Right, I wrote this too so I'll post it. Then I'll hold off for a while. And if anyone thinks these walls of text aren't suitable for the thread, let me know. I've written so much because I've been enjoying it.
Preamble
The Preamble covers the central distinction covered in the introduction to the CPR, between analytic and synthetic judgements. He begins in section 1 by looking at the
sources of metaphysical knowledge, and states that they are
a priori by definition.
A few words about
a priori and
a posteriori. These are about justification, i.e., how we come to know things, so they are
epistemological concepts. In the CPR Kant says that “There can be no doubt that all knowledge begins with experience”, but that “although our knowledge begins with experience, it does not follow that it arises from experience.” What this means is that it is experience that
calls forth knowledge, not that it is the
source. For example, it is in experience that we come to know about cause and effect in the first place, but only because events must be experienced in terms of a prior, independent (pure) concept of the understanding.
The crucial thing to know about the
a priori is that it is characterized by
necessity and
universality. In contrast to empirical knowledge, which is always contingent--it only
happens to be the case that the sun rose this morning--and applies only as far as we know to the cases we can observe,
a priori knowledge is what is always applied to everything that is relevant to it, everywhere and for all time. Thus we generalize from observation into laws, e.g., every event has a cause, the total mass-energy of a closed system remains constant, and E=mc^2.
All necessary truths must be known
a priori, because experience and induction can only give us contingency as Hume showed. E=mc^2, for example, might at first sight look like it's
a posteriori, because it's confirmed by experiment. But all that's really discovered in such an experiment is that E=mc^2 happened to be true on that occasion; the necessity and universality of the equation, it's law-like character, cannot be confirmed by experience.
But is all
a priori knowledge necessary? Historically most philosophers have thought so--it’s hard to think of anything a priori that doesn’t apply across the board necessarily. But Kripke argued that there is such a thing as contingent a priori knowledge. However I’ll leave that aside, because it’s is not the kind of
a priori that Kant is interested in.
It’s often said that Kant found a way between rationalism and empiricism, or a way to reconcile them, and it can be seen here. The rationalists had their
innate ideas, like the ideas that God is omnipotent or that time has no beginning and no end, which are thought to be necessary and universal. But Kant's
a priori knowledge is different: it consists of concepts or principles that are used to form judgements about the objects of experience, whereas the innate ideas are whole judgements already present in the mind and complete without any experience at all. Thus Kant accepts that experience is essential for knowledge (empiricism), but also accepts that necessary and universal truths can be known by the understanding (rationalism).
Briefly on this point, I think it's wrong to think of rationalism and empiricism here as equal, competing philosophies. Kant was in the rationalist tradition and, in a way, wanted to save it from scepticism by reforming it. Adorno puts it nicely in his lectures on the CPR:
...the synthetic a priori, in short, the incontrovertibly true and valid modes of knowledge that far surpass mere logic, may be described as the roast, the Leibnizian or Cartesian roast, while Hume and English scepticism provide the dialectical salt. — Theodor Adorno
Section 2 is about the types of knowledge that can be called metaphysical. Whereas the a priori-a posteriori distinction concerns how we know things, this is about
what we know. In other words,
a priori-a posteriori is about the justification of propositions and
analytic-synthetic is about the character of the propositions themselves, or about the sort of truths they are, or more precisely what makes them true or false. Whereas a priori-a posteriori is epistemological, analytic-synthetic is
semantic.
So Kant makes a distinction between judgements (we can think of judgements as propositions held to be true in human understanding), and this distinction applies to all judgements, whether they contribute
a priori or
a posteriori knowledge:
- Analytic: explicative judgements, ones that don’t tell us anything new but just bring out what’s already there.
- Synthetic: ampliative judgements, ones that are informative, i.e., they add something new.
Analytic judgments. Kant uses something like the containment metaphor he used in the CPR to define these. This is the idea that the subject of a proposition contains the predicate already, e.g., in “All bachelors are unmarried”, being unmarried is contained in the concept of a bachelor. In contrast, “Some bachelors are Mexican” is not analytic because the concept of bachelors has nothing to do with being Mexican.
Incidentally, the example he actually uses, of bodies being extended (analytic) and heavy (synthetic), is much less useful to us now. At the time, extension was a part of the concept of a material body (meaning a physical thing), both in physics and metaphysics, whereas weight was not. He was just using a familiar and uncontroversial concept.
He goes on to elaborate on his containment definition: an analytic judgement is one whose negation is a contradiction. Thus it is contradictory to deny that all bachelors are unmarried.
It’s easy to get a sense of what “analytic” means from this, but it’s a bit vague, and later philosophers--who had better logical tools than Kant, who was working with Aristotle’s logic--pointed out that his definitions are not general enough. For example, he has only really covered subject-predicate propositions, but he means analyticity to apply to more complex judgements, like those involving conditionals.
There are other logical problems, but it turns out that analyticity can be satisfactorily generalized:
A judgement and its negation are both analytic if and only if one of the pair is self-contradictory, or false by virtue of the definitions of words or its logical form. — Jill Vance Buroker
In any case, I find
true by definition or
true by virtue of the meanings of the constituent terms to be close enough approximations much of the time.
As Kant points out at the end of 2(b), all such judgements must also be
a priori, because it is logical form and the definitions of the terms involved that determine whether they’re true or false--not experience.
Synthetic judgments. These can be defined as simply the contrary of analytic judgements, i.e., they are judgements that are
not true by virtue of the meanings of the constituent terms. So it’s clear enough that
a posteriori judgements, i.e., judgements of experience, are all synthetic. But Kant says there are
synthetic a priori judgements too.
He classifies synthetic judgements like this:
1. Judgements of experience
2. Mathematical judgements
3. Properly metaphysical judgements
I’ve said enough about 1. And like
@Sapientia I don’t feel like covering the mathematics, whether 7 + 5 = 12 is synthetic or not, etc. My feeling has always been that mathematics is entirely analytic and that Kant was wrong on this. I don’t know how badly that damages Kant’s project--I suspect it doesn’t.
So that leaves metaphysics. Here he argues that although there are analytic judgements in metaphysics--I think of these like steps in solving a mathematical equation--the important ones are synthetic. Just like physics, with its propositions such as “air is an elastic fluid”, the whole point of metaphysics is to tell us something about reality, something that is not true only by definition. He gives the example that “all that is substance persists”, which is a conservation principle that serves as a foundation for physics (the quantity of matter remains constant in physical interactions). Other more controversial synthetic judgements of metaphysics are that reality is fundamentally made up of monads, that reality is fundamentally made up of matter, and that reality is divided between two substances, mind and matter. These aim at positive knowledge, not mere explication.
And of course they are also
a priori, so we can see that the
synthetic a priori will be Kant’s main concern.
So we can make a table of knowledge like this:
analytic synthetic
a priori ✓ ✓
a posteriori — ✓
There is no such thing as analytic
a posteriori, because what can be known based on experience cannot be true merely by definition or logically.
That’s enough for now. The next bit, the “General Question”, is where Kant introduces the central question: How are synthetic
a priori propositions possible?