Aesthetics is used by Kant in its etymological sense. Aesthesis means sensation, sensitive perception. Aestheta are all things perceived. (as opposed to voeta: all things intellegible). Kant does not use aesthetics as the Romantics (concerning matters of taste). See footnote on page 42 of the first critique.
An important difference Kant draws at the outset of the first Critique is between analytical and synthetic judgements. (p.30) The former are explanatory judgements that do not add any further content to our conceptions, the latter are augmentative in that they recurr to something external to the starting conception to complete its definition. The examples he gives are respectively: all bodies are extended (analytical); all bodies are heavy (synthetic). Judgements of experience are always synthetical, whilst experience itself is a synthesis of intuitions (but we will see later about intuitions).
Thus reason is capable of forming analytical a priori judgements (rationalists’ favourite) that are deductive, and that require the predicate to be extrapulated and derived from the subject. Although they are both universally and necessarily valid, they are not fertile, they are tautological. (the triangle has three angles).
Then there are synthetic a posteriori judgements (empiricists’ favourites) which are inductive, and founded on experience –when we interrogate Nature without asking question - but are not universally and necessarily valid.
Finally, we have synthetic a priori judgements. In maths, for instance, assertions such as 7+5=12 are synthetic judgements in so far as the predicate adds something new to the subject. One cannot arrive to 12 from 7, nor from 5. The predicative element is not derived from the subject by analysis but is added. Knowledge is therefore augmentative in this case. The fecundity of synthetic a priori judgement derives from the object, its universality derives from the subject and is a priori, the elements that provide universality are transcendentals: structures of our mind which do not come from sensation but would have no validity without it. Synthetic a priori judgement necessitate a content and a form. The former derives from the object, the latter from the subject. [see text on the Egyptians]
‘Metaphysics needs to make use of synthetic judgements a priori to be a science and widen up the range of our a priori knowledge’. (p.34)
Once Kant has established that science relies on a priori synthesis (numerous examples from maths, physics and geometry are provided in the text), it is the task of the critique to unveil the nature of such judgements in order to be able to judge where metaphysics has operated on their basis with or without foundation.
The foundation for analytical a priori judgements is the principle of identity and non-contradiction (due to their explicatory character). The foundation of synthetic a posteriori judgements is experience (due to their reliance on the experimental method and induction).
So, what is, Kant asks, ‘the incognita on which intellect relies when it thinks he has found outside of the subject A a predicate B that, whilst foreign, is connected to it?’ This is the copernican revolution his thought represents in 1769. Let us look at the elements of his thought first.
In the Dissertation of 1770 Kant introduces the ideas of intuition, sensation and understanding.
Things manifest themselves to us as representations or phenomena (from Greek fainomai: appear, show oneself). The way in which our knowledge relates to objects immediately is through intuitions. We can have empirical and pure intuition. Empirical intuition relates to an object by means of sensation. ‘an intuition can take place only in so far as the object is given to us. This is only possible, to man at least, on condition that the object affects the mind in a certain manner’.p41
The faculty of being object of modifications –affectations- or ‘the capacity for receiving representations (receptivity) through the mode in which we are affected by objects’ is called sensibility. Sensation is the modification –affectation- the subject receives –passively- from the object. Sensibility furnishes us with intuitions, through understanding they are thought and from there conceptions arise. p.41. The undetermined object of an empirical intuition is called Phenomenon and it is composed a matter (which corresponds to the sensation it gives raise to) and form (which is what makes it arrangeable within a set of relations). The former is given to us a posteriori (for instance, the heat and cold only arise in the subject after contact with an object), the latter, a priori, (since it cannot be derived by sensation, but represent the way in which sensation functions in the subject). It is only due to forms that there can be universality and necessity in the knowledge of things of the world in space and time. Form is the distincitve subject matter of metaphysics.
Phenomena or representations are therefore pure and transcendental, in so far as they can be arranged independently from sensation. ‘And we find existing in the mind a priori, the pure form of sensuous intuitions in general’. But there are also pure intuitions: these represent the ‘form’ of sensibility considered independently from matter (i.e. the concrete sensations affecting the subject).
These pure intuitions are space and time. This is revolutionary since before Kant space and time had been regarded as qualities of objects and as ontological determinations of their structures. Kant is the first to examine them as functions and principles of knowledge, thus, as pertaining to the knowing subject. These are relating forms (they function by relating sensations, arranging them).
Space then is an a priori form of sensible knowledge, more specifically it is the form (the mode of functioning) of external sense, arranging all things that appear outside. Objects are imagined as external to us and amongst themselves because they appear to occupy each a different space. There is the formal tendency to be modified by objects that are represented in a space different from ours.
Time is equally an a priori form of sensible knowledge, more specifically it is the form (the mode of functioning) of inner sense, arranging all things that appear inside. It is the formal tendency to arrange our states of mind and inner sense in a time where states of mind succeed one another. Here very important –retrospectively- are the consideration on the inner sense and consciousness of the self (page 59 of the critique of pure reason).
It is crucial here to remember that Kant talks of transcendental ideality and empirical reality of space and time the former in so far as they are not inherent to objects but only to our sensible intuition of them, and the latter in so far as no object can be given to our senses without being subject to them. Geometry and mathematics are founded not on the content but on the form of phenomena, the former depending on pure intuition of space, the latter on time (subtraction, sum etc).
As well as sensibility, knowledge has another source: the intellect. The intellect produces concept, sensibility sensations. Sensations are blind without concepts, concepts empty without sensations. Sensation gives us objects that the intellect then thinks. Transcendental aesthetics is the science of the laws of sensitivity, whilst logic the study of the laws of understanding. ‘Intuitions and conceptions constitute all elements of our knowledge. Both are either pure or empirical. They are empirical when sensation (which presupposes the actual presence of the object) is contained in them, pure when no sensation is mixed with the representation. Sensation we may call the matter of sensuous cognition. Pure intuition consequently contains merely the form under which something is intuited, and pure conception only the form of the thought of an object. Only pure intuitions and pure conceptions are possible a priori, the empirical only a posteriori.’ p.62
 Not here implicit critique to Bacon’s assertion that Natura nisi parendo dicitur, in order to progress, Kant stresses, reason must project. Reason is not a tabula rasa. Not Nature, but Man in his projectuality is posed at the centre of his discourse. Nature is described phenomenically, we see it not as it is but as it appears to us. We find in the object characteristics that have already been conceptualised in the subject.