Analytical judgments have their predicates that are wholly contained in their subjects. In our case, the concept “gold” includes the concept “yellow” and the concept “metal,” which only explain what consists of the concept “gold” rather than create judgments that are beyond the concept “gold.”
A criterion for this judgment’s analyticity is one’s ability to single-handedly determine this judgment’s truth through the principle of contradiction. An inevitable logical contradiction arises when one tries to deny this judgment. To deny gold is “yellow and metal” is to deny the a priori definition of gold. In other words, the argument’s premises (the definition of gold) contain the conclusion (“is yellow and gold”). One cannot claim “yellow and metal” are and are not part of the definition of gold at the same time. Thus, the truthfulness of this judgment can be determined through the principle of contradiction as long as we accept the definition of gold.
Kant thinks the principle of contradiction is a sufficient condition for determining the analyticity of a judgment. An analytic judgment only makes assertions regarding the internal structural components of a subject through the predicate. If one can decide whether its subject’s predicate contradicts the definition of its subject only by analyzing the definition of its subject, its predicate must aim to be only explicative of its subject’s parts. This means this judgment is limited to the domain of the subject, so this judgment’s truthfulness only depends on whether its predicate fits into the internal structure of its subject’s definition. Thus, only the principle of contradiction is required to determine the analyticity of a judgment.
One can express an a priori judgment about gold as an empirical concept. When we analyze the insides of the conceptual definition of gold, although the empirical observation gives this concept, how we have arrived at this concept is irrelevant to an analytical judgment about the concept itself. We make such a judgment by only dissecting the conceptual definition of the subject (“gold”) into smaller pieces and see if the predicate (“yellow” and “metal”) is part of these pieces, not by any a posteriori processes.
We can express at least two analytic judgments with an atomic concept as the subject—indecomposability and that it is a concept. Because we cannot decompose this concept any further, we cannot use any other predicates to describe it besides its indecomposability and that it’s a concept. If we deny the atomic concept’s indecomposability or that it is a concept, it is a logical contradiction because they are part of this atomic concept’s definition. On the other hand, a more difficult question is whether we can find an atomic concept to use it as a predicate for another subject in a judgment. “Idea” is arguably an atomic concept; we cannot break “idea” as a concept down any further. We can make analytical judgments with “idea” (e.g. “gold” is an idea). Therefore, it is possible to express an analytic judgment with an atomic concept.
“Monad,” a similar empirical concept, would make a difference to my argument above if we define “monad” as an indecomposable entity all matter depend on. We can still make analytical judgments about the conceptual components of monads (e.g. monads are indecomposable). However, I cannot find any matter whose definition contains the definition of “monad,” so making an analytical judgment with “monad” as the predicate is impossible.
You can also read: