Epistemology comes from the Greek combination of episteme (knowledge) and logos (theory), and is the branch of philosophy which attempts to give an account what we know (or can know) for certain, the structures of the various ways of human knowing, and the methods by which we can claim something is truly known (indeed the very possibility of such knowledge).
In short, it asks "What can I know" and "How can I know it?"

Justified true belief, of course!

How to you say it? I always have trouble pronouncing it.

As did I

Eh-Pist-Tem-ology with emphasis on the second syllable.

For months I mistakenly pronounced it Epi-Stem-Ology

A priori = prior to (independent of) experience of the outside world
a posteriori = dependent on experience of the outside world

The two terms when applied to statements or to ideas can also indicate a difference in how we know them to be true, or how we accept the evidence for the truth.
Thus, an a priori statement can be known to be true without reference to experience, for example a classic deductive syllogism or the statement "circles are round." On the other hand, an a posteriori statement can be known to be true only by referencing a fact of experience, for example, "this dog is spotted," or the inductive statement "all bodies fall toward earth."
Quite often,though, different philosophers will have slightly different meanings attached to the two concepts.

Two questions:

1. Are statements such as "Something exists" or "The universe is not empty" synthetic a priori? If not, how should they be classified? They are not necessarily true (an empty universe is logically possible), but they are certainly true ("the universe is not empty" could not be stated in an empty universe).

2. In mathematics, where does one draw the line between a synthetic statement and an analytic one? Mathematical statements can range from obvious tautologies such as 4=4 or 4+3=3+4 to complex theorems which have to be painstakingly proven. What was Kant's view?

1. I don't know that an empty universe is logically possible. Not if a universe is individuated by its members. How then could it be determined whether one empty universe was different from another?

2. Kant believed that mathematics was synthetic. He did not believe (his example) that the subject, 5+7 was contained in the predicate, 12. I don't see how the complexity of the equation would be relevant to whether the equation was analytic or synthetic. I would think that either all of mathematics was analytic, or all was synthetic.

But that problem would not arise if there were only one universe. Or more than one universe but only one empty one.



Well, it seems that 4=4 must be analytic, since it is true by definition. Let us, for the sake of argument, agree with Kant and say that 5+7=12 is synthetic. What is your view (and what was Kant's view) about such intermediate cases as 4+3=3+4, or 0x0=0, or 1x1=1, or 1x2=2? Are any of those true by definition?

Incidentally, does 4=4 count as a "mathematical" statement in the Kantian sense, or would he have regarded it as a purely "logical" statement (a tautology), and thus analytic?

Two questions:

1. Are statements such as "Something exists" or "The universe is not empty" synthetic a priori? If not, how should they be classified? They are not necessarily true (an empty universe is logically possible), but they are certainly true ("the universe is not empty" could not be stated in an empty universe).

2. In mathematics, where does one draw the line between a synthetic statement and an analytic one? Mathematical statements can range from obvious tautologies such as 4=4 or 4+3=3+4 to complex theorems which have to be painstakingly proven. What was Kant's view?