Although Hume does not himself use the terms 'a priori' and 'a posteriori', those categories do, roughly, correspond to the distinction that Hume draws between relations of ideas and matter of fact in the Enquiry Concerning Human Understanding. (The Enquiry Concerning Human Understanding is also referred to as the 'first Enquiry', as I will do in what follows, to distinguish it from the Enquiry Concerning the Principles of Morals, the 'second Enquiry'.) Now, by the by, but interestingly enough, Hume doesn't draw the distinction between relations of ideas and matters of fact, at least explicitly, in the earlier Treatise of Human Nature, much of whose first Book was recast in the first Enquiry, although he does draw a related distinction in Book 1, Part 3, Chapter 1 of the Treatise, between relations that depend on 'intuition' and 'demonstration', and have only to do with ideas, in contrast to other relations, which do not so depend on ideas, and thus do not admit of the sort of certainty characteristic of intuition and demonstration.

Near the beginning of Part 1 of Section IV of the first Enquiry, Hume explains that relations of ideas "are discoverable by the mere operation of thought, without dependence on what is any where existent in the universe," whereas, by contrast, matters of fact "are not ascertained in the same manner...the contrary of every matter of fact is still possible, because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if every so conformable to reality." Insofar as relations of ideas do not depend "on what is any where existent in the universe," they are akin to Kant's analytic truths, which depend, roughly, only on the meaning of their terms; matters of fact, which do depend on what is existent in the universe, depend on experience, and thus are akin to Kant's synthetic truths. As you quite rightly point out, there is no room in Hume's division between relations of ideas and matters of fact--which is sometimes called 'Hume's fork'--for the category of the synthetic a priori, which seems to straddle the realms of relations of ideas and matters of fact and thus to explode that supposedly exhaustive division.

Now you want to bring these distinctions to bear on Hume's famous thought experiment of the 'missing shade of blue', which he himself took to constitute a prima facie counterexample to his claim that all ideas are derived from impressions, that is, that all thoughts may be traced back to experience. (It's worth noting that in both the first Enquiry and in the Treatise, Hume actually considers the missing shade of blue before he introduces the distinction between judgments based on experience and those not based on experience and hence admitting of certainty. He therefore must not have thought that his 'fork' was related to the missing shade of blue.) The missing shade of blue might seem to constitute a counterexample to this view, because in this case, the thought of a color is arrived at without one having had experience of that previous color. Now Hume himself, after propounding the example, says that although "this may serve as a proof, that not every idea is derived from correspondent impressions...this instance is so singular, that it is scarcely worth our observing, and does not merit, that for it alone we should alter our general maxim." Although Hume may have thought the missing shade of blue "scarcely worth our observing," his readers have given it considerable attention, and you propose that one might understand the example, in Kantian terms, as marking a distinction between imagined and experienced colors, with the latter belonging to the category of the 'analytic a posteriori' and the former belonging to the 'synthetic a posteriori'.

It's not clear to me that this suggestion can work. After all, analytic judgments, for Kant, are not supposed to depend on experience, so it does not seem to me that judgments about colors--when one uses the terms 'analytic' and 'synthetic', one must refer to judgments, what might today be called assertions--can be called 'analytic a posteriori'; synthetic a posteriori judgments, for their part, just are what Kant calls straightforwardly synthetic judgments, since they depend on experience.

But while it's not clear to me that your suggestion can be brought to bear on the particular case of the missing shade of blue, the notion of analytic a posteriori judgments is itself a very interesting one, which Kant himself was not able to envisage, but which may nevertheless constitute a category that merits some consideration. For consider an assertion such as 'Water is H2O'. This is a claim based on experience, but it's necessary. It can't, however, belong to the category of the synthetic a priori, at least as Kant conceives it, since synthetic a priori judgments are supposed to explain the possibility of experience, but not themselves to be objects of experience; the claim can't be analytic, since it's based on experience. So it might seem that, in virtue of its necessity and the fact that it is a claim about experience, that such a claim is best construed as 'analytic a priori'. If this is correct, however, what does this show about Kant's own division of judgments into analytic and synthetic? Might that not have to be rethought in much the same way that Kant himself may be taken to have rethought Hume's fork?

