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).

The fact is that the correspondence between colour and frequency is rough and approximate. To some "colours" (and what does this mean?) there corresponds no wavelength, or no single wavelength, of monochromatic light. Examples are the browns, the appropriately named "non-spectral" purples, and white. (Black is also an example!) The colours form a circle (roughly) or a three-dimensional solid of which the circle is a cross-section at middle brightness in fixed illumination. This is colour space; and the frequency scale does not really model its overal complexity, except around the one corner at the edge: the spectrum. This is related to the fact that there are three types of cone which respond to coloured light, not four. There is no photoreceptor which peaks in the yellow, so when we see yellow it is the "red" and "green" cones that are being stimulated. Scientists tend to draw the conclusion that "colour is a sensation", as Maxwell put it. But this can't be right, as I see it, for the most part for the reasons given in Thomas Reid's philosophy of sensation and perception. The relation between colour and frequncy or wavelength has been an issue since the wave theory of light was introduced by Thomas Young, but the problem was there for Newton even though he held a corpuscular theory of light; the big particles stirred up red or "red" sensations (_n.b._ red sensations), and the little ones blue ones, but the "Rays" (paths?) made of these corpuscles were "strictly" not coloured.

I think the best place to begin is with the first sentence: "All the empirical objects that I perceive around me are structures of sensations." I think this confuses two things. The objects we perceive are things like tables, chairs, tin nickels and left-handed paper-hangers. And none of those things are structures of sensations. Now it may be that the way we perceive these things is by having various sensations, and it's also true that in some sense the sensations are manufactured in the brain, brought about with the causal assistance of the paper-hangers and such. But the machinery of perception isn't the same as what's perceived.

More generally, it's no surprise that we perceive things by way of stuff going on in our brains. But that stuff isn't what we see; it's what makes seeing possible.

So yes: the real world really is real (last time I checked). It's not composed of sensations, though sensations may be among the many things that make up the world entire.

There are real cars, with real sizes -- five feet high, twelve feet long, for example -- and they would be these sizes even if there was no observer to notice them. When a real car appears to an observer to be smaller, or larger, than it actually is, we can speak of its apparent size as opposed to its actual size; but the notion of an apparent size only makes sense in relation to an observer to whom the car appears to be one size rather than another. That is why Prof. Moore considers the real size of a car to be an intrinsic property while the apparent size of a car is a relational property.

The distance between a car and an observer does not translate into a difference in the apparent size of that car to that observer since a distant car may appear to be its real size to some observers, and a nearby car may appear to be bigger or smaller than its real size to some observers. Thus, there is no general answer to your question about what distance a car must be in order for us to see its real size. Some people, in some circumstances, are very good at seeing the real size of a car at a distance; others are not.

Finally, it is important to remember that there is no such thing as an apparent car. If someone seems to see a car of a certain size when there is in fact none to be seen, that is a fact about the observer -- not an intrinsic fact about a non-existent car nor a fact about a relation that exists between an observer and a non-existent car. The temptation to reify 'apparent objects' is partly responsible for the sort of confusions that you express in your question.

