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This is a key distinction in all my work. The truth is, I first started using these words in order to try to meet girls. I heard they swoon if they think you know Latin. Apparently, I heard wrong, as I've remained a bachelor my whole life.
So, to paraphrase Robin Williams, if you can't make love to them, philosophize to them. Something like that. After giving up on the ladies, I began to use this distinction as a way of describing the basis of a statement or judgment—how we know something to be true. To say that a claim is a posteriori is to say that I know it through, after, of by means of observation or experience. I know that this table is brown, for example, simply by looking at it.
By contrast, if a statement is a priori, its truth can be established independent of, or prior to, experience. So, for example, I don't have to do experiments to determine that 2 apples + 3 pears= 5 pieces of fruit. It seems I can make that determination in advance of any particular observation.
The mark of an a priori claim is that it is necessarily true: it is inconceivable or unimaginable that 2+3 might not equal 5. A posteriori claims are only contingently true, meaning that it is conceivable they might be false. A chair, for example, doesn't have to be brown. It could be any color; I have to see it to know which color it is.
Well, they're still battling over these words in the 21st century, so I guess I was on to something important here. Here, we are talking about the relationship between the subject and predicate terms in a claim. Take a statement like: "The table is brown." Here, the subject is "the table" (what the claim is about) and the predicate is what is said about that subject—in this case that it is brown.
Okay, so a synthetic claim is one in which the predicate term lies "outside of" the subject term. Let's come back to our exciting example about the brown table. Even better, since I'm feeling in a daring mood right now, let's change it to: "The table is blue." (I think you can begin to see now just why I was such a captivating lecturer.) I can analyze the notion of "table" all I want, but I won't find in that concept the idea of blueness. Nothing about a table has to be blue. Instead, I must look outside the concept of table and rely on experience in order to connect the terms "table" and "blue."
With an analytic claim, by contrast, the predicate term is contained within the subject. Take the statement: "All bachelors are unmarried" (I use my sad life as an example). Here, it is obvious that an analysis of "bachelor" reveals the notion of "unmarried." The statement is, we would say, true by definition; the predicate simply states what the subject means.
Now we're getting to something truly important. Let's put together what we've just been learning. Given the above distinctions, there are four possible combinations of statements—or, rather, three, since no statement can be both analytic and a posteriori. We have synthetic a posteriori, analytic a priori, and synthetic a priori judgments.
All a posteriori claims are synthetic. All analytic claims are a priori, and because of that, they are usually referred to simply as analytic. And last but by no means least, we have synthetic a priori claims. To say that a judgment is synthetic a priori means that the predicate lies outside the subject, but also that the judgment is true or false independently of experience. To put it differently, this is a claim which is necessarily true, but which is not merely a matter of definition.
Allow me to explain.
Let's take an example: "The shortest distance between two points is a straight line." This claim is necessarily true, but the concept of "being a straight line" is not contained in the subject "shortest distance" (compare this to the statement: "The bachelor is unmarried," for example). I give a similar account of "7+5=12": analyze "7" and "5" all you want, but you won't find "12" within these concepts.
We find synthetic a priori judgments outside of mathematics as well. "Every event has a cause," for example, cannot conceivably be false, but "having a cause" is not part of the meaning of "event." Translation: if you look "event" up in the dictionary, the concept of "having a cause" will not be part of the definition, even though every event must have a cause.
Now we come to the payoff, the thrilling climax of this part of our investigation. In fact, I'm so excited you can probably almost see the drool dribbling down my chin. The key question, the question that will guide my whole first Critique is this: how are synthetic a priori judgments possible? What must be assumed in order to explain the existence of such a peculiar class of statement?
The short answer is: a lot. Spoiler alert: I think the answer has to do with how our consciousness is organized.
You probably think you know what "transcendental" means, don't you? I'll bet you think it signifies something like "going beyond normal human perception or experience"? Well, that's what ordinary (read: uneducated) people might mean by the word, but in my writing that is what is meant by "transcendent" (that's "transcendental" without the -al). And the transcendent realm is just what philosophy cannot deal with.
Ah, but when you add the two letters on the end in my works, you get an entirely different concept—and the key to a whole new approach to philosophy. In the wonderful world of Kant—a world I am blessed to inhabit continuously—a transcendental perspective denotes a view aimed neither at experience nor at a supposed domain beyond experience. Rather, it is what I like to call "the conditions of the possibility of experience"—which is to say, the logical underpinnings which allow for our ordinary experience of the world. What concepts have to be assumed in order for me to even have an experience in the first place?
That's the sort of question I'm concerned with. And the sort of transcendental knowledge you get in response is what it is philosophy's proper concern to provide. Or so I claim.
