If I say that 50% of birds are black, and so I then say that I have a 50% chance of choosing a black bird if I pick a bird at random.

Is this an a priori or a posteriori proposition?

Given the premise it is true, but the premise itself requires empirical evidence.

  • So, the proposition is in the form "A & B"? "Half of birds are black & I have 50% chance to pick a black bird"?
    – rus9384
    Jan 26, 2019 at 17:44
  • This proposition is analytic, it is essentially a tautology, so yes, it is a priori by the traditional terminology. It makes no difference whether it speaks of birds, cards in a deck, balls in a box, or even and odd numbers.
    – Conifold
    Jan 27, 2019 at 2:29
  • The relevant factor here is NOT if the premises require empirical evidence but if there are more than two possible outcomes. Results with three or more outcomes will be based on science. In THIS CASE the result must be a single outcome: an A or a B. This is OR is an exclusive OR. That is you cant possibly have both more than half and less than half simultaneously and maintain the 50 %. You can only have one solution. Because there is one possibility and no other possibility the proposition is analytic. This is called logically necessary proposition. You dont have a choice in outcome results.
    – Logikal
    Jun 26, 2019 at 15:17

2 Answers 2


"A priori” and “a posteriori” refer primarily to how, or on what basis, a proposition might be known. In general terms, a proposition is knowable a priori if it is knowable independently of experience, while a proposition knowable a posteriori is knowable on the basis of experience. The distinction between a priori and a posteriori knowledge thus broadly corresponds to the distinction between empirical and nonempirical knowledge.

Thus, "a proposition that require empirical evidence" is not a priori.

  • Well, a proposition "If half of birds are black, I have 50% chance that a bird I pick is black" could be considered a priori. But as the one who believes everything is learned including mathematics, I do not consider that. Yet, as this question is asked, I guess, the asker believes in a priori statements.
    – rus9384
    Jan 26, 2019 at 17:41

The question is

Is a proposition a priori if the premises require empirical evidence?

Jason S. Baehr describes a priori and a posteriori as "ways of knowing", but they can also be applied to propositions and arguments:

The a priori/a posteriori distinction is sometimes applied to things other than ways of knowing, for instance, to propositions and arguments. An a priori proposition is one that is knowable a priori and an a priori argument is one the premises of which are a priori propositions. Correspondingly, an a posteriori proposition is knowable a posteriori, while an a posteriori argument is one the premises of which are a posteriori propositions. (An argument is typically regarded as a posteriori if it is comprised of a combination of a priori and a posteriori premises.)

If one accepts this, then an argument containing premises that are knowable a posteriori, such as the one in the OP's question, would be classified as a posteriori.

Baehr, J S. A Priori and A Posteriori. Retrieved on June 25, 2019 from the Internet Encyclopedia of Philosophy at https://www.iep.utm.edu/apriori/

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