The surface grammar of the sentence “It’s hot in here” suggests that the sentence is about an objective state of the room. Let’s start there. There are two features of the assertion of this sentence that make you think it might not be about the temperature of the room: first, the assertion is based on a subjective experience of mine, and second, it uses the vague term “hot”. Let’s start with the first consideration. Notice that any claim anyone makes about contingent states of the external world is, if it’s a justified claim, going to be based on that person’s sensory experiences. If I say “You forgot to turn off the burner on the stove,” my claim will probably be based on seeing the flame, but my statement is a statement about the burner, not about my visual experience. Or if I say, “Something’s burning,” it’s probably because I smell the scorched butter, but it’s still the butter I’m talking about. (Guess what I did this morning making breakfast.) Contrast these cases with cases where I really do mean to talk about my sensory experiences: “It looked as if the burner was still on from where I was sitting,” “I smelled something that smelled just like butter burning.” In your case, the contrast would be between my saying: “It’s hot in here. (So turn on the air conditioning.)” with my saying: “I feel so hot all of a sudden. (I must be having a hot flash.) The first claim is a claim about the temperature in the room, and can be corrected, if it’s false, by someone else: “No, it’s not; it just feels that way to you because you’ve been sitting in an overly air-conditioned car.” The second claim is a claim about my subjective experience, and no one else is in a position to correct me about that. You say that we are “only perceiving” the heat in the room, and not taking any kind of “empirical index.” But in fact, “taking an empirical index” is exactly what perception is. (And I really like that phrase!) Our eyes, ears, nose, tongue, and skin are highly sensitive registers of specific physical magnitudes. The “brute” information about these magnitudes is then processed by specialized neurological systems into representations of the external world, which we can access consciously and report on. Now think about what’s going on when I report, on the basis of looking at a thermometer, that the room is 85 degrees. The thermometer is functioning just like my skin does, reacting in a regular, law-governed way to changes in the ambient temperature. And in reading the thermometer and reporting on it, I am acting just like my own sub-personal (or unconscious) information-processing systems in accessing and reporting on the information delivered by my sense receptors. There is this difference between the two cases – a difference that might contribute to your thinking of the thermometer reading as “more objective” than the report based on the way the room feels to me: in the case where I read the thermometer, my evidence is publicly available, whereas in the case where I base my claim on the way the room feels, my evidence is available only to me. But that difference doesn’t affect the objectivity of the claim made – in both cases, I claim something about the room. Now: what about “hot”? There are two things that you might be picking up on here. The first is that “hot” is an imprecise term. That means that the content of my claim is somewhat indeterminate: how hot does a room have to be to count as hot? Where is the boundary between hotness, and mere warmth? Insofar as it seems to be up to me to fix the answers to these questions, the truth or falsity of the claim appears to be up to me. After all, you and I could differ on what counts as “hot.” (Think about the silly chili pepper symbols they put next to foods in some Mexican or Indian restaurants. They tell you that a three-pepper dish is going to be hotter than a one-pepper dish, but how hot, in absolute terms, is a three-pepper dish?) This is a problem about calibration, or rather about about synchronizing your calibration system with mine. Having some kind of external register that we can both refer to – like a thermometer – can help with this problem, but it doesn’t eliminate it. It only helps if we take for granted that our perceptual experiences of the states of the external register are synchronized. (Think about worried parents trying to decide whether to call the pediatrician: “Does he look pale to you?” “Would you call that a ‘rash?’” “I wouldn’t say the vomiting was ‘projectile.’”) Furthermore, note that the “precision” of a thermometer is only relative – the marks on a thermometer have width, after all, and the level of the mercury might fall within the space of a single mark, rendering the reading “85 degrees” vague. Is it 85.1 degrees or 85.3 degrees? The thermometer at my house couldn’t tell you. But now the second thing about “hot” is that it’s an adjective that begs for a complement. There’s no such thing as “absolute hotness:” what’s hot for a room is not at all hot for an oven. So the claim that something is “hot” seems to need qualification; we need an answer to the question “hot” for what kind of thing? Terms that behave like “hot” are sometimes called “syncategorematic” – they are only meaningful “with a category,” only in the context of modifying something. But to say that they must be used in connection with some kind of thing is not to say that that thing has to be explicitly mentioned. If I say, “it’s hot in here” my listeners will probably figure out that I mean to say that it’s hot for an interior room. (Compare: I stick my head a little ways into the oven to check whether it’s working: “Whew! It’s hot in here.”) We human beings are (as the eminent psycholinguist Lila Gleitman says) are geniuses at pragmatics – at figuring out pretty complex thoughts on the basis of very stripped down verbal expressions. Sometimes we don’t have all the information we need to interpret what a speaker is trying to convey on the basis of what they say: if someone in another room shouts: “It’s way too cold!” I might not be to tell that she’s talking about her coffee, which is only 85 degrees, or the room, which is 72. But often enough, a shared context, or shared knowledge of the speaker’s context, can solve the problem of finding the presumed comparison. Bottom line: there’s no reason to think that the surface grammar of your sentence is misleading. The statement “it’s hot in here” is a statement about the room.

The issue here seems to be verbal. It's not clear that ordinary language has a settled answer to the question whether "sound" refers to the vibration in the air, or to the experience that the vibrations cause. If we fix on the former, then there have been plenty of sounds that never led to any experiences. If we fix on the latter, then sounds and experiences of a certain sort are one and the same thing. But there's no deep fact about which is the "right" way to think of it.

