The idea of a priori knowledge is not that it’s intuitive, but that it is not dependent on experience for it to be conceivable. Though addition may be hard to teach without examples, it abstractly makes sense without reference to anything in the physical world. Similarly, the truth of the statement “a bachelor is an unmarried man” does not require any experience to know—its truth comes from the definition of the word “bachelor”.
The idea of a priori knowledge is not that it’s intuitive, but that it is not dependent on experience for it to be conceivable.
If I am understanding your statement here correctly, you are saying that a priori knowledge hinges on the idea that concepts can be acquired independently of experience. If that is what you are saying, then you would be incorrect. Very few philosophers who accept the idea of a priori knowledge—or more appropriately: a priori justification—think that human-beings ever acquire concepts innately or that they can otherwise conceive of them independently of experience. A proposition is knowable a priori if it is justifiable by appeal to pure reason or thought alone. Conversely, a proposition is knowable a posteriori if it is justifiable in virtue of experience; where any relevant, constitutive notion of experience would have as its meaning (a) some causally conditioned response to particular, contingent features of the world, and (b) doxastic states that have as their content information concerning such contingent features of the actual world as contrasted with other possible worlds.
Somebody defined the operation of addition—it did not arise out of pure thought alone, as is evidenced by the fact that nobody bothered to define some other operation by which two compounds could be combined to produce a lesser quantity of some other compound (at least until people began formalizing chemistry). There are an infinite number of possible operations, most of which are completely meaningless for any purpose we would put them to. Knowledge of addition isn’t knowledge at all until you have something to add.
“Qwerms are infantile eloppets.” Is this a true statement or not? I could -define- a qwerm to be an infantile eloppet, but that doesn’t represent any knowledge; in the pure abstract, it is an empty referential, devoid of meaning. Everything in the statement “a bachelor is an unmarried man” is tied to real-world things, whatever knowledge is contains there is experience driven; if the words mean something else—and those words are given meaning by our experiences—the statement could be true or false.
Kant, incidentally, did not define a priori knowledge to be that which is knowable without experience (the mutation of the original term which Ayn Rand harshly criticized), but rather that which is knowable without reference to -specific- experience, hence his use of the word “transcendent”. If putting one rock and another together results in three rocks, our concept of mathematics would be radically different, and addition would not merely fail to reflect reality, it would not for any meaningful purpose exist. Transcendent truths are arrived at through experience, they simply don’t require any -particular- experience to be had in order to be true.
In Kantian terms, a priori, I know if I throw a rock in the air it will fall. My posterior knowledge will be that the rock did in fact fall. There are other transcendental things, but transcendental knowledge is generally limited to those things which can be verified by experience (he argued that transcendental knowledge could not extend beyond those experiences we can anticipate). Without going into his Critique of Pure Reason, which argues for some specific exceptions (causality and time, for example) as bootstraps to get the whole mess moving, future philosophers by and large completely ignored what he had written about transcendental knowledge in general, and lifted it out of the realm of experience entirely. (With some ugly results, as you’re left with nothing but tautologies.)
Somebody defined the operation of addition—it did not arise out of pure thought alone, as is evidenced by the fact that nobody bothered to define some other operation by which two compounds could be combined to produce a lesser quantity of some other compound (at least until people began formalizing chemistry). There are an infinite number of possible operations, most of which are completely meaningless for any purpose we would put them to. Knowledge of addition isn’t knowledge at all until you have something to add.
The problem here is that you seem to be presupposing the odd idea that, in order for any proposition to be knowable a priori, its content must also have been conceived a priori. (At least for the non-Kantian conceptions of the a priori). It would be rare to find a person who held the idea that a concept be acquired without having any experience related to it. Indeed, such an idea seems entirely incapable of being vindicated. If I expressed a proposition such as “nothing can be both red and green all over at the same time” to a person who had no relevant perceptual experience with the colors I am referring to and who had failed to acquire the relevant definitions of the color concepts I am using, then that proposition would be completely nonsensical and unanalyzable for such a person. However, this has no bearing on the concept of a priori knowledge whatsoever. The only condition for a priori knowledge is for the expressed proposition be justifiable by appeal to pure reason.
