Well, it appears that this blog draws to it a significant
number of grammar mavens. Who knew? Rather than quibble further about the correct
classification of “a priori” and “a posteriori,” let me take a few moments
to explain what is actually at stake.
Analytic judgments, Kant says, are judgments in which the
predicate unpacks or spells out what is already contained in the subject. Hence, he calls them “explicative.” In the judgment “All bachelors are unmarried,”
for example [I like the old-time favorites], the subject term “bachelor” is
defined as “unmarried man.” The judgment
“All bachelors are unmarried” simply explicates what is contained in the
concept of the subject. Synthetic
judgments, on the other hand, such as “Most bachelors are unhappy,” add
something to the concept of the subject.
Hence Kant calls them “ampliative.”
[I am expounding Kant here, so don’t pester me with modern revisions of
this classical story, please.]
There are some judgments whose truth can be know independently
of and hence prior to experience. The judgments can, in other words, be known a priori. “All bachelors are unmarried” is such a
judgment, as are all analytic judgments according to Kant. There are other judgments whose truth can be known
only on the basis of, or after, experience. These judgments can, in other words, only be known
a posteriori. “Most bachelors are unhappy” [supposing this
to be true, as I, a married man, confidently believe] is an example.
Can analytic judgments be known a posteriori? Yes. One can imagine a team of not too bright sociologists
wanting to know whether all bachelors are unmarried. They get a grant, round up some graduate
students, draft a three question survey, and identify a carefully chosen representative
sample of the population. They ask each
subject three questions: Are you a
bachelor? Are you a man? Are you married?” After a careful statistical analysis of the
results, they draft a journal article in which they report that, within the
margin of error, 100% of bachelors are unmarried. A secondary result is that, within the margin
of error, 100% of bachelors are men.
Kant can state with confidence that the proposition “All
bachelors are unmarried” is universally and unconditionally, hence necessarily,
true. It can be known to be true a priori. But the sociologists are only able to state
that the proposition “All bachelors are unmarried” is confirmed with a high
degree of probability, within the margin of error. Hence they have only established it a posteriori.
Can a synthetic judgment be known a priori? It would seem not,
for, as Kant recognized shortly after delivering the Inaugural Dissertation of 1770, there does not seem to be any way
in which we can have knowledge a priori
about the independently real.
The Critique of Pure Reason
is devoted to this problem.
I trust all of this is clear. The question for Kant is: Can we know a priori the truth of certain propositions [most notably the Causal
Maxim] that are synthetic? One can, in
abbreviated form, express this as the question “Are there any synthetic a priori propositions?” if one
wishes. But to my ear, anyway, that is a
misleading way of articulating his central question.
I don't think analytic judgments can be known a posteriori. What the "not too bright sociologists" know a posteriori is the judgment "All SURVEYED bachelors are unmarried", which of course is not analytic. The analytic judgment in question is "ALL bachelors are unmarried", and surely that ("ALL") can be KNOWN only a priori. (This assumes, of course, that "surveyed bachelors" is not identical with "bachelors".)
ReplyDelete1. "All SURVEYED bachelors are unmarried" is analytic. or
ReplyDelete2. So make the survey cover all bachelors.
3. If the truths of arithmetic (or at least some of them) are analytic, then there a posteriori cases galore.
Dear prof.,
ReplyDeleteAs Acastos above me, I am doubtful about the claim that Kantian analytic judgements are knowable aposteriori. My reason for this doubt is that in the fourth chapter of Introduction B, Kant states that "[I]t would be absurd to found an analytic judgement on experience." and explains the absurdity by pointing out that for making analytical judgements, nothing beyond the possession of concepts making up the judgements is required. So, the "not too bright sociologists", you mention in the example should, in my opinion, know that all bachelors are unmarried before they appeal to experience, just by framing the judgement in question (which they presumably need to do, if they are to test it as hypothesis).
Auerbach: For Kant, the truths of arithmetic (save identities) are all synthetic. It was precisely thinking that the truths of arithmetic were analytic that, according to him, led all previous dogmatists (Leibniz) and sceptics (Hume) astray.
ReplyDeleteAlso, you can't make the survey cover all bachelors, since you won't capture bachelors of the future.
Yes, I know. I wasn't expositing Kant.
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ReplyDeleteI. M. Flaud: Correct, in order to frame the judgemnt that all bachelors are unmarried, one have to have whatever experience is required for the possession of concept 'bachelor', which is an empirical concept. But once you are in possession of this empirical concept, no other experience is required for knowing that all bachelors are unmarried. This contrasts with synthetic judgement such as 'most married men are unhappy' (which I, as bachelor, happen to believe :)) knowledge of which requires not only experience required for mere possession of empirical concepts 'married man' and 'unhappy' but also experience in which the concepts are contingently connected.
ReplyDeleteBut there is an important point here. Kant thought that pure mathematics did not even require experience to acquire such concepts as line and triangle, because these could be could be constructed in pure intuition. I will go into this at length in my lectures.
ReplyDeleteThank you -- the question of the empirical origin or otherwise of concepts, versus a priori or a posteriori justification of judgments in which these occur, are separate.
ReplyDeleteIncidentally, I purchased your book, "Kant's Theory of Mental Activity" (Kindle and hardcover editions) and then read four or so reviews of your book through JSTOR (alumni access to library services is all I have to show for a Ph.D. in mathematics--a regrettable waste of time otherwise). The reviews were enough to induce a depression from which I have yet to fully recover. I am nevertheless committed to your forthcoming lectures.
Good grief. What did the reviews say?
ReplyDeleteSuppose Saul, after learning his integers, addition and subtraction, multiplication, and a few moments of working out some cases, announces to his mystified parents, "Mother, Father, did you ever notice that if you pick two integers, subtract one from the other, and then add them, and then multiply the two results, you get the first times itself minus the second times itself?" It would seem that Saul would have learned from experience the universal and necessary truth that (a-b)*(a+b)=a^2 - b^2....
ReplyDeleteBy the way, the Kindle version of Kant's Theory of Mental Activity has an occasional typo. Is there a way to report these so that they get fixed?
ReplyDeleteAndrew, Saul would indeed have learned that, with considerable frequency, a-b etc etc, but he would not have learned that Necessarily a=b etc etc.
ReplyDeleteAs for typos, I have not a clue how one would address those. Are they bad?
Thus far little things such as the Kindle version has, "As an undergraduate, I was privileged to attend Clarence Irving Lewis’ lectures *at* Kant...." The paper version has *on*.
ReplyDeleteWell, yes little Saul did not learn that necessarily A, but he did learn A, which is necessary and universal to boot.
ReplyDeleteBy the way, again, the Kindle edition of the Critique doesn't have the page numbers of the two editions. Grrrr....