This topic is discussed in the initial section of the first Critique, called the "Transcendental Aesthetic." (No wonder people love to teach my work; even just saying the names of the chapters makes you sound smart.)
Now, I'm Kant, remember, so by "intuition," I don't mean what you think I mean—a hunch or something like that. No, for me, "intuition" means that which is given through the senses. If I look at that good old table, for example, my intuitions are of a mass of colors and shapes.
I claim that space and time are the two forms of intuition, the two ways in which all perceptions of the world are necessarily structured. Space is the form of outer experience, while time is the form of inner experience. So, in my view, space and time are not objectively real, in the sense that they exist entirely apart from the human mind.
But they are not purely subjective, either; we don't randomly choose to experience the world in this way. We just do, and we can't help it. Space and time, then, are "transcendentally ideal"—necessarily existent features of the world, but only as the world presents itself to any human mind.
And so, as I'm sure you've guessed already, this is how I explain the possibility of the synthetic a priori truths of mathematics. Geometry, as an account of spatial relationships, describes the outer form of the intuitions. Arithmetic depends on the linear succession that is expressed by time as the inner form of the intuitions. It all fits together so neatly it just has to be true, right?
For me there are two components to every thought: intuitions and concepts. Intuitions, as we've seen, are the representations given through sense perception, while concepts are the general rules relating those representations to one another. As I state—famously and, I think it's fair to say, quite beautifully: "Thoughts without content are empty; intuitions without concepts are blind" (source).
Okay, so it's not poetry, but it's still a lot more readable than most of my stuff. It's my fancy way of saying that if you don't have both a concept and an intuition, then you ain't got nothin'—at least nothing in the way of a coherent thought.
Anyhow, just as we can talk about the forms of the intuition, we can also talk about the forms of the understanding. I call the forms of the understanding the categories.The categories of the understanding are the most general sorts of concepts there are—the a priori rules for organizing our intuitions. I claim there are exactly twelve categories, including such notions as causality, subsistence, possibility, and necessity. Why twelve? Don't ask—you'll certainly get an answer, but it will be long and complicated, and you'll be asleep before I'm done.
The point is that the categories represent the most fundamental way that our thinking is organized. A thought that is not filtered through one of these 12 conceptual forms is not a thought at all. Got it?
When I first burst onto the philosophical scene, they claimed I was such a phenomenon that I was almost a noumenon. What does that mean, you ask? Actually, I have no idea, but it sounded kind of good, so I decided to find some use for those words in my philosophical system.
In my writing, this has to do with a distinction between two different ways of looking at the world. To speak of a "phenomenon" is to speak of an object as appears to us, the object as structured by the forms of the intuition and the categories of the understanding. The "noumenon" is the object as it is in itself (in German, das Ding an sich), independent of the human mind. As such, the noumenon is intrinsically unknowable; we can only know the phenomenon.
Perhaps at some point you may have heard a cynic say something like this: "Oh, yeah, philosophy—that's the subject where you can prove pretty much anything you want. What's the point?"
It's not too surprising that some people would say such things; philosophy's definitely not for everyone, after all. But what is surprising is that I, Immanuel Kant, king of philosophers, agree.
Okay, admittedly, I'm not saying that all philosophy is worthless. What I have in mind is speculative metaphysics—especially attempts to answer questions about the ultimate beginning of the universe, about whether God exists, about whether there is free will, and so forth. I show that these kinds of questions inevitably lead to contradictions or "antinomies." That is, you can give equally good arguments for both sides of the question.
But, don't worry, philosophically minded Shmoopers—all is not lost. The key is to avoid the attempt to go beyond all possible experience in our inquiries. Happily, with my transcendental approach, I provide such an alternative.
If that sounds sort of stern and strict, it's because it is. After all, we are talking about morality here, people, and moral laws command us with no ifs, ands, or buts. It's not: "Don't lie, if you want to be happy and have a lot of friends." No, this is an unconditional requirement: "Do not lie!" End of story.
So, while I refer here to "moral laws," at bottom there is only a single moral law. That's why I will often talk about the categorical imperative. Now, being Kant, I can't resist giving a number of different formulations of "the" categorical imperative, but I claim these formulations are all equivalent: they all imply exactly the same set of moral do's and don'ts.
You can think of it this way: if you decided that the golden rule was the one, big, huge, important moral law, there are lots of things you wouldn't do. You probably wouldn't lie, cheat, steal, or kill, because you wouldn't want anyone to do that to you. So the golden rule would be like the categorical imperative, and the entire set of things you wouldn't do based on that golden rule is like a system of smaller laws inspired by that one big categorical imperative.
(But just remember that my categorical imperative is not the same as the Golden Rule—which is far too simplistic and familiar to be a Kantian principle, obvs.)