### Questions

1. (Introduction) Explain the distinction between ``a priori'' and ``a posteriori,'' and between ``analytic'' and ``synthetic.'' Why must all analytic judgments be a priori? Give examples, other than Kant's own examples, of judgments which are analytic, synthetic a posteriori, and synthetic a priori, according to Kant. Why is it surprising that some synthetic judgments (according to Kant) are also a priori? Why does Kant think it important to show how such synthetic a priori judgments are possible? (Give at least one reason.)

2. (Aesthetic) Explain Kant's distinction between (human) ``intuitions'' and ``concepts.'' How does an intuition, as opposed to a concept, relate to an empirical object? What is the matter of our intuitions, according to Kant, and what is their form? How does existence of a (pure) form of (human) intuition explain why the laws of geometry, for example, can be known a priori (by humans), and how does it restrict what they apply to? That is: how can we know that the laws of geometry do not apply to things in themselves?

3. (Metaphysical Deduction) Using simple empirical examples (other than Kant's own), explain what ``concepts'' are, and what role they play in typical ``judgments.'' Explain why, according to Kant, the various fundamental types of judgment correspond to fundamental pure concepts of the understanding (categories): what role does the understanding play in both cases? (You need not talk in any detail about the Table of Judgments or the Table of Categories, although if you can discuss a specific example of correspondence, that would be great.)

4. (Transcendental Deduction, part I) A deduction, according to Kant, establishes the legitimacy or ``objective validity'' of a concept -- that is, it explains how we know that the manifold of appearances can be synthesized (by the imagination) in such a way as to be unified by that concept. Explain (1) why, according to Kant, we don't normally need a deduction of empirical concepts; (2) why, if we do want a deduction of an empirical concept, it will be what Kant calls an ``empirical deduction''; and (3) why an alleged empirical deduction of a pure concept (for example, of one of the categories) would not be a deduction at all.

5. (Transcendental Deduction, part II) The transcendental unity of apperception means the possibility of thinking the whole manifold of appearances together as mine. What does that have to do with the categories, according to Kant? What does it have to do with the possibility of there being an object of experience--that is (according to Kant), the possibility that something guarantees the appearances will agree with each other according to a rule?

6. (Schematism) Explain why an empirical concept, such as the concept dog, does not apply directly to appearances (or images) of dogs. What role does the faculty of imagination play in allowing such a concept to be applied? How does this involve a ``schema''? Give another example which shows the role of the imagination and its schemata in the case of mathematical concepts. Why is there a special problem with there being schemata for pure concepts of the understanding, such as the categories?

7. (Analogies) The Highest Principle of All Synthetic Judgments is, roughly, that the appearances must be such that they can all be thought together as mine (in the unity of apperception). What does this have to with the categories, and with the schemata of the categories? How does it rule out certain synthetic judgments as (not self-contradictory, but) empty? How does it make other synthetic judgments a priori? Explain this in particular with respect to the judgment that every event has a cause (Second Analogy).

8. (Phenomena and Noumena) The Transcendental Analytic has shown that all the objects of our knowledge are mere appearances. Explain why this seems to mean -- that is, why it might tempt us into the mistaken conclusion -- that we do, after all, know something about the way things are in themselves. Why might it seem to show that things in themselves are substances (whose accidents we know)? And why might it seem to show, on the other hand, that things in themselves are causes (whose effects we know)? Why, if either one of those were correct, would we know something about noumena -- that is, objects which an understanding can think on its own, without sense? (Note that it is not obvious that ``noumena,'' so defined, are the same thing as ``things in themselves.'')

9. (Amphiboly) Consider the concepts of identity and difference. Explain why we must be able to apply them to objects if we are to think of those objects under concepts (for example, to think that all objects of a certain kind are dogs, or that some of them are). How, according to Kant, can we actually apply these concepts (of identity and difference) to objects: that is, what makes two objects different? (Hint: how is space involved?) Why would that not work, according to Kant, if the objects of our knowledge were noumena?