For Kant Objectivity is directly based on the Imagination, because it is the Imagination as faculty that allows us to project Synthetic A Priori of Space and Time, or now Spacetime. For Kant Geometry is synthetic A Priori because it is based on the Imagined Singular of Space. What is interesting is that there are four terms.
Analytic A Priori = Concepts that do not depend on Precepts that can be analyzed in themselves without external input.
Synthetic A Priori = Space, Categories, Schemas
Analytic A Posterori = Analysis of synthetic percepts
Synthetic A Posteriori = Percept based experience
The whole purpose of Kant’s Categories is to define the Object of Newtonian Physics, go ground Science. Thus objectivity comes from the projection of Synthetic A Prioris like space, Categories, Schemas. Schemas relate the Categories to Time. The Categories are presented in a static dialectical form, Hegel too them and made them dynamic and proliferated them in his logic. Categories become disseminated as Derrida liked to say.
Schlick says something similar later in his Logical Positivism which was prior to Wittgenstein’s (He pushed Wittgenstein to the fore as the leader of the LP movement), following Hilbert he wanted to disconnect concepts from percepts, and make concepts mutually referent, and thus produce an axiomatic platform free of percepts. So we can see that the Analytic Apriori is related to the mutual definition of concepts free from any experience by Reason. On the other hand the Synthetic A Posterior is the experience as a whole of whole things in which we are flooded with percepts. Kant critiques Pure Reason saying we cannot use Reason alone due to the Antimonies and so he had to build a bridge between Reason and Experience, Concept and Percept as Schlick called them. Kant does that by taking the corner cases of Synthetic Apriori and Analytic A Posteriori and giving them meaning. We want to analyze syntheses produced by experience, but we can only do that on the basis of our own projection of the synthetic A Priori of Space, Categories and Time (Schemas). So our ability to Analyze phenomena from experience using reason, is based on our counter projection of the infrastructure that is the basis of our reasoning. So there is actually a balance here between Analysis and Synthesis in the corner cases that connect Conceptual reason and Perceptual experience.
Now if we go back to Plato we see that Kant is working within the context of the Divided Line which is composed of Non-representable and Representable Intelligibles in the Ratio half of the divided line and Grounded and Ungrounded opinion/appearance on the Doxa Side of the Divided line. Kant is trying to build a bridge between the sides of the divided line rather than merely distinguishing them as Plato is doing. Plato’s divided line gives us the basic infrastructure of our Western worldview. Kant is saying that instead of dividing these faculties from each other they should be working together because reason on its own goes astray. Plato on the other hand thought Reason on its own could see the higher forms, going from the representable intelligibles of Geometry to the unrepresentable intelligibles like the Good.
In order to connect Ratio and Doxa Kant exploited the corner cases which mixed Analysis/Syntheis with A Priori/A Posterori. And this is a similar structure to the corner cases that I talk about in my post on Gestalt/Flow//System/Process See http://think.net/2011/05/06/namesake-discussion-gestaltflowsystemprocess/
What I think the Analytical Philosophers forget is this balance between A Posterori Analysis and A Priori Synthesis. When Hegel was adopted by Marxism as their basis which they not only turned on its head (going from idealism to materialism) but mostly misunderstood, then it made sense that the British and Americans would adopt Analysis as their fundamental philosophical method during the cold war. Thus the rift between Analytical Philosophy and just plane old European Philosophy which is now called Continental Philosophy (Europeans just kept doing philosophy within their tradition, so we should really call it the Mainstream philosophical tradition in the West, with Analytical Philosophy being the spin off and probably a dead end). But if we go back to Kent Synthesis and Analysis are always balanced both in the sides rooted in Rato and Doxa, and in the corner cases that he uses as a bridge.
Now my own dissertation called Emergent Design attempts to explore this territory even further by realizing that the projection of Spacetime is not a homogeneous plenum as is normally thought but that different schemas are projected at different scopes. Seems this idea has not taken root previously, as far as I can find. So I posit the possible existence of a General Schemas Theory and I formulate a Hypothesis S-prime to test, that there is a very specific set of schemas that form a hierarchy of scopes, and a couple of rules that govern the relation between the schemas and various dimensions. See http://emergentdesign.net for more info on that (I can now self-promote more brazenly because Quora changed its policy on that.) It is fascinating to me that no one seems to have asked the question as to what is the next higher thing beyond the system, that contains all the templates for organizing Spacetime that are different from the system. That is what Schemas Theory is and it studies not just Systems but also Monad, Pattern, Form, System, Meta-System (OpenScape), Domain, World, Kosmos, and Pluriverse. And the rules are that there are two schemas per dimension and two dimensions per schema. That is Hypothesis S-prime. Couldn’t resist slipping that in, because it is my major contention as a candidate hypothesis to bootstrap Schemas Theory into a real discipline. For more about the history of Schemas see Umberto Eco’s Kant and the Platypus.
So the basic idea is that we are projecting the Schemas by which we render things in spacetime intelligible differently at different scopes. These scopes nest without any gaps (I can’t find any, can you?). The schemas underlie all objects, but especially designed artificial objects created by humans. They also underlie the structure of language. So they bridge between the Logos within us and the substrate of the Physis which is spacetime. All objects are defined in terms of these templates of understanding of objects in spacetime that we project. But interestingly all our analysis of objects given by experience, or a Priori Concepts, is in terms of the schemas and their relation to geometry via dimensionality. So you can see in this the wisdom of the balance in Kant between analysis and synthesis corner cases. Synthesis makes possible Analysis. But in two ways. A Posteriori Analysis via conventional concepts operates on A Posteriori Synthesis of precepts. For that to work the infrastructure of scopes needs to be projected for us to find it in the phenomena and thus be able to take them a part at in a hierarchical manner. But also it is the Synthetic A Priori of the Schemas inside as related to dimensionality and through that to geometry that representable intelligibles are created, so that the unrepresentable intelligibles (non-representable concepts) can be indicated, i.e. using words within the schematically organized language we use to reason with. So schemas are the interface between Analysis and Synthesis both on the A Priori side and the A Posterori side.
