Preface
1) sad state of metaphysics vs. science. No sign of advancement.
2) Apology for Hume who has shown that the causal relation (A posited B necessarily follows) is not a child of reason, (i.e., knowable on the basis of conceptual analysis) but it is a "bastard of the imagination impregnated by experience."
How H. awakened K. from his "dogmatic slumber."

Preamble
1) Analytic vs. synthetic judgment:
Explicative (analysis of concepts) vs. ampliative (ex. All bodies are extended, vs. some bodies have weight).
2) A-priori vs. a-posteriori judgments:
Justifiable without reference to experience vs. need experiential justification (ex. 2+2=4 vs. Regan was president).
3) Grid:

                                Analytic                                         Synthetic

A-priori                        Yes                                                  ??

A-posteriori                  No                                                 Yes
 

4) Maths is

1. a priori: Math judgments are a-priori because we know them to be universal and necessary, which they couldn't be if they were justified from experience.
2. synthethic: although some principles used in maths (the whole greater than the part) are analytic, proper math judgments are synthetic because
• 4=2+2; the concept of 4 doesn't include those of 2 and +.

NOTE: Leibniz's or Frege's reaction.
• "the straight line between two points is the shortest"; the concept of straight is qualitative, not quantitative and so can't include it.

6) Is Metaphysics possible as a science?
NOTE: ultimately, the answer is 'no'
In the Critique the issue is treated synthetically, i.e., from considerations of the very nature of reason
In the Prolegomena the issue is treated analytically. We know two synthetic a priori disciplines:
i) pure maths
ii) pure physics
If by using a transcendental argument we find out what the only conditions which make them possible are, then we can see whether these conditions can possibly apply to metaphysics.
 
7)Intuition vs. concept.
Concept:

• it is a general representation, i.e. a representation of what is common to several things. It turns out to be a rule of the understanding for holding several representations in a unity; e.g. to think of a body is to think of extension, impenetrability etc. together.
• it refers to object mediately, through their marks.
• to apply a concept is actively to conceive of something as falling under it, i.e., to form a judgment.
• to conceptualize is to be active.

• It is a singular representation
• it refers to objects immediately by exhibiting them in sensibility.
• to intuit is to be passive, i.e., receptive.

1) Since geometry is synthetic, it must have recourse to intuition:
      a) exhibition of figures (ex. 180 degree and triangle)
      b) proofs by congruence
      c) possibility of indefinite extension of lines.
      d) tridimensionality of space.

Space provides both the medium and the constraint for geometrical construction. In other words, not merely the laws of logic, but the nature of spatiality (a brute given of human sensibility) determine geometry and what objects are geometrically, and not merely logically, possible.
NOTE: non-Euclidean geometry shows that geometry is not analytic, in the sense that the notion of triangle is not sufficient to generate the property that its internal angles amount to two right angles: one needs extra assumptions

2) Since geometry is a-priori, the intuition must be pure (a priori). Space is a pure intuition in the sense that spatiality provides the framework in which things are intuited. In other words, space is a form of intuition, and as such a transcendental condition for empirical intuition.
NOTE: An analogous story holds for Arithmetic and time.
 
3) Space/time as the transcendental conditions of empirical intuition.

• The colored glasses example and its inadequacy (space/time couldn't be a feature of things in themselves and be forms of sensibility, since as forms of sensibility they belong to things only qua intuited, and therefore cannot belong to them independently of being intuited).
• Because space/time are the transcendental conditions of empirical intuition, we perceive appearances (transcendental idealism). Things in themselves are not in space/time; however, as given  in experience, they are, that is, theyy appear to us in space/ti.me

• Ideal: mind-dependent
• Real: mind-independent.
• Transcendantal: X is transcendentally so and so if X is so and so at the level of philosophical reflection.
• Empirical: X is empirically so and so if X is so and so at the level of ordinary or scientific reflection.

• Empirically real: what belongs to the intersubjective realm of human experience, e.g, space/time, appearances in the transcendental sense, i.e., "things" in the empirical sense ,e.g. tables, chairs, planets etc.
• Empirically ideal: private data of individual human minds, i.e., appearances in the empirical sense, e.g., my thought of the table, your idea of Saturn etc.
• Transcendentally real: what is referred to independently of sensible conditions (space/time), i.e, "things" in the transcendental sense (things in themselves, noumena).
• Transcendentally ideal: a-priori conditions of human experience (space/time).

5) since geometry is based on space, the form of intuition, it must hold of anything which is perceived in space, i.e., it must hold of all outer appearances.
If we perceived not appearances, but things in themselves, we couldn't be sure that they must obey the laws of (Euclidean) geometry.
Problem:
K. proves too much: Gauss and non-Euclidean geometries.

6) distinction between critical (transcendental), empirical, and mystical idealism:

• critical idealism (Kant) does not deny that things in themselves  exist independently of us. It merely claims that we know them only as they appear to us, i.e., through the lenses of space/time.
• empirical idealism (Descartes) claims that appearances in the transcendental sense (tables, chairs etc., i.e., what K would consider things in space/time) are things in temselves, i.e. takes what's empirically real as transcendentally real.
• mystical idealism (Berkeley) claims that appearances in the  empirical sense (private ideas) are things in the transcendental sense.

