles, particularly the principle of non-contradiction, in fact govern all our thinking. For course, we sometimes contradict ourselves, and this is precisely the point where clarity and distinctness come in. For Kant, logic is normative in the sense that it governs all thought insofar as it is clear and distinct. Insofar as our thinking is clear and distinct, the principle of non-contradiction will in fact govern all our thought. We flatly will not contradict ourselves while we are thinking in this manner. Clarity and distinctness are opposed to obscure and confused: thought which are hazy, muddled, or we ourselves do not fully understand. Clarity and distinctness conditions therefore have to do with the grasping a thought than preserving its truth.

The terms denotes sort of consciousness attached to our thinking, where we attend consciously to what is contained in more concept or representation. This is what our phrase “knowing what we have in mind” seems to suggest. Take the negation of the A1 discussed above: a triangles is not a three sided figure. When you think this thought, it is not actually clear what you have in mind. It would be impossible to make clear the idea of a non-three sided triangle; that is, one literally cannot think such a thing clearly or distinctly. Logic for Kant consists in the rules of clear and distinct thought. In this picture, Kant gives a large role in his logical thinking to the principle of non-contradiction. He thinks it is flatly impossible for one and the same thinker to think both a proposition and its negation at the same time.

This is precisely where analyticity comes back in, for Kant uses non-contradiction as well as clarity and distinctness to spell out this notion. Let’s deal with the former first. Kant thinks that analytic truths are thought through the principle of identity, and their negation would violate the law of non-contradiction. This principle, if we recall, is a law of clear and distinct thought, thought wherein we have consciously made explicit what we are thinking. This process of making a concept clear and distinct Kant calls analysis. Furthermore, Kant thinks the analysis of the subject concept in an analytic judgment just is the proof of its truth. Let’s take another example of an analytic judgment, and see how this is supposed to work. Take the statement,

(A2) All bodies are extended

Let’s say we are obscure and confused about what this judgment is supposed to amount here, but make the judgment nonetheless. Even when we are thinking the judgment in this obtuse manner, we will be implicitly thinking of the concept of extension as we think of the concept body. We may not be exactly sure that we are doing; our thoughts may be hazy in some respect. Yet, when we attend to our concept of body, we realize that we think of the concept of a body as an extended thing. That is just what it is to be a body; or put differently, when we pick out things as bodies, we always use extension as a criterion for doing so. When we make explicit what we are thinking, we explicitly realize that we always already think the concept of extension in the concept body. Conversely, when we try to think of the judgment’s negation, we would be unable to do so in a clear manner: we could not picture, or conceive of, an non-extended body.

This, then, is what Kant has in mind by containment. He has in mind the idea that insofar as we think the subject concept, we already think the predicate concept along within. Realizing that the subject concept contains the predicate concept is just equivalent to making the subject concept explicit (that is, getting clear on what we are thinking when we think it). In this sense, analytic judgments are merely explicative: you can’t learn anything you didn’t already know from them, assuming you already had the subject concept. This is also why analytic judgments are one and all a priori: they require no special appeal to experience for their justification, and are necessarily true in virtue of their constitutive concepts alone.