Distinction Series: Analytic Judgments and Synthetic Judgments

The distinction between analytic and synthetic is perhaps Kant's most important distinction; it played a substantial role in the organization of his thought, and on the substance of the central question of his critical philosophy: "how are synthetic judgments a priori possible?" Because of this, it feels like a natural place to start even though many will be familiar with the distinction.

(It is important to note that I am discussing judgments and not propositions. The difference I am drawing between these two is roughly the difference between an action [judgment] and a representation of an action [proposition].)

The Distinction

The distinction between analytic and synthetic judgments doesn't involve all judgments, but only judgments that concern the connection of a concept and predicate. These judgments are determining judgments (as opposed to reflecting). So the parent category of this distinction is determining judgments generally concerning how the predicate is connected to the concept. 

Judgments can be considered in many ways, but in this case we only need to consider that judgments involve a relation between a concept and a predicate. In analytic judgments, the predicate is contained in the concept, while in synthetic judgments the predicate is not contained in the concept (it may be helpful to call the predicate in a synthetic judgment a 'determination').
The parent of this distinction (determining judgments generally) is an abstract category that belongs to critical philosophy. All determining judgments are either analytic or synthetic.

(For Kant's working out of this distinction see the Critique of Pure Reason A6/B10.)

Phenomenological Demonstration

I'll start by illustrating a synthetic judgment. First, I'll select a concept of an object. I'll consider a table. I imagine a table with three legs, then a table with four legs. (Through imagining the table we are representing it to ourselves, that is, reproducing an image through the imagination.) From this I can see that the concept of table does not contained a specific number of legs analytically. If it did I would only imagine tables with a specific number of legs. Thus the judgment of the number of legs a table has involves a synthesis.

Transitioning now to an analytic judgment, I will take the same example of a table. I try to imagine a table that has no extension, and am unable to do so. Now, I'm not certain what 'table' means to any of my readers*, but I expect that like me they are unable to represent a table with no extension, which would illustrate how extension is analytic with our concept of table.
Concepts of objects that can't be represented can apparently also be used in analytic or synthetic judgments. In this case one can't make trial of the status of the judgment with a representation, but can only give an exposition of what is contained in ones concept in order to see what is there or not.

* I will comment more on this in the section on "Ambiguities and Questions."

Importance in Kant's Work

With the distinction between analytic and synthetic judgments comes an important matter for reflection: if an addition is being made to something, then this addition must come from something else; so, from where do we acquire material suited to the extension of a concept? Also, we can ask: speaking generally, can a concept be extended in many ways, and if so, in what ways can a concept be extended?

Because Kant determines the only material for the extension of concepts that would give us knowledge would be from experience, the (pure) concept of existence itself is oriented towards experience. (We can use our imagination to determine concepts further, but Kant seems to think that, outside of mathematics, nobody will agree that this is a legitimate way to secure more knowledge.) Because dogmatic metaphysics (as Kant criticizes it) attempts to attain to knowledge from pure concepts without any experience, the entire enterprise of seems to fail, and exposes the need for a new grounding. Kant provides this new grounding for the judgments of metaphysics via moral philosophy.

Much more could be said about this, but I seems appropriate for another post.

Ambiguities and Questions

(This is a work in progress. Please comment on this post with any questions, and I can hopefully address them.)

It is very important to point out that the meaning of words is not being directly considered in the distinction between analytic and synthetic judgments. A judgment is produced by an individual, and requires a concept. A word may evoke different concepts at different times, and for different people. So, Kant is aware of the possibility that some people will identify yellow with gold analytically, some people will not.

Q: If an analytic judgment only repeats what is contained in a concept, why does it feel like we learn something when we reflect on a concept in order to bring out what is contained in it?

A: It seems that we are learning something about ourselves (our understanding, our concepts), and so our self-concept is being determined.