Something else worth keeping in mind: language doesn't map onto the world in any simple, direct way, and in particular we need to be careful about letting the fact that we have the noun "sound" fool us into thinking that there is some thing in the world -- a sound -- whose location (in the head? in the landscape?...) needs to be sorted out.

The Guinness Book of Records says (or at any rate, used to say) that the world’s longest lasting rainbow was continuously visible over Sheffield for some six hours on 14 March 1994. Here's a picture (I had an office in the Arts Tower at the time which is why I know about it!)

Now, did the Book of Records do some research to check that at every single second from 9am to 3pm, someone or other was perceiving the rainbow? I very much doubt it! I guess that the Book of Records supposed that, to establish the record, it was enough to have grounds for thinking that, at any moment in those six hours, someone suitably placed and looking in the right direction would have seen the rainbow (it was continuously perceivable, though not necessarily continuously perceived).

And the Book of Records is speaking here entirely in accordance with our ordinary ways of talking about rainbows as continuing to exist unperceived. I see a dramatic double rainbow, go to fetch someone to see it, and when we get back to the window say "oh good, it is still there". And what makes it the same rainbow that is still there at those two different times? Indeed, what makes it the same rainbow that is visible at a given time by differently located people, given that it would look to be in a very slightly different location to them? Nice questions! Presumbably the answers will appeal to something to do with the continuity of what would have been seen over time had we been looking, or the continuity of what would be seen if we moved from one viewing position to another.

Anyway, we certainly do talk of seeing the same rainbow again after a temporal gap, when perhaps no one happens to be looking. We do talk as if rainbows can continue to exist unperceived.

But ok, should we talk that way? Given what we know about the mechanisms by which we come to see rainbows as we do, should we really talk about them sometimes as if they are real persisting things than can exist unperceived?

Well, why not? I'm inclined to be pretty relaxed about this. Talk as you like -- so long as you are not misled!

Rainbows are variously like rabbits, rivers, ripples, holograms, and mirror images, in each case in some ways and not in other ways. In different contexts, we might want to stress different similarities or dissimilarities among such things. Perhaps a small child will be helped a bit to understand what is going on if you say "Rainbows aren't really there you know, there isn't a real coloured arch in the sky". But equally, if the same small child starts to think of rainbows as a kind of waking dream or a private illusion, then we might say "Oh it is really there, I can see it too!".

Which suggests that here (as elsewhere) the dichotomy "real"/"not real" is a crude tool -- and what we (seem to) talk about doesn't in fact sharply divide into two neat categories.

But still, the similarities between rainbows and central cases of "real" things are probably enough to give point to those everyday, Book of Records, ways of treating rainbows as real things that can exist unperceived. So we might as well, to that extent, continue to fall in with our ordinary language practice here.

So long as we do not mislead ourselves ...

Your view about the possibility that people perceive things radically differently is an old philosophical puzzle. The so-called "inverted spectrum" hypothesis is the most common variant. Assuming that color space is organized symmetrically, so that one can switch primary colors like red and green, or blue and yellow, while maintaining all the similarity relations among them, it seems someone could see red wherever others see green and yet there be no difference in their behavior. As you point out, they would learn to call red things "red", even though they looked green to them. Perhaps there could be inversions of other properties as well. So is this really possible?

One way of approaching the issue is to distinguish between what we might call the "representational content" of a perceptual experience and its "qualitative character". The representational content is what the perceptual experience is "saying" about the world around you. So if you see a red apple, your visual experience is "telling you" that there is a red, round object, an apple, at a certain location. The qualitative character is the subjective "feel" of the experience, what it's like for you to be seeing the apple. Given this distinction, we can ask whether the possibility of a behaviorally undetectable inversion - a difference in experiences that can't be detected by what the people say or how they act - applies to both the representational content and to the qualitative character, or just one (or, indeed, neither).

There are good reasons for thinking that an inversion with respect to what the experience is representing is not possible. The point is that on a very plausible theory of what determines what the experience is representing, a theory that grounds the representational content in the facts about what conditions in the world reliably produce the experience, the sort of inversion you are imagining won't occur. Since both people are experiencing what is reliably produced by the same wordly conditions, their experiences will automatically count as representing the same conditions. However, when it comes to the more elusive feature of qualitative character, it does seem possible that an inversion occur. Some philosophers try to argue that such inversions aren't possible, but I, for one, have never been convinced by their arguments.