1) The categories:

• Quantity, Quality, Relation (sbstance, cause, community), Modality

Problem: issues of the validity of the list.
• the most basic concepts of the understanding obtained by analyzing types of judgment.
• a-priori.
• the need of a transcendental deduction (TD) in order to prove that the categories are justifiably employed with respect to intuition. (quaestio facti vs. quaestio juris). Hence, TD provides a link between intuition and understanding.

• we leave out the issue of objective reality, i.e, that empirical intuitions do fit the categories
• Space/time (the sensible conditions of experience) don't need a transcendetal deduction; the categories (the intellectual conditions of experience) do.

sec 16: introduces the basic notion of transcendental unity of apperception (TUA), the "I think."

1. it is analytically true, i.e., it is logically necessary, that it be possible for the "I think" to accompany all the representations of the subject.

Note: the claim affirms the necessity of a possibility,i.e., it is not necessary that the subject be reflectively aware of all her representations, only that it be possible for her to be aware of them.
2. the representation of a manifold as a manifold requires a single complex thought. Representing the manifold A, B, C, requires a single thought of A, B, C: just having a thought of A, a thought of B, and one of C won't do it.
3. the representation of a single complex thought requires a single thinking subject: a set of distinct thoughts of the elements of a whole cannot be equivalent to the thought of the whole itelf (Example: different people saying "what a nice day").

Note: traditional unity of consciousness (e.g. Descartes and Clarke); however, TUA is not empirical consciousness
4. but a single thinking subject can represent a manifold as a manifold (i.e., have a single complex thought) only if it is possible for her to become aware of her identity with the subjects thinking each component representation of the manifold. For example, if the manifold contains representations A and B and the complex thought of the manifold is C, then it must be possible for the subject thinking C to be aware of her identity with the subject thinking A and with the subject thinking B.
5. however, in the Treatise Hume has shown that inner sense does not provide a representation of the thinking subject.
6. Hence, the subject thinking C can be aware of her identity with the subject thinking A and with the subject thinking B only by combining A and B in one single consciousness and being aware of being the subject who's doing the combining. That is, the consciousness that A and B are representations for the subject presupposes the subject's awareness of thinking them together as C.
7. In sum, the identity of apperception of a manifold contains a synthesis of representations and is possible only through the consciousness of that synthesis.  Roughly put, we can represent manifolds (i.e., attach the "I think" to representations of manifolds) only if we consciously join together their component representations.

sec 19: links the activity of judgment to that of transcendental synthesis. A judgment is the assertion of a unity of representations by means of the copula "is" (example: "This is a dog").
But the unity brought about by judgment and that brought about by transcendental synthesis are one and the same.
Problem: Why should it be so?
So, the unification of the intuitive manifold under a concept, i.e., the representation of an object, is an act of judgment.

sec. 20: draws the conclusion that since judgments are subject to the categories, and the transcendental synthesis of the intuitive manifold is an act of judgment, the intuitive manifold must be subject to the categories.

3. The Analytic of Principles: Second Analogy .

Prelimaries:

• Tries to prove the every-event-some-cause principle (vs. Hume in the Treatise), not the same-cause-same-effect principle (vs. Hume in the Enquiry).
• An event is the becoming of something, i.e. the succession of states of an object (example: water freezing and turning solid; Joe going out and slipping on banana peel).
• Subjective vs. objective succession, i.e., succession of representations vs. representation of succession (example: house vs. ship).
• A causal link is a universal and necessary (exceptionless) rule according to which one thing follows another.

1. All event perception requires successive perceptions of an object, otherwise one could not contrast the new state with the old one.
2. But the successive perceptions of an object are merely a necessary, not a sufficient condition for the experience of an event (example: house/ship).
3. The sufficient condition for experiencing an event is that the perceptions be thought of as being in an irreversible order. Only thus can one distinguish the experience of a succession from a succession of experiences.  For example, house-perceptions coneptualized as reversible (e.g. perception of roof before or after that of windows); but ship-perceptions coneptualized as irreversible.

NOTE: this does not mean that the representations are perceived in that order, only that they are conceptualized in that order.  I conceive the ship as being at A before B, but I may perceive it at B (see the smoke) beofre I perceive it at A (hear the whistle).  Perceptions don't constitute experience of events without being conceptualized.
4. The irreversibility of the order of perceptions can be conceptualized only by the application of an a-priori rule, which in this case is the category of causality (actually, the schema of causality).  The idea here is that an empirical concept would not guarantee irreversibility.
5. Since the category (actually the schema) of causality is a precondition for the possibility of experiencing events, it is also the precondition for the existence of events as objects of possible experience.