There are a couple of ways we might go here. Thinking about the sky, it's a pretty good bet that most people with normal color vision (roughly, people who can pass a color-blindness test like this one ) will say that the sky is blue and will agree that a good many other things are blue, even if they've never seen them before. And so while there is a certain amount of arbitrariness and convention in just where we draw the lines between colors and while the names themselves are certainly matters of convention, there are facts about human physiology here as well. Thus, one way to think about colors is in terms of the responses of "normal" individuals in "normal" conditions (where both of those "normals" are not altogether easy to pin down.)

Another way is to think about the physical characteristics of the things we apply the color words to. For example: light with frequency around 450 nanometers is blue light. If the light reflected from a body has this frequency, we call the body blue. But things are a bit complicated here. We can't identify colors with frequencies in any simple way because non-monochromatic light (light that's a mixture of frequencies) will typically appear to be a definite color.

So color is not a simple matter. There are objective elements having to do with our visual systems, objective elements having to do with the properties of physical objects and the way they interact with light, and there are conventions about where certain boundaries get drawn. A really good account would be even more complicated. For example: context makes a difference to what a color looks like. Here's one example and here's another, related one. What we can say pretty confidently is that it's not just a matter of convention, though the full story calls for a good deal more expertise than I have.

In general, the fact that everyone agrees on something is not really enough to make it true. The fact that everyone believes that Brazil is the best team in the World Cup doesn't mean they will win the Cup, or be the best team.

On the other hand, if I believe that Jennifer is my best girl, then she is my best girl. If we all thought that blue was the best colour, then it would be: "our best colour", so perhaps it could be said to be the best colour.

So I think "the best" is used in two ways in your excellent question. (1) It just means "the best" by some external standard, goal-scoring perhaps, so that "Brazil is the best team" means that Brazil will win the Cup. (2) It means that blue is our best colour, the best colour of all of us, the one we all like the most, then it is the best colour - of all of us - though not in the first sense.

I think perhaps it is a little difficult to know how to understand what the fact of being the best colour is. There is something good about each of the colours, no? And also, what are the tests of excellence in a colour? What makes a colour good, better, the best? If it's brightness, then black is a bad colour, and white is a good one. If it's richness, then purple is pretty good, and glossy black. Grey is a bit dull, but some people find it muted and elegant. A sparkling yellow sun on a spring morning has a great colour. So we need to decide what the criteria or standards are here. That might be hard. Or there might be lots of different ones. The best butter knife is not necessarily the best weapon.

Why should the redness of a red object not be a fact? We say of this tomato here, "Look, it's red." We know this proposition is true because we can see that the tomato is red, just as we know that the tomato is heavy - heavy for a tomato, anyway - because we can weigh it in our hand. The same thing applies to shape, supposing that we come to know the shape of something by visual inspection rather than by measurement. Now if our red object is viewed in green light, it turns black, because the light with colours at the middle of the spectrum, the green light, is complementary to the red light that the tomato "reflects", if we can say this. (In what way is a tomato not like a mirror?) The red tomato "absorbs" the green light.

I think that your question goes deeper, however. This redness of the tomato might be thought not to be a physical fact, if you believe those philosophers who are impressed by the existence of an "explanatory gap", as it has come to be called, between physical and phenomenal phenomena, or by Frank Jackson's thought-experiment about Mary, the brilliant colour scientist who knows absolutely everything physical about colour that there is to know, but is confined to a grey-scale environment, and who, on her release from that environment, learns what the colours are like, or what they look like, if you like. But it seems open to argument whether the fact that the redness of the tomato is not a physical fact means that it is not a fact of any kind. You contrast a "fact" with "an experience of consciousness", but I wonder whether the "experience of consciousness" does not itself count as a fact. I think that philosophical analysis would have something to say here.

