I describe here the division of judgments into kinds from Kant’s Critique of Pure Reason.
First, judgments are divided into a posteriori, or empirical judgments, and a priori judgments.
- A posteriori judgments are divided into particular empirical judgments and inductive judgments.
- A priori judgments are divided into pure a priori and impure a priori judgments.
The rest of this blog post will define each of the kinds in that order, with page numbers from the “B” edition of the Critique in parentheses.
0. Contents
1. A posteriori, or empirical judgments
A posteriori judgments are drawn from some experience, upon which they depend; (B2) so, they are always synthetic. Now, “experience teaches us, to be sure, that something is constituted thus and so, but not that it could not be otherwise”; because of this, a posteriori judgments always have no necessity, and no true or strict universality. They may have assumed and comparative universality, as will be explained next. (B3)
1.1. Particular empirical judgments
Particular empirical judgments are empirical judgments about particular things. They are always a posteriori and they lack any kind of universality. They are said to be derived immediately from experience; an example would be your judgment that a bridge has collapsed, made after you have seen it collapsing. (B2)
Not all particular judgments are empirical, because some of them involve a pure concept of the understanding which confers necessity and strict universality to the judgment; see §2.2 of this post. (Prolegomena, §20, fn1)
1.2. Inductive judgments
Inductive judgments may also be called a priori secundum quid, or “a priori in some respect”, but not a priori simpliciter, or “a priori simply speaking”.1 This is because, while they are not independent of all experience, they may be said to be independent “of this or that experience”, since they involve judging about something before you see it actually happening. For example, you may judge that your house will collapse right after you have undermined its foundation. You know this before actually seeing the house collapse, but only because you know from experience that “bodies are heavy and hence fall if their support is taken away”. (B2)
This is to say that these judgments have “empirical universality”: they are drawn from a general rule, but the general rule is itself drawn from experience, through induction.
Empirical universality is an “assumed and comparative” kind of universality (B3) which is “only an arbitrary increase in validity from that which holds in most cases to that which holds in all”, as in the proposition “all bodies are heavy”. (B4) That is, we cognize that bodies are heavy “as far as we have yet perceived” and arbitrarily decide that this must hold for all bodies.
To emphasize their inferior certainty in comparison with a priori judgments, I tend to refer to inductive judgments as “probable”, but Kant did not do this.
2. A priori judgments
A priori judgments are “those that occur absolutely independently of all experience” (B2), so that they have necessity and strict universality. (B4) They may be either analytic or synthetic, and investigating the latter kind was a major aim of Kant’s. (B73)
2.1. Pure a priori judgments
These are a priori judgments that contain no concepts drawn from experience, (B28) though we still find that all of these are nevertheless only valid in empirical use, (B170) i.e., they may only be used to judge about appearances.
Synthetic pure a priori judgments include all properly mathematical judgments, (B741ff) as well as the various principles of the transcendental philosophy (B25ff; table at B200) and the supreme principle of morality. (Groundwork, passim) Various analytic judgments may be trivially drawn from these by clarifying the concepts that they involve.
2.2. Impure a priori judgments
These are a priori judgments that contain some concepts that are themselves drawn from experience, although the judgments made about them are valid a priori. (B3) This is most clearly the case with analytic judgments about empirical concepts, such as “all bachelors are unmarried”:2 although we learn about bachelors and marriage from experience, the judgment that bachelors are unmarried is a priori because it is analytic. Crucially, however, there are other ones, such as the typical judgment that “every alteration has its cause”: although “alteration is a concept that can be drawn only from experience” (B3), this judgment is nevertheless demonstrable a priori, since it is a formulation of the Second Analogy of Experience. (B232ff)
It seems that, in general, although impure a priori judgments concern a concept drawn from experience, they receive the character of necessity and strict universality from a pure concept of the understanding that is involved in them. So, the judgments may even be about particular things, as long as they conceive of those things as being under a universal law. For instance, if instead of judging that “the sun shines on the stone and then it becomes warm”, we judge that “the sun warms the stone”, we conceive of the sunshine under the pure concept of cause, and therefore give it a necessary and strictly universal connection to the heat, making the judgment a priori, though impure. (Prolegomena, §20, fn1)
3. Footnotes
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This name itself does not come from the Critique of Pure Reason, but from the Metaphysik Mongrovius, printed in the Lectures on Metaphysics volume. I quote the relevant passage:
Something is [...] a priori in some respect <secundum quid> when I cognize something through reason, but from empirical principles, e.g., if I throw a stone horizontally – so that it does not fall straight down – one can determine the curve a priori, but according to laws of gravity, which we cognize a posteriori. (pp. 112–113)
While the Critique does not use this term, it nevertheless clearly describes such judgments without using the name, as a footnote to the Cambridge edition of the Critique indicates.↩
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Obviously, here I mean the judgment that “all bachelors are unmarried” made by someone whose concept of “bachelor” is expressed by the definition “unmarried man”. I only even mention this in a footnote because some people try to read the analytic/synthetic distinction as applying to “propositions” being true “in virtue of the meanings of words”, and word meanings are obviously never all that fixed, and those people therefore think they are being very smart by pointing out that “bachelor” sometimes has other meanings, and therefore that the distinction does not work very well after all when used about propositions in this way. I think that, regardless of how other people have used the distinction since his time, this is simply not what Kant was talking about.↩
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