Summary: Critique of Pure Reason (page 8)

We have already seen the distinction between a priori and a posteriori judgements. Kant now introduces a new distinction: that between analytic and synthetic judgements.

A judgement consists of a subject and a predicate.

For example: This horse is black. Here, horse is the subject, and black is the predicate.

The predicate can relate to the subject in two ways: either it is contained within the concept of the subject, or it is not.

Let us take an example: the judgement "This dwarf is small." The concept small is already contained within the very concept of dwarf. One cannot be a dwarf without being small. There is an identity between these two concepts.

This is an analytic judgement.

Now consider a second example: "This dwarf is rich." The concept rich is not contained within the concept of dwarf itself. Some dwarfs are not rich.

This is a synthetic judgement.

An analytic judgement does not expand our knowledge—it merely makes explicit the (implicit) content of a concept we already know. It clearly analyses something that is already thought, though perhaps in a confused manner, within the concept.

A synthetic judgement, on the other hand, improves our knowledge. When we say, "This dwarf is rich," we convey to someone something they did not previously know and could not deduce by simply analysing the concept of dwarf.

The examples Kant gives of analytic and synthetic judgements are:

"All bodies are extended" (analytic judgement)

"All bodies are heavy" (synthetic judgement)

However, we find these examples less clear, as it is not immediately obvious why extension should necessarily belong to the concept of body, while weight does not.

We can now better understand why Kant states that through the predicate, analytic judgements add nothing to the concept of the subject but merely decompose it by analysis into its partial concepts, which were already thought within it (though only confusedly)...¹

…whereas synthetic judgements add to the concept of the subject a predicate that was not originally contained within it.

How do Kant’s distinctions now fit together—between a priori/a posteriori judgements on the one hand, and analytic/synthetic judgements on the other?

Analytic judgements are always a priori. This is because analytic judgements do not rely on experience; their sole function is to clarify what is already implicitly contained within a concept, by analysing it. There is no need to refer to experience to know that this dwarf is small.

Now, let us turn to synthetic judgements.

All a posteriori judgements are synthetic. Experience expands our knowledge. I need to refer to experience to determine whether this dwarf is rich (for instance, by speaking to him, checking his bank account, etc.).

Yet, somewhat surprisingly, there are also a priori synthetic judgements.

This is striking because Kant repeatedly insists that knowledge is confined to the limits of experience.

And yet, here he seems to suggest that some judgements expand our knowledge (and are therefore synthetic) while remaining a priori.

Kant provides examples of a priori synthetic judgements: mathematical judgements.

For instance, "7 + 5 = 12" is not an analytic judgement because the concept of 12 is contained neither in that of 5 nor in that of 7.

This makes it a synthetic judgement, yet it is still a priori, because, as we have seen, mathematical judgements are a priori. If they were empirical, they could not constitute universal and necessary laws—which, nonetheless, they do.

The genius of a thinker sometimes lies not in providing an answer to a problem but in formulating a new problem.

Here, Kant’s philosophical breakthrough consists in posing the following question:

How are a priori synthetic judgements possible?

Properly formulated, this question asks:

How is it possible for certain judgements to expand our knowledge without being based on experience?

Why are a priori synthetic judgements valid in mathematics and certain other disciplines, but not in metaphysics?

This brings us back to the problem we had set aside earlier when reading the second Preface. Setting it aside was the right decision, as it has now allowed us to deepen our understanding and refine the question itself. To ask why there is valid a priori knowledge in mathematics is ultimately to ask:

How are a priori synthetic judgements possible?

Once again, grasping the significance of this problem—and then understanding the answer Kant provides—is key to comprehending the overall meaning of the Critique of Pure Reason.

¹ Our translation. The references for the quotations are available in the book Kant: A Close Reading