Kant's analytic/synthetic propositions

Question

In the Critique of Pure Reason, an example of an analytic proposition is that all bodies are extended, and an example of a synthetic proposition is that all bodies are heavy (A7|B11), however in the Prolegomena, an example of a synthetic proposition is that some bodies are heavy (Ak. 4:266-7).

I don't understand if 'heavy' means 'having mass', or it means 'of great weight' or 'hard to lift'. If it means that it has substantial mass, then I don't understand why it should be a synthetic proposition?

It seems to me that having mass is already within the concept of a body. So how did Kant decide it was synthetic? Could it be that it is synthetic because we could 'show' that it is a posteriori?

Answer 1

Analytic and synthetic judgements

His definition is rather straight and it seems as if you correctly applied it: analytic essentially means 'already thought within the concept itself':

Either the predicate B belongs to the subject A as something that is (covertly) contained in this 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. (CPR A6|B10)

Providing the quote

Kant states:

...if I say: “All bodies are extended,” then this is an analytic judgment. For I do not need to go outside the conceptc that I combine with the word “body” in order to find that extension is connected with it, but rather I need only to analyze that concept, i.e., become conscious of the manifold that I always think in it, in order to encounter this predicate therein; it is therefore an analytic judgment. On the contrary, if I say: “All bodies are heavy, ” then the predicate is something entirely different from that which I think in the mere concept of a body in general. The addition of such a predicate thus yields a synthetic judgment. (CPR A7|B11)

That is exactly what you referred to in the OP. Nothing interesting here, as he does not seem to think he had to provide any reasons for that. The questions therefore is totally legit and leaves us with the task to provide an answer.

Why heaving mass is adding something to the concept of 'body'

It is crucial to understand which concept of 'body' Kant means here. In his Metaphysical Foundations of Natural Sciences from 1784 Kant writes:

A mass of determinate shape is called a body (in the mechanical meaning). (Ak. 4:537)

This means that he clearly cannot refer to a mechanical (or physicist's) definition of 'body' in the Prolegomena or CPR. I hope it also clarifies that Kant probably did not think of particularly heavy bodies, but bodies that have mass. This leaves us essentially with a geometrical definition:

A "geometric body" of classical mathematics is much more regular than just a set of points. The boundary of the body is of zero volume. Thus, the volume of the body is the volume of its interior, and the interior can be exhausted by an infinite sequence of cubes. (Source: Wikipedia)

And to come to the conclusion that all (or at least some) geometrical bodies are heavy, we need mass, therefore this judgement is synthetic. Basically, as all bodies in experience are indeed mechanical bodies (i.e. there are no massless bodies in the world, just in thought), the general phrase holds although it is not a priori true. And it is tempting us to reduce body to mechanical body.

Conclusion

Therefore, your confusion probably arises because you already had a mechanical definition of the concept of 'body' in your mind (for which - indeed - "bodies are heavy" is an analytic judgement), whereas Kant supposedly speaks of geometrical bodies in the first Critique and the Prolegomena, i.e. defined shapes enclosing space. But arguably mechanical body already in itself is a synthetic proposition, i.e. there is already something added to the concept of 'body' - namely mass. I do not think that this has anything to do with a priori or a posteriori, as the number of principles a priori is very small and taking this into account rather confuses than clarifies.

Answer 2

The idea that the predicate of an analytic judgement is thought to be contained within the concept is somewhat confusing unless it is understood in the context of the following:

"Analytical judgements (affirmative) are therefore those in which the connection of the predicate with the subject is cogitated through identity; those in which this connection is cogitated without identity, are called synthetical judgements." (CPR, A6/B10)

In terms of logic, an identity can be thought of as defining how one thing may (although with some exceptions) be substituted for another. Quine, for example, sustains this same point:

"Functionally a definition is not a premiss to theory, but a license for rewriting theory by putting definiens for definiendum or vice versa." (W. V. Quine, "Truth by Convention")

Quine also asserts that such statements are vacuous in that they are "incapable of grounding the most trivial statement," and this is precisely what they should be considering the purpose for which Kant made the distinction.

Given that he believe that some synthetic propositions are necessarily true, Kant needed to distinguish them from analytic judgements which he also considered necessarily true. Therefore, his definition of analytic judgements must be understood such that it maintain the property of necessity. In the case of analytic judgements, necessity is rooted in nothing more that convention or agreement. If it is thought to have any other basis, it ceases to be analytic:

"[Analytic judgements] add in the predicate nothing to the conception of the subject, but only analyse it into its constituent conceptions, which were thought already in the subject, although in a confused manner;" (CPR, A6/B10)

Putting it into practice:

For putting these principles into practice, I don't believe that there is a better rule of thumb than doubt. If a proposition gives rise to any doubt whatsoever which cannot be verified by a simple review of an established convention, it is not an analytic proposition. Similarly, if an analytic proposition is used to assert something which is doubted by another, that doubt must have its basis in nothing more established convention. Otherwise it is not an analytic proposition.

For example, suppose a group of people decided to adopt the following definition: "Body — that which has both extension and mass." That's fine as long as it's acceptable to everyone involved. However, problems might arise if someone should choose to use it as a synthetic proposition. Upon encountering an object, somebody might assert, "It's a body, so, by definition, it must have mass."

Rather, the reasoning should proceed as follows:

1. This object has extension. — synthetic
2. It has mass. — synthetic
3. A body is defined as having extension and mass. - analytic
4. This object is a body. — synthetic (the definition applied by substitution)

The crucial point to be noticed here is that the application of the definition must be a consequence of the properties and not the other way around. In other words, by calling it a body, it is already presupposed that the object has extension and mass (i.e. according to the example's definition). Error arises when the properties are viewed as a logical consequence of the definition.