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Kant's Synthetic A Priori Judgments

A Constrained Rant by The Famous Brett Watson, 16-May-2003.

In his Inaugural Dissertation (On the Form and Principles of the Sensible and Intelligible World), Immanuel Kant claimed (for the last time, it seems) that our reason allows us to represent things as they are, as opposed to things as they appear. The model of cognition which he felt allowed him to make such a claim involved the distinct segregation of "sensible" objects and "intelligible" objects, with the distinct powers of "sensibility" and "intellect" having respective jurisdiction over them. This solved for him a conflict between the philosophies of Leibniz and Newton, but he soon realised that his victory came at an unacceptable price.[1]

If it is not the world of experience that provides the intellect with the objects of which its ideas are true, what reason is there for thinking that there are any such objects? And if the ideas of the intellect are quite independent of the sensible world, how can intellectual principles such as the law of cause and effect — which is a presupposition of Newtonian science and as such must surely be accorded objectivity — have valid application to the spatio-temporal world?

— Sebastian Gardner, Kant and the Critique of Pure Reason[2]

The divorce of the sensible and the intelligible, it seems, would simply not do. Yet getting them to live with each other seemed just as difficult; the motivating factor in Kant's suggestion of the divorce in the first place. Similar difficulties in making sense of metaphysics had caused Hume to retreat into sceptical denial, but Kant found this refuge unacceptable. Metaphysics was necessary, so he felt, and thus the search began again for a way to bridge the gap between the two.

In the Critique of Pure Reason, Kant finally felt that he had been able to bridge this gap, reconciling the powers of sensibility and intellect. Perhaps the key insight which made this reconciliation possible was the recognition that both rationalist and empiricist camps, despite their diametrically opposing views on many points, had made, as he saw it, a common error with regards to the sources of knowledge. Hume classified knowledge in the following way.

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain. ... Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality.

— David Hume, An Enquiry Concerning Human Understanding[3]

Leibniz made a similar distinction, classifying knowledge into "truths of reason" and "truths of fact". The primary argument between rationalism and empiricism was the question of where metaphysical knowledge fits into the scheme of things: Leibniz deemed it a truth of reason, whereas Hume saw "causation" (in the sense of metaphysical necessity) as being amenable to neither class, and thus disqualified it as knowledge.[4] In the Critique, Kant agrees with the objections raised on both sides, proposing a resolution via his novel third alternative.

In the Introduction to the Critique, Kant discusses the generally accepted classes of knowledge using the terms a priori, empirical (which is his preferred term for a posteriori), analytic, and synthetic. Prior to the Critique it was generally accepted that a priori was coincident with analytic, and a posteriori (Kant's "empirical") was coincident with synthetic. By careful definition and discussion of the terms, Kant argues that we should abandon this notion of coextension, and recognise the necessary existence of synthetic a priori judgments; a novel classification.

Kant defines a priori knowledge as that kind of knowledge which is held independently of all experience, whereas empirical knowledge is possible only through experience. He further qualifies a priori with the adjective pure when the proposition in question contains no empirical elements, citing "every alteration has its cause" as a proposition which is a priori but not pure on the grounds that "alteration" is an empirical concept. Only a priori concepts, says Kant, can have properties like strict necessity and strict universality, since these properties could never be ascertained empirically. All mathematical propositions, for example, are a priori.[5]

Similarly, Kant distinguishes between analytic and synthetic judgments, describing analytic judgments as those in which the subject overtly or covertly contains (or excludes) the predicate, such that the truth of the proposition is determined entirely by (the meanings of) the terms themselves. Synthetic judgments are those which are not analytic, meaning that the terms alone are insufficient to determine the truth of the proposition. As examples, Kant suggests, "all bodies are extended" as an analytic judgment, and "all bodies are heavy" as a synthetic judgment.[6] Regardless of how compelling (or not) the examples are, the analytic/synthetic distinction itself was not controversial (or even novel) at the time.