Furthermore, there are facts about colour, phenomenological ones, which came to interest Wittgenstein after he gave up the logical atomism of the Tractatus in which the world is the totality of facts, not things. (It's important to note the point of the contrast here - it is facts, rather than things, of which the world is said to be a totality.) So the later Wittgenstein thought that the earlier Wittgenstein was wrong about something, even though in the end even the later Wittgenstein rejected the idea that the phenomenological facts are facts in the same way as regular facts, such as the existence of an ugly heavy desk in front of me. An example of a phenomenological "fact": though some blues are lighter than some yellows, yellow is lighter than blue. There is no pure brown, and there could not be a brown traffic light. White is the lightest colour. Red cannot be greenish. All of these propositions feel as though they express facts, and Wittgenstein really has to struggle to make the fascinating claim stick that "there is no such thing as phenomenology, but there are indeed phenomenological problems" (_Remarks on Colour_, I-53). There are problems expressed by claims such as "Green can be transparent, but white cannot" (although Wittgenstein also observes that the opacity of white is no more a property of white than the transparency of green glass is a property of the colour green), but are there no facts to resolve these problems, even if not phenomenological ones?

On the whole, I do believe that the easy distinction you make between facts on the one hand, probably physical facts, and ineffable experiences on the other, with no factual aspect to them, does not quite square with the facts!

You are right that, in the Tractatus, Wittgenstein claims that the world is the totality of facts. And it is also plausable to think that the experience of red (seeing red) may be difficult to express informatively in words, especially if you were to try to convey what it is like to see red to someone who is color blind or completely blind from birth. But I don't think Wittgenstein needs to deny this. I believe that, for Wittgenstein, the term 'fact' means something like 'state of affairs' and so one may speak similarly of the fact of you seeing red now and the state of affairs of you seeing red now, without this implying any difference between what you refer to as the fact that red exists and the actuality of red.

Perceived color is a matter of retinal and neurological processing. People with full color vision see a variety of spectral inputs (from single frequency to mixed frequencies) as purple. Perhaps you are asking, could people who perceive red and blue normally see a mixture of red and blue as anything other than purple (in the same circumstances)? I don't think there are any cases of this kind of odd color perception, so it may well be that our 3-sensor color perception system will always perceive a mixture of red and blue as purple. Does that mean it is a "logical truth" that red and blue make purple? Only in the same sense that it is a logical truth that if you can hear the note A and hear the note C you will hear the combination as a minor third.

"Opposite" is not in this connection a very well-defined word. "Complementary" is more precise, but then we should inquire: physical additive complementary, i.e. such as to cancel the test colour in light superposition and produce neutral or white; physical subtractive complementary, i.e. such as to cancel the test colour in pigment mixing and produce neutral or black; psychologically complementary - it is unclear what this would mean, but it could have to do with the placing of the test in a colour space based on the psychologycal "unitary" hues, i.e. those that do not look as though they contain a "trace" of any other hue in the space.

There are some interesting studies of brown, and one of them (I think) is my own, in Jonathan Westphal, Colour: A Philosophical Introduction, Blackwell, Oxford, 1991 - the chapter on "Brown". Are we allowed to sound our own trumpets on this website? I'm not sure, but anyway this might get you started. The thing to remember is that brown surfaces have roughly the same reflectance as yellow ones, but they are quite a bit dimmer. It is as though brown is really a low-reflectance yellow, so one thing you might try is to see what the afterimage colour of brown is - is it similar to the violet afterimage of yellow, but dimmer? Afterimage complementaries give you yet another - psychological - sense of "opposite"!

