Two experiences (e.g., of seeing a stop sign) would be similar. That’s what makes us different from Funes the Memorious: we can selectively forget, and thereby we can selectively abstract what two non-identical experiences have in common, the underlying invariant across all instances — and as a consequence we can categorise, name, and, in general, learn and talk. (If we were stuck in Funes’s world of infinitely faithful rote memory, every instant would be unique and incommensurable with every other except perhaps along a fretless continuum of degrees of similarity (that we would be powerless to do anything about or with).
Harnad, S. (2005) To Cognize is to Categorize: Cognition is Categorization, in Lefebvre, C. and Cohen, H., Eds. Handbook of Categorization. Elsevier.
Real human beings hardly notice and quickly forget the details of experience, and especially the irrelevant details. (Relevance depends on our purposes, and on consequences: like it or not, we have to learn what features distinguish toxic and edible mushrooms, if we need to eat mushrooms to live.)
So selective perceiving and remembering is going on, and must. (That is why there could never be a Funes the Memorious, except perhaps on a passive life-support system — and even then he could never think or talk: he could just feel!)
So, yes, there is a lot more than merely the passive recording of successive, unique, incommensurable instants, all grading continuously into one another. But we can’t take credit for it, because all that selectivity — even the active, consciously learnt part — is basically done for you by brain mechanisms for category learning and detection that we are only beginning to understand and that our armchair phenomenology simply takes for granted without even realising it.
Feelings would be unanalyzable wholistic chunks if we didn’t have a lot of innate and learned selectivity and abstraction going on. But we do.
But let’s not lose sight of the point at issue: My belief P that the distance from (x1,y1) to (x2,y2) = SQRT [(x2-x1)**2 + (y2-y1)**2] (i.e., Pythagoras, your example), or, to take a simpler case, my belief Q that a mouse is smaller-than-a-breadbox.
First, does one specific instance of my believing P (understanding P and feeling that P is true) differ from one specific instance of my believing Q (feeling that Q is true)? Yes, of course, just as one instance of tasting chocolate ice-cream differs from one instance of tasting vanilla ice-cream. And what about two instance of believing P? They differ in the same sense that two instances of eating chocolate ice-cream differ.
Do they have something in common? Sure, all four feelings do: P, Q, chocolate and vanilla. In fact, every feeling has something in common with every other feeling — and something different too. We are tempted to say, however, that some feelings have more in common than others, and that is true, but we should also ask how and why, rather than take it for granted.
(The pertinent exercise here is to remind ourselves of the diagonal argument in Watanabe’s “Ugly Duckling Theorem“: The only reason the 5 small yellow ducklings look more like one another than like the large gray gosling is that our perceptual and computational systems “privilege” differences in size and colour (i.e., weight them differentially in feeling space: Watanabe calls this a “bias.”) If our brains instead coded all differences on a par — spatial position, being closer to duckling X than Y, having the same number of feathers — including, by the way, subtle “higher-order” features such as not-having an even number of feathers, or having the same number of feathers as the middle duckling has epidermal cells, etc. — if all classifiable differences were felt to be on a par, then all ducklings would indeed be infinitely similar and infinitely different, and incommensurable.)
In reality, however, the reason everything does not feel infinitely similar/different to/from everything else is because features are not coded on a par (we are not Funes the Memorious). Some things look, or come to look, more alike than others, some features “pop out,” etc., and this is what allows us to categorize our experiences instead of being awash in an intractable, unnavigable flux.
But none of this resolves the zombie (feeling/function) problem, because our brains could just as well have privileged and abstracted certain useful traits over others in our adaptive interactions with the world without ever having bothered to make any of it — whether tasting an ice-cream or judging whether or not it is true that a mouse is bigger-than-a-bread-box — feel ike anything at all! The feeling, “veridical though it may be” is functionally supererogatory: As always, only the doing capacity is functionally needed, or causally efficacious. The feeling is just a superfluous frill.
(And the mind/body problem is and always was no more nor less than the “feeling/function” problem: why/how are some functions felt functions? That is also the “zombie” problem: Not imagining whether there could be zombies, but explaining how and why we are *not* zombies — without resorting to telekinesis.)
