Building Blocks for the Critique of Pure Reason: analytic vs. synthetic judgement.

Here is Kant’s outline of the difference between analytic and synthetic judgements:

In all judgements in which the relation of the subject to the predicate is thought (if I consider only affirmative judgements, since the application to negative ones is easy) this relation is possible in two different ways. Either the predicate B belongs to the subject A as something that is covertly contained in the concept A; or B lies entirely outside the concept A, though to be sure it stands in connection with it. In the first case I call the judgement analytic, in the second synthetic. Analytic judgements (affirmative ones) are thus those in which the connection of the predicate is thought through identity, but those in which the connection is thought without identity are to be called synthetic judgements.

The distinction itself is well known in analytic philosophy, and I won’t dwell on it for long. The standard examples go as follows.

In the judgement ‘All bachelors are unmarried’, the predicate – ‘are ummarried’ – adds nothing to the subject – ‘all bachelors’. Bachelors are married by definition, so, as Kant puts it, ‘the predicate [are married] belongs to the subject [all bachelors] as something that is (covertly) contained in this concept’.

However, in the judgement ‘All bachelors smoke cigarettes’, the predicate – ‘smoke cigarettes’ – does add something to the subject. There is nothing in the concept ‘bachelor’ to justify our judgement. Of course, it might turn out to be true, but the only way we can determine this is by looking beyond the concept into the world to see if all bachelors do in fact smoke. Again, using Kant’s phrasing, ‘[smoke cigarettes] lies entirely outside the concept [all bachelors], though to be sure it stands in connection with it.’

If I can go on a tangent quickly, the thought that the predicates of synthetic judgements lie outside their concepts but still stand in some connection to them is an interesting one. Obviously its a necessary qualification: there is a particular type of connection that characterises the subjects and predicates of possible synthetic judgements. For example, ‘my dog is hungry’ is a possible synthetic judgement; ‘the number ’2′ is hungry’ is not. Although being hungry is not contained in my concept of my dog, it is still connected to it in some way, where as the only thing connecting the number ’2′ and being hungry is their non-connection…

Anyway, Kant expands his definition to include the role played by each type of judgement in building our store of knowledge:

One could also call the former judgements of clarification, and the latter judgements of amplification, since through the predicate the former do not add anything to the concept of the subject, but only breaks it up by means of analysis into its component concepts, which were already thought in it (though confusedly); while the latter, on the contrary, add to the concept of the subject a predicate that was not thought in it at all, and could not have been extracted from it through any analysis.

All judgements based on experience are synthetic, as experience itself would be redundant if there were no need to look beyond the concept. Kant’s example is the connection between the concepts ‘body’ as subject, and ‘weight’ as predicate. There is (says Kant) no necessary connection between these concepts. Nonetheless, the concept ‘body’ designates a certain kind of object that we come across in experience, allowing us to connect other parts of experience (i.e. further predicates) to it:

I can first cognize the concept of body analytically through the marks of extension, of impenetrability, of shape, etc., which are all thought in the concept. But now I amplify my cognition and, looking back to the experience from which I had extracted this concept of body, I find that weight is also connected with the previous marks, and I therefore add this synthetically as a predicate to that concept. It is thus experience on which the possibility of the synthesis of the predicate of weight with the concept of body is grounded, since both concepts, though the one is not contained in the other, nevertheless belong together, though only contingently, as parts of a whole, namely experience, which is itself a synthetic combination of intuitions.

A few points, before we move on. Experience provides the possibility of the synthesis of the concept and predicate, which means that the resulting judgement (‘bodies are heavy’) is characterised by the features I outlined in my earlier post: contingency, specificity, and falsifiability. The concepts are found to belong together as part of a whole which is itself synthetic: experience.

Its worth noting that this might suggest two distinct levels of synthesis: one at which experience itself is constituted, and another at which general judgements based on this experience are made. Alternatively it might suggest a single process of synthesis, so that contingently true judgements come about in exactly the same way – by the same faculties undertaking the same processes – as experience itself. Another way of putting this would be to say that EITHER there are two distinct forms of synthesis – synthesis of intuition (the ‘raw material of sensible sensations’ that are prior to experience proper), and synthesis of cognitions (whose material is experience in the robust sense, synthesised intuitions). OR an identical process is involved in both. Either way, the implications are enormous, and more than I can cover in this post.

So, experience provides the material for a posteriori synthetic judgements. But with a priori synthetic judgements, this extraneous material is entirely absent. And here Kant asks his most important question:

If I am to go beyond the concept A in order to cognize another B as combined with it, what is it on which I depend and by means of which the synthesis becomes possible, since here I do not have the advantage of looking around for it in the field of experience?

In other words, how are synthetic a priori judgements – judgements that amplify rather than clarify our a priori knowledge – possible? What material is available for synthesis?

Of course, Kant has yet to show that such judgements are possible. This comes in section V of the <B> Introduction, and I’ll deal with it properly in a later post. At this point, he uses the following proposition as an example: ‘Everything that happens has a cause’.

Hume had apparently shown that there was no necessary connection between our concept of an effect and our concept of its cause. Kant seemingly assents to this:

In the concept of something that happens, I think, to be sure, of an existence that was preceded by a time, etc., and from that analytic judgements can be drawn. But the concept of a cause lies entirely outside that concept, and indicates something different than the concept of what happens in general, and is therefore not contained in the latter representation at all.

The idea is that it ought to be necessarily true that ‘Everything that happens has a cause’, and yet this cannot be an analytic a priori judgement (because the concept of a cause is not necessarily connected to the concept of something happening), nor can it be a synthetic judgement based on experience (because then it would only be contingently and specificly true). So if we are right in saying that necessarily, everything that happens has a cause, our justification can only come from an a priori synthesis. A priori because this will characterise the judgement as necessary, universal, and non-falisfiable; synthetic because the two concepts do not belong together of themselves.

Kant puts it as follows:

How then do I come to say something quite different about that which happens in general, and to cognize the concept of cause as belonging to it, indeed necessarily, even though not contained in it? What is the unknown = X here on which understanding depends when it believes itself to discover beyond the concept of A a predicate that is foreign to it yet which it nevertheless believes to be connected with it? It cannot be experience, for the principle that has been adduced adds the latter representations to the former not only with greater generality than experience can provide, but also with the expression of necessity, hence entirely a priori and from mere concepts.

So synthetic a priori judgements rest on an unknown = X, which is distinct from experience. We now know some of the characteristics of such judgements, even if we are not sure about the existence or features of the unknown = X that grounds their possibility. Why are they important? Kant says:

Now the entire aim of our speculative a priori cognition rests on such synthetic, i.e. ampliative principles; for analytic ones are, to be sure, most important and necessary, but only for attaining that distinctness of concepts which is requisite for a secure and extended synthesis as a really new acquisition.

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