If your question is whether “your computer,” which I take to be an ordinary personal computer, has perceptions as you do, then the answer is clearly “no.” Your computer has input devices such as a keyboard, and possibly a scanner, a video camera, and a microphone. Such input devices transducer analog physical processes into discrete digital symbols, and those symbols are stored in various locations in the computer and then can be manipulated in concert with computer programs and further input. Your brain also takes input from external physical stimuli such as light, sound waves, etc. It also transduces those signals into other forms, typically chemical and then electrical signals. Those electrical signals – action potentials, are then propagated to other locations in the central nervous system. So both the brain and your computer transducer signals and do things with them. One could call both processes “perception”, though the actual mechanisms in your pc and your brain are functionally different, and it is a bit misleading to describe them both as perceptual mechanisms.

A related question is whether computers could have perceptions, that is, whether we could build computers which transduce external stimuli in the same way our brains do. This question is harder to answer, and it’s one widely debated in the philosophy of mind and cognitive science. Part of the reason this is such a difficult question to answer is hinted at in your question. Our perceptual systems begin with external physical stimuli, but we wind up with “thoughts and emotions.” So to build a computer which takes in such stimuli and stores or outputs thoughts and emotions would require that we not only have a functional account of the mechanisms by which we receive such stimuli and begin to transduce and store it, but a full account of what the mind/brain does with such information in order to bring about the rich experiential life we enjoy.

Yeah, these are the kinds of questions that lead many of us to "Argggh!" They're also the kind of questions that I approach with a great deal of trepidation because they are knottier than knotty. So, please understand that what I say here by the nature of this kind of exposition will be very rough and overly simplistic. You'll also probably find more than a few of my colleauges to disagree. But anyway, let's barrel right on with it.

I don't think you can be absolutely sure that what you see is what's "real"--though you really ought to take some time to parse out what you mean by that word because it's LOADED. I take it that you mean by "real" something like what's out there independently of us. In a sense, actually, my best shot is that what you or we see isn't exactly real in that sense. Do remember that old Aristotelian question, "When a tree falls in the forest and there's no one around to listen, does it make a sound?" Well . . . get ready . . . almost yes, but no. No in the way that it's not precisely right even to talk about "trees" and "forests" existing independently of us. Before you call for an ambulance to pick me up, what I mean by that crazy sentence is that what we experience is a kind of product of a number of factors, roughly our perceptual faculties and what seems to exist independently of us and interacts with them. The sound of a tree falling, for example, is the product of (1) our sense of hearing and (2) something like sound waves. Without either of these factors there's no sound. (If you think about it, this is actually obvious. Just ask any deaf person, or go into a silent room.) We contribute some of what goes into experience, and the external stuff contributes some of it. That goes for all the other dimensions of our experience of a tree falling or just a tree. Since in this sense there is no "sound" without the hearing of sound, then it really isn't meaningful to ask whether the sound we hear is the same as the sound that's out there. You see, there is no sound out there. Sound, like every other perceptual experience, exists in the relationship the relationship between us and what's not us. (Actually, I shouldn't even say "us"; but let's just let that slide.) No objects of experience strictly speaking exist out there. Now, it doesn't follow from this that nothing exists beyond us. I think there are pretty convincing, if not absolutely convincing, reasons to think so--at least I'm convinced. The shorthand way I'd put it is that the world we experience is external reality as it appears to us through its interactions with us. (And we are what we experience of us in the course of that interaction--there, I've said it.)

About your eye, I'd say you interpret what you see as a scratch, and your interpretation works better than others. So, go with it.

About whether we experience reality the way it "should" be experienced. I don't think there's any way reality "should be perceived". It just is perceived, and we make the best of it we can.

About "proving" the distance between your hands, I'm not sure what you mean. Once you've accepted hands and distance as meaningful, once you're in that relationship, you pick up (or have someone else pick up) a measuring tape and measure.

About seeing three dimensinal pictures at the movies, I'd say you see two-dimensional pictures that you full well know are two-dimensional and interpret them or imagine them as representations of three-dimensional things. You don't really think of them as three-dimensional; otherwise you'd duck when someone shot towards the screen or a robot exploded, or something.