It’s difficult to understand why anyone would ever get excited about Kant’s question “how are synthetic a priori propositions possible?” It’s an incredibly abstract question. Everything must be placed in context. That seems to lack any import beyond academic import. We have analytic a priori concepts. I think the concept “bachelor” and immediately think “unmarried male”. There’s nothing in an analytic a priori judgments or concepts that, to use Kant’s language, “amplifies” my concept of “bachelor”. “Unmarried male” is already contained in my concept of “bachelor”. It’s a matter of definitions. That’s why I can know it independent of experience. The NSF won’t fund a study for research into whether bachelors are unmarried males as there’s nothing to learn. We know it by definition.
With synthetic a posterior judgments, my knowledge is amplified. When I go to Morocco for the first time, my concept of Morocco is expanded. I synthesize the subject “Morocco” with my new experiences, learning something that I didn’t know before. This is the magicians theory of knowledge. Every magician knows that you can’t pull a rabbit out of a hat without first putting it into the hat. There’s nothing in the mind, according to the empiricists that wasn’t first put there. That’s empiricism. The rule of the magician.
But the synthetic a priori is real magic. From thought alone you’re getting more out of the hat than you put there in the first place. When Kant says that 7+5 = 12 is not an analytic a priori judgment, nor a synthetic a posteriori judgment, but a synthetic a priori judgment, he’s saying that when we go through these calculations we learn something we didn’t know at first, something that’s absolutely certain but that we didn’t know at the outset, and that this isn’t merely a matter of definitions nor is it a matter of experience (the five senses). Through thought we get more than we started with. It would appear that with thought we can violate the principle of the conservation of matter and energy: we get more than we started with… At least, if synthetic a priori propositions are possible. This is real magic. This is a real mystery.
We might not be impressed with coming to know something more through thought alone in arriving at the sum of 12, but the issue has much broader implications than Kant explicitly suggests in the first Critique. Situate the issue in the absurd debate between nature and nurture. Those on the nurture side are magicians. They say there’s nothing in a person’s mind that wasn’t first put there by how they were nurtured by their caregivers and their social environment. If you’re brought up in a hateful, bigoted, abusive environment you’ll be a hateful, bigoted, abuser because that’s all you were ever brought up with. If you’re on the nature side, your hat is already full. Some sort of genetic code makes you a hateful, bigoted, abuser. Tough luck. That’s what you are.
But if synthetic a priori propositions are possible… Well that’s a game changer. If synthetic a priori propositions are possible this means there’s a power of thought… A power to go beyond teaching or environment and a power to go beyond your nature. If synthetic a priori propositions are possible this means you have the power to introduce something new into both your own thought and the world through thought. This means you’re beyond history, even while mired in history, and beyond your nature. You can think beyond yourself and make yourself beyond yourself. What is really at stake in the synthetic a priori is freedom; your capacity to be self-determining and self-creating and your capacity to be something other than a Nazi even though you’ve only ever been exposed to Nazis and have nazism in your biological nature. This is what Badiou is talking about when he talks about the Event, what Zizek is talking about when he talks about the Subject as the gap, and what Deleuze is talking about when he talks about the New… A power of thought to invent through thought and not simply because something else entered into the hat through the five senses. Kant’s real question is a question about what the power of thought is, about what it means to invent or think and create the new. It’s the question of real freedom. And that is why the question “how are synthetic a priori propositions possible?” is a question worth taking seriously and getting excited about.