It seems necessary that analytic judgments be a priori; once a judgment has been recognised as analytic, surely no reference to experience is needed, as the truth of the proposition can be determined simply by examining the terms. That being so, non a priori (i.e. empirical) knowledge is necessarily not analytic (i.e. synthetic) as a matter of logic. But these (apparent) implications do not preclude the possibility of knowledge which is both a priori and synthetic. Such knowledge, if it exists, would have the remarkable property that it grants us, without the need for experience, knowledge of truths which are not mere tautologies. When viewed in those terms, it seems almost spooky!

But do synthetic a priori judgments exist, and when (if at all) are we actually justified in calling them "knowledge"? Indeed, they do exist; it's not unreasonable to say that all the really "interesting" judgments are exactly of this kind. "Every event has a cause" is an example — one that is immediately recognisable as the kind of judgment accepted as knowledge by the rationalists (although they failed to recognise it as synthetic). But the antithesis, "no event has a cause", is also a synthetic a priori judgment: the fact that I can phrase it negatively without producing a contradictory or meaningless statement is sufficient to demonstrate that it is synthetic, and its claims to universality and necessity preclude it from being determined empirically.

How do we determine which (if either) of these can be considered knowledge? What are our grounds? Kant says that, whereas we can appeal to experience in the case of empirical judgments, we need some substitute source of appeal, "X", in the case of synthetic a priori judgments, since ordinary experience can no longer help us. That the need for this mysterious "X" has not been recognised in the past, says Kant, was the cause of many long and fruitless speculative arguments and investigations.[7]

Other examples of fields containing synthetic a priori judgments include pure mathematics and pure science. Pure science might raise an eyebrow at first, given as how it is firmly rooted in the empirical, but scientific laws like Newton's laws of mechanics are synthetic a priori judgments: they make necessary and universal claims (thus a priori) which are more than simple logical imperatives (thus synthetic). And mathematics, although rich with logic and proof-by-contradiction (and thus apparently analytic, as supposed by Hume), is ultimately synthetic at its roots, and thus synthetic at its leaves (since it is not possible to arrive at an analytic result from a synthetic base, even when each step along the way is analytic). That mathematics is ultimately synthetic is by no means obvious, but Kant's stance on the matter seems to have been vindicated with time; if my (admittedly naïve) understanding is correct, Gödel's incompleteness theorem has demonstrated that no fully satisfactory purely analytic account of mathematics can ever be forthcoming.

Similarly, all the important statements of metaphysics are synthetic a priori propositions.[8] When viewed this way, the problem of metaphysics becomes one of determining how to make synthetic a priori judgments in that domain. Given the success of mathematics and natural science, which also deal with synthetic a priori judgments, there seems cause to hope for at least some semblance of real progress in the field when the appropriate rules of the game are recognised.

These "appropriate rules", says Kant, must arise from reason itself, but not unbridled reason, free to speculate as it pleases. That, presumably, would be no better than a kind of natural science which operates speculatively from an armchair and never goes out of doors for a reality check. But metaphysics has no access to the great outdoors in the way that the natural sciences do (or else rationalism would have been less problematic). So the best "reality check" we can offer on reason is reason itself: reason scrutinising itself; a critique of pure reason.

When once reason has learnt completely to understand its own power in respect of objects which can be presented to it in experience, it should easily be able to determine, with completeness and certainty, the extent and the limits of its attempted employment beyond the bounds of experience.

— Immanuel Kant, Critique of Pure Reason[9]

It's perhaps simplistic to hope that reason might completely understand its own power (and a less than complete understanding may suffice for some purposes), but the direction suggested here certainly seems worthwhile. Armed with the recognition that there are synthetic a priori judgments which, in metaphysical claims, require a non-obvious source of justification, "X", we should examine the nature of the facts before us, and scrutinise our own ability to make judgments (or not) based on those facts.

