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:
- This object has extension. — synthetic
- It has mass. — synthetic
- A body is defined as having extension and mass. - analytic
- 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.