This is why C.S. Peirce is so important because he is a Kantian that takes Hegel seriously without any influence from Marxism. He has his philosophical principles First (isolata), Second (relata), Third (continua). And the center of his philosophy is on the Third, the mediation. He approaches traditional logic based on that principle from Hegel, and discovers things like Abduction, for instance as the third way of thinking using Hypothesis as done in science which was not recognized by the tradition which only thought about Induction and Deduction. But there are three ways to arrange the premises of a logical syllogism, but it was Peirce to first think hard about the third arrangement and give it a meaning, that was the basis for Pragmaticism (Every one is doing Science, formulating and testing hypotheses, in their daily lives continually and that is how we solve pragmatic problems.) Also Peirce made the distinction between Precison of Analysis that takes apart and reduces to rubble phenomena, and Precission (with two ss) which is looking at the part in the context of the synthetic whole. He says we have forgotten about Precission which he took from the Medieval Philosophers and brought back as the alternative to analysis that merely destroys what ever it looks at. Non-invasive MRI and PET scans are examples of modern techniques that could be said to exemplify this approach.
It certainly takes imagination to look at things through the lens of Precission rather than reductive analysis, because you cannot just take the whole synthesis apart and look at the parts in isolation. Rather you must look for the way the parts are articulated in the context of the synthetic whole of which they are a part, and thus you must look at them in situ in the living whole of which they are an integral part.
This brings me by a circuitous route to the myth of Adam and Eve. It is clear that just as the Abraham story is about why we should not do human sacrifice giving a primal scene for the end of human sacrifice which was rampant in the ancient world if we are to believe Greek mythic sources. So Adam and Eve can be seen as the primal scene for the end of the Matriarchal Society and the beginning of the Patriarchal Society. Matriarchy means the women never leave home, fertility is a resource to be preserved, so husbands come to visit briefly, and it is the brother who acts as a Father to the child. Matriarchy is not some sort of paradise where women were in control, but like the Handmaidens tale it was a society where fertility was a scarce resource and thus it was preserved and not traded away. Patriarchy is where the bride goes to live with the Husband’s family and thus women become a traded commodity in the Patriarchal Society. Be that as it may, the key is to see that in a Matriarchal Society when seen in mammals in general there is an alpha male who has a territory and a harem, and there are beta males trying to take both the territory and the harem away. This is a bi-modal population so there are also outcast males and females, as well as the pharmacon who is outcast by all. Now in this kind of social group the females are faceless. In other words they are all alike as a group to the Alpha Male, i.e. they are his possession as a group. But in Patriarchal Society the face of the female becomes important, and this is why we have the lifting of the veil for the first kiss in marriage ceremonies even today. But here is the point. Adam was alone, this is when he was an Alpha Male and his territory (the garden) and his harem as faceless was part of him, inside of him. But Adam became a husband because Eve was drawn as a rib from his side. And so he became the first patriarch in the Semitic line and presumably the human line that traced its linage for the first time through the father rather than the mother. [By the way my standard joke about this is that Matriarchy was tried for at least 25 millennia prior to Adam the first Patriarch, and it has only been about 6000 years since then. And it takes some time to work the bugs out of any new system and we have not had much of a chance yet to do that. We had Matriarchy for at least 25 millennium and during that time not even a light bulb was invented, less well a washing machine, or a dish washer. So we should give this new thing Patriarchy a chance. Also I ask for volunteers from women to stay home with their fathers as is done in Matriarchy, and I don’t get many takers. When we study Matriarchy as it really was we find that Patriarchy was actually, believe it or not, a liberation of women, because for the first time they were important as individuals and their faces mattered, they did not blend into the harem so they had no individual characteristics that were recognized. But unfortunately this new individuality meant that they became according to Levi-Strauss a commodity to be traded. So we should be given more time to do that by the supporters of a return to Matriarchy.] But the key point which is normally hard to explain is why Eve was made out of a rib. But if we take the foregoing as a possible interpretation, then we can see that the rib is something inside the body that sticks out and can be counted even when it is in the body of the human being. So the rib signifies something that is inside but differentiable by Precission. When we take that thing out, and Analyze it with precision, then we get Patriarchy. Suddenly the face becomes important when the female is not just part of the male as in matriarchy but actually becomes a human in her own right standing beside her husband (she is still thought about in terms of needing husbandry). So I went though this whole story just so I could point out that in this transformation, the difference between Synthetic Precission and Analytic Precision.
Now going back to Kant we can see that the relation between Precision and Precission allows us to understand better the corner cases of Analytic A Posterori and Synthetic A Priori. Analysis in reduction strives for Precision. But Synthesis by maintaining the whole still allows Precission. And thus it is not true that reason cannot do anything with respect to the parts within the whole. Rather it can explore the mereology from the outside using non-invasive techniques as we are finding out with the brain with fMRI and PET scans. Everything from some perspective is transparent. It is just a matter of finding out what the approach is that gives us that perspective. So a more sophisticated approach is to use Precission and Precision where appropriate in our studies rather than only using Analysis and throwing up our hands saying we have no way to deal with synthesis and dialectics. We have fallen behind the curve due to the Cold War taboo. If it were possible for Adam to embody the difference between Precission and Precision, in the difference between Matriarchal and Patriarchal then surely as his inheritors we should be able to handle it as part of our mental gymnastics. The only real development was Sartre’s Critique of Dialectical Reason which treated Dialectics Dialectically rather than like a mechanism as the Marxists always had.