The fact is that brown is not neutral. At its reflectance level, grey is the neutral. But I'm not sure what you had in mind with the phrase "representing the balance of primary/secondary/tertiary (etc.) colors. I think you may be mixing the metaphysical primary/secondary quality distinction with the physical distinction between "additive" and "subtractive" primaries.

This is a fairly frequent concern. The correct answer is that there is a sense of "colours" in which black and white are not colours (they are not chromatic colours) and a sense in which they are colours (they are achromatic colours). So if we count the achromatic colours (black, white and grey) as colours, then black and white are colours. (Brown is an interesting case, as it is a colour which is partially achromatic.) In the same way, we can ask whether zero and infinity are numbers. Usually they are treated as numbers, and they have their own mathematical symbols. We can manipulate them in calculations and so forth. But in another sense "zero" denotes the absence of a number, and so does the symbol for an infinite number. Q: "How many chickens were there in the kitchen?" A: "A number." Q: "What is the number?" A: "Zero"! Aristotle's view was that the smallest number is two, as one of something is not a number of somethings. "There were a number of people there." How many?" "One." In this sense two is the first crowd-like or milling number. One won't mill around. Logicians face the same difficulty in explaining that in their sense "some" means only "at least one".

The situation is that colours arrange themselves into three dimensions: saturation, hue, and brightness. Hue is colourfulness, the colourfulness of red, yellow, blue, green and so on, and colourfulness does not include black, white and grey. Colourfulness is the circling hue dimension at maximum saturation, and the achromatic colours lie in their own vertical dimension at the center of the solid whose surface is this colourfulness or saturation. White has zero saturation, and we make other pigments of various chromatic colours less saturated - paler - by mixing in white pigment. (It is an interesting question why this concept - paleness - has a "special relationship" only with white.)

So at the end of the day the fact is that in one way black and white behave as colours, and in another way they work to create diminutions and absences of colour. Wittgenstein was right (in his Remarks on Colour) to see a puzzling element of necessity, a necessity as hard as logical necessity, in these striking facts.

First, take a look at Question 2384 and its answers, which are closely related to your question. Your question is related to what is called the "inverted spectrum", a philosophical puzzle posed by John Locke, one version of which is this: Is it possible that objects that have the color you describe as "red" are seen by me as if they had the color you describe as "green", even though I also describe them as red, and vice versa? Posing the problem is difficult; e.g., objects arguably don't "have" colors, but reflect light of certain wavelengths, which are perceived by us as certain colors. "Is the color that I perceive as, and call, red the same as the color that you perceive as what I call blue?" is another way of posing the puzzle. Part of the problem is that there doesn't seem to be any way to decide what the answer is (if, indeed, it has an answer). What experiment would decide between these? Perhaps such color-perceptions (more generally, what are called "qualia") are such that a functionally complete theory of the mind (or brain) would not enable us to distinguish between them. For more on this, see the Stanford Encyclopedia of Philosophy article on "Inverted Qualia".

There are two different, but related, issues here, on neither of which is there universal agreement among philosophers (but, then again, is there ever?).

First, there's "Molyneux's problem": Can a person born blind who later gains sight distinguish a cube from a sphere merely by sight (assuming the person could distinguish between them by touch)? There's some empirical evidence that the answer is "no". The psychologist Richard Gregory has investigated this.

But closer to your specific question is the philosopher Frank Jackson's thought experiment about "Mary", a color scientist who lives in a completely black-and-white world but who is the world's foremost expert on color perception. She has never experienced red. Would she learn anything if she experienced it for the first time? I.e., is there anything "phenomenal" to the experience of red over and above what physics can tell us? Jackson originally argued that there was, i.e., that Mary would learn something from the experience of red, namely, what it's like to see red, but he has recently changed his mind. The novelist David Lodge has explored the Mary story in his novel Thinks....

For more on Jackson's thought experiment, see the anthology edited by Peter Ludlow, Y. Nagasawa, and D. Stoljar, There's Something about Mary (MIT Press, 2004).