Moreover, I’m inclined to say that, qua feeling, unconnected with differential action, all feelings are incommensurable with the objects of which they are meant to be reflections or representations. At best, they are correlated with them (in that I feel chocolate when I eat chocolate and not vanilla). But I am sure there is a higher-order version of the inverted-spectrum problem that can be resurrected for all of feeling-space (qualia space), according to which no feeling really “resembles” the real-world property it is meant to be a feeling of (or caused by): it only feels as if it is. (Feeling is just seeming.)
This is probably a variant of Wittgenstein’s Private Language Argument: What could it mean to err in one’s subjective feelings? One can act erroneously; one can speak erroneously (saying something is True when it is False, or when others disagree). But what does it mean to say that chocolate does not really taste like chocolate (Dan Dennett’s Mr. Chase and Mr. Sanborn come to mind)? or that THIS feels more like what it really is than THAT? Again, we seem to be back into the incorrigible circle of “feels-as-if-it-feels”: Descartes is right that I cannot doubt that I am feeling what I am feeling when I feel it; but the incorrigibility of my feeling that I have a tooth-ache — even when I have no tooth, and when neurology says I am experiencing referred pain from an ear infection — does not imply anything about any commensurability between feelings and whatever they might be caused by or correlated with or representative of in the real world.
For present purposes, not only does believing that P feel different form believing that Q, but believing that P this time feels different from believing that Q the next time. Thanks to our Watanabe “biases,” we are not Funes the Memorious; we can detect the recurrent invariants, so we can feel that although my P-feeling this time is not identical to my P-feeling that time, they are nevertheless both P-feelings rather than Q-feelings. In other words, yes, we can categorize beliefs just as we can categorize concrete objects.
Yes, feelings are unique, hence different, every time, but no, that doesn’t mean we cannot ignore the differences and selectively categorize and identify them anyway.
But when I challenge the idea that there is nothing that it feels-like to believe that P, I am not trying to suggest that it follows that we cannot abstract and categorize beliefs, just as we abstract and categorize perceived objects. I am only trying to point out that our “cognitive” activity is just as felt as our “perceptual” activity, and that this fact — the felt nature of these functions — is equally problematic in both cases.
It is not possible to bracket the problem of cognition (or intentionality, or belief, or whatever you want to call it) and treat it separately as unproblematic mental territory, zombie-immune. Either it is just as problematic as tasting ice-cream, or it’s not mental (and merely functional, i.e., zombic). Feeling suffuses all of mental life, perceptual and “cognitive”; it is what makes it mental, and problematic. The rest is just unproblematic function: doings rather than feelings.
Let’s compare “twoness” as a perceptual experience (a direct perception of numerosity) with “2+2=4” as a piece of propositional thought. I say both “there’s 2 (things)” and “2+2=4” are thoughts we can have, that feel-like something to have, and mean, and experience (all those are the same thing).
They do feel different from instance to instance, but we can overcome the Borgesian uniqueness with a Watanabean bias, selectively abstracting some “aspects” of the feeling over others. (I doubt, though, that the exercise actually takes place at the felt level: I think our brains do the selection/abstraction for us, then hand the outcome to us on a platter, garnished with the right feeling, and give us a free co-authorship, as if it had been our discerning tastes that had generated the dish…)
I am not adept at phenomenology, so I can’t really introspect and describe what’s happening in my head very well, but I suspect that analysis is unconscious (zombic) and our feelings are after-the-fact, always gerrymandered to square with the computations (or other dynamics) that they did not themselves engender (or constitute: how/why would feelings be computations?)
If tasting chocolate, and recognizing its chocolate while at the same time recognizing that tasting the same chocolate on a number of feelings is always a different feeling too, then exactly the same goes for believing that “the cat is on the mat.” “The cat is on the mat” is a proposition, P. It feels like something to understand what P means (including, no doubt, knowing what a cat is and a mat is, so no doubt images are involved). To believe P is to have the feeling of knowing what P (and its components) means and are, and to feel that P is true. (It feels different to feel that P is false. And, yes, there is something all true propositions have in common, but there is also a lot about them that is different; and different to is believing that P on different occasions.)
The zombie problem, meanwhile, just perdures: How and why does it feel like something to believe that P? Why is it not enough simply to have the datum and just act accordingly, zombily?