Introductory points:

a) contrary to the oppositional thinking we've seen dominate modern thought - e.g., doctrine of double truth, etc. - Kant is the first major figure in the modern period to undertake a genuine synthetic (as opposed to a reductionistic) project

b) In particular, over against faith/reason dichotomies - Kant's project can be understood as developing a synthesis of modern science and ancient ontology (martin) - or, a modern synthesis of faith and reason. This is modern in that the 'faith' side is in fact reason once again - Kant is perhaps the high point of the Enlightenment faith in reason. But he nonetheless holds together both science and a deterministic understanding of the world, on the one hand, and absolute human freedom and the ability of reason to establish values on the other. In familiar terms - the ideality of time/space and the reality of human freedom.

Jones makes the point in slightly different terms - that while the doctrine of the double truth had begun originally in order to make space for physics over against the incursion of theology and tradition - the on-going successes of modern science had given it such power that now the tradition was on the defensive, if not on the decline.

Kant's Copernican revolution - rests on the turn in scientific method, recognizing that the activity of mind/the perspective of the observer plays a role in determining what is observed/what is known.

While avoiding pure idealism - Kant notes that science "must adopt as its guide...that which it has itself put into nature." (j, p.17)

Previously, we have assumed the correspondence theory of truth - that our knowledge must adopt itself to objects. Kant's Copernican turn is to try the hypothesis that objects must adopt themselves to our knowledge.

This will, as Kant suggests (p. 18) not only establish the possibility of a priori knowledge - namely, we may know a priori of things only what we put into them. This trust, however, works so as to reconstitute Newtonian science in the face of the Humean critique - and to undermine with even greater finality the possibility of metaphysics.

Quite clearly - although Jones does not make this clear - Kant accomplishes this by following the Humean strategy, i.e., the critical turn, the examination of reason by reason itself (the critique of pure reason).

(One might also notice here how Aristotelian Kant is - first of all, with the distinction between form and content) In a judgment (explain - judgment: subsumes the particular under the universal (see Smith p. 48) - either determinant or reflective) The content of judgment is delivered by what Kant calls sensible intuition (Anschauung). It is this side of judgment that is bound up with the correspondence theory of truth. If I judge that there is a centaur in my office (content), - if there "really" is, then the judgment is true (in terms of correspondence)

At the same time, however, judgment takes on a certain form: it is the form of judgment that Kant thinks results from the activity of mind and is universal and a priori.

As Jones neatly puts it: knowledge is a cooperative affair in which both mind and object make a contribution, and mind contributes the relations while objects contribute the relata. e.g.,

• space/time
  more particularly, the relations of attribution (the rose is red) and
  causation, etc.
  

Jones:

• ...attribution is one of the types of questions that the mind asks nature and in terms of which, accordingly, nature answers. Thus, all the particular questions (or experiments) that scientists ask take one or the other of certain basic forms... Now, if all the questions asked of nature were to have one or the other of certain basic forms, obviously all the answers given by nature would have these same forms, and there would then be some knowledge about nature that is independent of all particular experiences. Or again, suppose the new hypothesis is to be correct and that we know the types of judgment, that is, the basic ways in which the mind relates (or organizes) its experiences. We would then have absolutely certain knowledge, not about this particular experience ("This rose is red"), but about the form of all experience (ordered under the form "is").
• In other words, it would not be necessary that the particular rose by red; Hume was correct about this - the rose might be white or yellow. But it would be necessary, if Kant's hypothesis is correct, that experience be organized into things-having-properties, for this way of perceiving things proves to be one of the universal forms of human experience. Hence, despite Hume's attack, there does exist a "necessary connection" among matters of fact - not a necessary connection between this particular fact A and that particular fact B, but a necessary connection, or structure, that organizes experience into an "A-is B" type. (pp. 20-21)
  

The Kantian statement of the problem: "How are synthetical a priori judgment possible?"

distinguish between:

analytic/synthetic

a priori/a posteriori a posteriori a priori

analytical null warranted by law of contradiction

synthetical warranted by synthesis: see Kant's definition experience A 6f. B 10f. (Smith, p. 48)

Question of synthetic judgments broken down: how are synthetic a priori judgments possible in mathematics

How are synthetic a priori judgments possible in natural science?

Are synthetic a priori judgments possible in metaphysics?

Simply understand: Kant argues that synthetic a priori judgments occur in mathematics and in natural science (i.e., as Jones points out, in the proposition "every event has a cause"

Jones is too easy here: Kant is not merely asserting what Hume denied. On the contrary, Kant agrees w/Hume that the content of our experience fails to show a necessary connection between a "cause" and an "effect." His claim is that we nonetheless experience the world according to the structure of causality - because this is a structure our mind develops and injects into experience.

Kant's argument here (his deduction - transcendental?) is simply that such a structure is a necessary condition for experience. As Jones puts it,

These standard forms "sort" the content of experience into standard patterns. Though the materials that are thus organized into patterns are not necessary//Hume is correct//, the patterns themselves are necessary, for without them the variable contents would only be a chaotic jumble, not the well-ordered content we actually experience. Accordingly, if there are any standard forms, of the judgment is not contained in the subject) and that is also a priori (because it is contributed to experience by the mind and is therefore universal and necessary for all experience.) Thus Kant's hypothesis can be rephrased to mean that there are, after all, judgments in the fourth quadrant, and that these judgments are warranted neither by experience nor by the law of contradiction but by an organizing principle of the mind. (26)

The a priori in mathematics - pp. 27 ff. 1) mathematical knowledge - contra Hobbes - is synthetic 2) mathematical knowledge is a priori.

Day 3: Note meaning of term "transcendental" p. 29, 33, 38 -

argument for space as a framework of (?)

Contra Newton, space is not an absolute reality, independent or ourselves. Nor is it merely a relational reality established (Leibniz) by sense and imagination. Kant saw (example of the gloves) that "space" as a framework of our experience, involves more than only Leibnizian relations between parts.

Our apprehension of space is sensuous ("aesthetic") rather than intellectual (Leibnizian). The mind organizes its experiences spatially - and so we can be certain that all the mind's objects have spatial characteristics.

This then, for Kant, establishes the possibility of a priori synthetic judgments - e.g., geometry. Since space is not an independently existing entity (ala Newton), but a way in which the human mind organizes its experience, "...what the geometrician investigates is not the properties of outer objects but the modes of our faculty of intuition (outer perception). Hence, again, any properties found to characterize a particular region of space (for example, that the space here and now is such that triangles formed in it have interior angles equal to 180 degrees) will characterize space everywhere, for the geometric properties in questions are a projection of the human mind." (30)

So, as Kant indicates here "Our explanation is thus the only explanation that makes intelligible the possibility of geometry, as a body of a priori synthetic knowledge."

More radically, Kant's explanation redeems mathematics as a science of reality. Mathematics "fits" or applies to reality because it is a contribution mind makes to the world in the first place.