But in this essay, I am primarily considering the significance of "synthetic a priori judgments" without following the Critique through to the last page. I therefore part ways with it at this point, with Kant foreshadowing the remainder of the work.

It seems apparent that Kant has picked up a significant error in both the rationalist and empiricist camps. As Gardner puts it, synthetic a priority is anomalous for both empiricism and rationalism, "since these philosophical traditions either fail to recognise that experience must have a structure (empiricism) or falsely suppose it to derive from logical principles (rationalism)."[10] That, in and of itself, is significant to philosophy as a whole, and neither rationalism nor empiricism can stand, unaltered, in light of it.

It also seems hard to deny the importance of these allegedly synthetic a priori judgments. In retrospect, if Hume's model of "relations of ideas and matters of fact" had been true, the world would be a fairly boring place. Computers would have been much more useful than they are in the field of philosophy, since they are eminently useful for managing relations of ideas, and the remaining part of knowledge would have been attainable by "going and having a look", assuming you found reason to care. Kant's model leaves us with hidden truths; truths which may be attainable, in part at least, but which cannot be reached by applied logic alone. Perhaps Kant would have appreciated Proverbs 25:2 in light of his observation: "It is the glory of God to conceal a thing: but the honour of kings is to search out a matter."[11]

Even if we grant that synthetic a priori judgments are the key to metaphysics (as they are to mathematics and natural science), it is far from given that a critique of reason will show us to have faculties sufficient to the task of researching metaphysics, or that we will be able to identify or access the mysterious "X" necessary to justify any given judgment. But since these potential troubles are beyond the scope of the present essay, let us instead question whether an alternative view of knowledge can undermine Kant's argument.

Gardner mentions a possible attack on the analytic/synthetic distinction by "Quine and others" (no specific papers are named), but declines to elaborate on it, citing an "underlying metaphysical picture so remote from Kant's that it may be held to one side in the present context."[12] I confess that applying Quine to Kant sounds like it may be entertainingly destructive, so let us call briefly upon Two Dogmas of Empiricism[13], a likely Quine candidate, and see if any sense can be made of Kant's model after the dust clears.

In "Two Dogmas of Empiricism", Quine contends that the classification of certain propositions as "analytic" is based on nothing more than dogma. Specifically, he agrees that logically tautologous propositions should be classified as analytic, but takes exception to synonymy of terms as a criterion for analyticity. Thus "no unmarried man is married" qualifies as analytic, but "no bachelor is married" is problematic. Kant would say that the subject ("bachelor") contains (the negation of) the predicate ("is married"), thus the statement is analytic. Quine contends that the "containment" or "synonymy" which identifies the statement as analytic is not sufficiently well-defined to produce a general test of "statement S is analytic in language L" for variable S and L. He feels that we are in error to have attempted classification of such a statement, and explains the error in the following terms.

It is obvious that truth in general depends on both language and extra-linguistic fact. The statement 'Brutus killed Caesar' would be false if the world had been different in certain ways, but it would also be false if the word 'killed' happened rather to have the sense of 'begat.' Hence the temptation to suppose in general that the truth of a statement is somehow analyzable into a linguistic component and a factual component. Given this supposition, it next seems reasonable that in some statements the factual component should be null; and these are the analytic statements. But, for all its a priori reasonableness, a boundary between analytic and synthetic statement simply has not been drawn.

— W.V.O. Quine, Two Dogmas of Empiricism[14]

Does this problem impact Kant? It's not clear that it does. Quine declares the analytic/synthetic distinction fuzzy or dogmatic, but leaves us the distinction of "logically tautologous" and "not logically tautologous". The net effect of reclassifying analytic and synthetic statements into these (implicit) categories would be for some of the "analytic" statements to be regrouped with the "synthetic" statements. Everything which was a "synthetic a priori judgment" remains so. At worst, it seems, there are some additional such judgments which we can no longer take for granted as knowledge.

