Notes from Lemos’ An Introduction to the Theory of Knowledge
A priori knowledge or justification is independent of experience. It is knowledge that is justified by an argument of some kind.
Examples of a priori knowledge:
all swans are swans
all squares are rectangles
whatever is red is colored
7 + 5 = 12
if some men are Greeks, some Greeks are men
These proposition do not need arguments, nor is their truth inferred from other sets of propositions. They are self sufficient claims. Our knowledge of these propositions is not based on what we know through sources such as perception, memory or introspection. These propositions are reasonable and internally consistent. Such propositions are known as basic or immediate a priori justification.
Nonbasic or mediate a priori justification is inferred from basic a priori justification or knowledge. For instance, Pythagorean Theorem is not basically justified, but can be justified for us to believe a priori through deducing or inferring from other propositions that are justified for us a priori.
In this regard, a priori justification seems to have a foundational structure.
Kant approaches a priori knowledge by asserting that it is knowledge or justification independent of experience. See his Introduction to The Critique of Pure Reason.
S is justified a priori in believing that p = Df. S’s belief that p has some degree of justification that does not depend on any experience.
Therefore, a priori is different from empirical justification. However, Lemos points out that one might have both an a priori and an empirical justification for believing a proposition. The idea of justification that does not depend on experience becomes problematic and is the source of critique i.e. one needs some experience in order to form the concept of square, even if that concept becomes self evident consequentially.
A priori justification is a problem for coherence theories of knowledge. Pure coherence theories hold that all beliefs are justified solely in virtue of their relations to other beliefs. Hence, no beliefs are justified on the basis of experience. If this were true, then all justified beliefs would have some degree of justification which is not dependent on any experience. Therefore all justified beliefs are justified a priori. In this context, pure coherence has a problem as it seems that some knowledge and justified belief does depend on experience.
Another context and criticism of the above logic is to show that a priori depends on reason alone. The above logic is an unsatisfactory negative account; it asserts what justification does not depend on. Also, one could assert that a priori does depend on experience, as reason is a certain sort of ‘purely intellectual’ experience. In this way, to take reasoning or self-evident justification as things that ‘seem’ to us to be true, ‘seeming’ itself is an intellectual, phenomenological experience.
The Analytic-Synthetic Distinction
“Traditionally, it has been characteristic of empiricism to hold that our a priori knowledge and justification is confined to analytic propositions. In contrast, rationalism holds that there are some nonanalytic, or synthetic, propositions that we can know or be justified in believing a priori. Empiricists thus hold that the scope of our a priori knowledge and justification is narrower than rationalists take it to be.” Lemos, p193
An analytic proposition is where the subject and predicate are the same: all swans are swans
where the predicate is conceptually contained within the subject: all bachelors are unmarried
If a priori justification is confined to analytic propositions, it is a narrow field of justification. Any proposition that is not analytic is synthetic. Thus, all swans are white is a synthetic proposition.