Hello. Thank you for reading this. I'm in grave need of philosophical counsel please. I cannot 'get' the distinction between 'a priori' and 'a posteriori'. It seems to me that anything that is known must be, in some way, related to experience.
I'm troubled by this thought experiment: If a baby was born with a terrible genetic condition which excluded all the human senses, what would the child 'know'? Without the 'experience' of the senses, what could the child ever know? Not even syllogism would be possible; without experience, language would not be available to the unfortunate child. And I imagine that this would be true of numbers too.
To answer your good question, one needs to distinguish between the role experience plays in the acquisition of knowledge and the role it plays in the justification of knowledge. You're absolutely right that without experience humans would not be able to develop cognitively; they would not be able to acquire knowledge of anything at all. So experience, like oxygen, is needed in order for us to become knowers. But to say that some proposition is known a priori is not in conflict with this claim. To say that some proposition is knowable a priori means that one's justification of the claim need make no reference to information obtained through the senses. We can justify Pythagoras' Theorem without any information provided by our sense organs (take a look at any proof of it and you'll see that this is so). Hence, it is knowable a priori – even though no one could have known it unless they had had the experiences needed in order for their minds to develop.