I think the situation can be explained better than that, however, by re-applying Kant's "Copernican revolution" idea. When I say "no bachelor is married", I know this to be a true analytic a priori judgment, because I know what I mean by "bachelor" and "is married". I have privileged access to that information, since I constructed the statement from the meaning I intended to convey. Whether or not I can ever determine that someone else means the same thing when they say it is a different question, and not one that appears to need much attention in the context of a critique of pure reason. Quine's target is the empiricist audience, so he is doubtless not defending against a Kantian response. Even so, he comes close to addressing my approach in the following extract.

I do not know whether the statement 'Everything green is extended' is analytic. Now does my indecision over this example really betray an incomplete understanding, an incomplete grasp of the "meanings," of 'green' and 'extended'? I think not. The trouble is not with 'green' or 'extended,' but with 'analytic.'

— W.V.O. Quine, Two Dogmas of Empiricism[15]

In the unlikely instance that I were to make the claim, "everything green is extended", I would use it in the analytic sense that "everything green" contains the concept "body", which in turn contains the concept "is extended", so I'll dismiss Quine as simply not trying hard enough on this occasion. After all, if something is not extended, how can it have a property of colour? Perhaps he intended the subject and predicate to be more conceptually detached, such as in, "everything green is loneliness". I can safely say that I do not know whether that is an analytic statement, on the grounds that I have no idea what it means.

Quine's ultimate claim is, "The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges."[16] If we allow this to stand, unchallenged, does it form a serious conflict with Kant and the significance he attaches to synthetic a priori judgments? Modulo the differences between Quine's "experience" and Kant's rational introspection, I think the two are eminently compatible, which comes as a surprise, given Gardner's reservations about the matter.

Both Kant and Quine appreciate that the field of knowledge is seriously underdetermined by experience: Quine states so explicitly, and Kant urges caution because of the unknown "X" factors inherent in synthetic a priori judgments, which may or may not be accessible. Kant hopes that his approach can raise metaphysics to the level of the natural sciences, and Quine states that ontological questions are, under his model, on a par with questions of natural science. The only obvious difference of any apparent significance is that where Kant has a cunning plan for using synthetic a priori judgments to guide him, Quine merely opts for "pragmatism" in adjusting his fabric, which isn't saying much.

So much for the Earth-shattering "kaboom" I was expecting. Still, why complain? I like them both.


  1. Sebastian Gardner, Kant and the Critique of Pure Reason (Routledge, 1999); see pp. 18-19
  2. Gardner, Kant, p. 19 (emphasis in original)
  3. David Hume, An Enquiry Concerning Human Understanding (Collier and Son, 1910); see §IV, pt I
  4. Gardner, Kant, p. 52
  5. Immanuel Kant, Critique of Pure Reason translated by Norman Kemp Smith (Macmillan Press, 1929); see pp. B2-4
  6. Kant, CPR, pp. B10-11
  7. Kant, CPR, pp. A9-10
  8. Kant, CPR, p. B18
  9. Kant, CPR, p. B23
  10. Gardner, Kant, p. 62
  11. Proverbs 25:2, King James Version
  12. Gardner, Kant, p. 61
  13. W.V.O. Quine, From a Logical Point of View (Harvard University Press, 1953); see pp. 20-46
  14. Quine, Two Dogmas, pp. 36-37
  15. Quine, Two Dogmas, p. 32
  16. Quine, Two Dogmas, p. 42


Gardner, Sebastian, Kant and the Critique of Pure Reason, Routledge, 1999

Hume, David, An Enquiry Concerning Human Understanding, Collier and Son, 1910

Kant, Immanuel, Critique of Pure Reason translated by Norman Kemp Smith, Macmillan Press, 1929

Quine, Willard Van Orman, From a Logical Point of View, Harvard University Press, 1953

Nutters.org Author: The Famous Brett Watson
Date: 2003-05-16
Public Domain: the author waives copyright on this document. Other sources (if any) are quoted with permission or on the principle of "fair dealing" and retain their original copyrights.