1. The connection between A and B is law-like.
2. The connection between A and B is totally accidental.

Does K answer Hume?
Possible reply:
H. must distinguish between a mere subjective sequence of perceptions and an objective sequence of perceptions because his theory of habit grounding his views of causality presuppose such a distinction. But, if K. is right, this distinction presupposes causality.
Problem: why must H. distinguish between subjective and objective succession?  The fact that the representations generating the mind are in an individual mind does not entail that they don't constitute an objective succession.
 

4. The Refutation of Idealism

Distinction between

• Dogmatic Idealism as in Berkeley: the notion of outer (i.e., material) object is incoherent.  Hence, material objects don't exist

NOTE:  For K. this a version of idealism has been rejected by showing that space is the form of outer intuition.
• Problematic Idealism, e.g. Descartes in Meditation 1: no direct evidence that outer objects exist.

1. I am conscious of my existence in time, i.e., I have experience, i.e., am aware of the succession of representations.

NOTE: the idea, here, is that even Descartes in the First Meditation would have to admit this.
2. Since I don't perceive time itself, in order to determine the temporal relation of these representations there must be  "something permanent in perception," otherwise I could not become aware of their succession in a common time (I couldn't order them).

NOTE:  this is, in effect, the point of the First Analogy
3. I don't have any intuition of my particular empirical self (Hume's point)

NOTE: the idea here is that one might claim that the self could constitute what's permanent in perception.
4. All the representations in inner experience are fleeting (Hume's point)
5. I can't have any intuition of the unity of apperception because the unity of apperception is not an intuition but an intellectual representation and as such not an item of inner experience.
6. Hence, no object or representation of inner experience provides the "permanent in perception" required.
7. Hence, the "permanent in perception" must be found in the actual dyachronic existence of represented objects of outer sense

NOTE: K. is careful in pointing out that he's talking about the existence of outer things, and not merely about that of their representations.

• (2) is questionable: to determine temporal relations, all is needed is regularity (e.g. regular motion or regular flashes of light) not permanence
• the transition from (6) to (7), the heart of the argument, is unclear.  From the fact that no object or representation of inner experience can provide the "permanent in perception" it merely follows that is must be in outer experience, be it in mere representations of outer objects or in outer objects themselves.  On what grounds does K. rule out the former?

Possible replies:
• Inner experience and outer experience are heterogeneous in that inner experience cannot provide the material for outer experience (in Lockean terms, reflection cannot provide the material for sensation)
• It cannot be in mere representations of outer objects because these are as constantly changing as those of inner experience, and can be reidentified only on the assumption that they refer to permanent outer objects.

1) The only type of metaphysics possible as a science is that given in the Aestetics and the Analytic, i.e., a study of the transcendental conditions of experience, i.e., a Metaphysics of Experience.
NOTE: the point made in the Solution to the general question.

Now K. passes to study the fallacious part of metaphysics.

2) Distinction between

• concepts (can be given in experience)

Ex. application of the notion of causality to every event in the world.
• ideas (go beyond possible experience by being applied to the totality of possible experience taken as a whole).

Ex. application of the notion of causality to the world as a whole in saying, say, that God is the cause of the world.
When thus applied, concepts become transcendent and the alleged knowledge gained from them illusory: Intuitions without concepts are blind; concepts without intuitions are empty.

Ideas can be grouped under three labels: Psychological ideas, Cosmological ideas, Theological ideas (we do only a part of the second)

3)The cosmological ideas (the antinomies).

A)
The antinomies are an example of the sort of trouble reason falls into when passing beyond the limits of possible experience.
An antinomy is a pair of apparently contradictory propositions which follow from the same assumptions.
An antinomy is solved by:

• showing that the apparently contradictory propositions follow from a set of assumptions which is internally inconsistent

Ex. A round square is round; a round square is not round: In this case the two propositions are contraries (and both false), not contradictories (of which one must be true)
• showing that the propositions in question are merely apparently contradictory.

Ex. "The end of life is death" (end as terminus) vs. "The end of life is not death" (end as goal): Here one sees that the two propositions do not talk about the same thing.

NOTE: K insists that the proofs given for the thesis and antithesis are correct, but there is much doubt about this.

The solution (we do just (1) and (3))
(1):

1. Spatio-temporal objects exist only in experience (noumena are not in space/time)
2. But the world as a whole, i.e. as one object, is not an object of possible experience

NOTE: the idea here seems to be that the alleged "facts" of the infinitude/finitude of the world are not empirically accessible
3. Hence, the very notion of attempting to find the spatio/temporal determinations of the world is inconsistent.
4. So, the antinomy stems from an inconsistent notion, that of the world as a whole as an empirical object, i.e., as an object of possible experience.
5. Hence, the two horns of the antinomy are both false.

1. Universal causation applies to persons viewed as phenomena; freedom to persons viewed as noumena. But  I, as a noumenon, am a principle of action which acts uncaused (agent causation a la Clarke), while I, as a phenomenon, am subject to universal causation.
2. Hence, the two horns of the antinomy are both true, but they apply to different areas

NOTE: Implicit rejection of compatibilism, vs. Lk. and Hume.
Problem: how does the noumenon affect the phenomena (i.e., actions)?