The idea of a priori knowledge is not that it’s intuitive, but that it is not dependent on experience for it to be conceivable. Though addition may be hard to teach without examples, it abstractly makes sense without reference to anything in the physical world. Similarly, the truth of the statement “a bachelor is an unmarried man” does not require any experience to know—its truth comes from the definition of the word “bachelor”.
If I am understanding your statement here correctly, you are saying that a priori knowledge hinges on the idea that concepts can be acquired independently of experience. If that is what you are saying, then you would be incorrect. Very few philosophers who accept the idea of a priori knowledge—or more appropriately: a priori justification—think that human-beings ever acquire concepts innately or that they can otherwise conceive of them independently of experience. A proposition is knowable a priori if it is justifiable by appeal to pure reason or thought alone. Conversely, a proposition is knowable a posteriori if it is justifiable in virtue of experience; where any relevant, constitutive notion of experience would have as its meaning (a) some causally conditioned response to particular, contingent features of the world, and (b) doxastic states that have as their content information concerning such contingent features of the actual world as contrasted with other possible worlds.
Somebody defined the operation of addition—it did not arise out of pure thought alone, as is evidenced by the fact that nobody bothered to define some other operation by which two compounds could be combined to produce a lesser quantity of some other compound (at least until people began formalizing chemistry). There are an infinite number of possible operations, most of which are completely meaningless for any purpose we would put them to. Knowledge of addition isn’t knowledge at all until you have something to add.
“Qwerms are infantile eloppets.” Is this a true statement or not? I could -define- a qwerm to be an infantile eloppet, but that doesn’t represent any knowledge; in the pure abstract, it is an empty referential, devoid of meaning. Everything in the statement “a bachelor is an unmarried man” is tied to real-world things, whatever knowledge is contains there is experience driven; if the words mean something else—and those words are given meaning by our experiences—the statement could be true or false.
Kant, incidentally, did not define a priori knowledge to be that which is knowable without experience (the mutation of the original term which Ayn Rand harshly criticized), but rather that which is knowable without reference to -specific- experience, hence his use of the word “transcendent”. If putting one rock and another together results in three rocks, our concept of mathematics would be radically different, and addition would not merely fail to reflect reality, it would not for any meaningful purpose exist. Transcendent truths are arrived at through experience, they simply don’t require any -particular- experience to be had in order to be true.
In Kantian terms, a priori, I know if I throw a rock in the air it will fall. My posterior knowledge will be that the rock did in fact fall. There are other transcendental things, but transcendental knowledge is generally limited to those things which can be verified by experience (he argued that transcendental knowledge could not extend beyond those experiences we can anticipate). Without going into his Critique of Pure Reason, which argues for some specific exceptions (causality and time, for example) as bootstraps to get the whole mess moving, future philosophers by and large completely ignored what he had written about transcendental knowledge in general, and lifted it out of the realm of experience entirely. (With some ugly results, as you’re left with nothing but tautologies.)
The problem here is that you seem to be presupposing the odd idea that, in order for any proposition to be knowable a priori, its content must also have been conceived a priori. (At least for the non-Kantian conceptions of the a priori). It would be rare to find a person who held the idea that a concept be acquired without having any experience related to it. Indeed, such an idea seems entirely incapable of being vindicated. If I expressed a proposition such as “nothing can be both red and green all over at the same time” to a person who had no relevant perceptual experience with the colors I am referring to and who had failed to acquire the relevant definitions of the color concepts I am using, then that proposition would be completely nonsensical and unanalyzable for such a person. However, this has no bearing on the concept of a priori knowledge whatsoever. The only condition for a priori knowledge is for the expressed proposition be justifiable by appeal to pure reason.