This is part of the Hard Problem of Consciousness: why is there any such thing and how does it work? It is Hard because we cannot even see what a solution would be. Even if we discovered patterns of neural activity or anything else that reliably and in great detail matched up with the experience, it seems that that still wouldn't tell us why there is such a thing as that experience, and would not suggest any test we could apply to a synthetic imitation of the patterns.
(7) If we met an alien life-form, how could we tell if it was suffering?
The world is already full of alien life-forms -- that is, life-forms radically different from yourself. How do you decide, and how should you decide, which of the following suffers? A human being with toothache; a dog that has been hit by a car; a mouse bred to grow cancers; a wasp infected by a fungus that is eating up its whole body and sprouting from its surface; a caterpillar paralysed and being eaten alive by the larvae of that wasp; a jellyfish stranded on the beach that a playful child has thrust its spade into; a fish dying from the sting of a jellyfish; a tree with the sort of burr that wood carvers prize for its ornamental patterns; parched grass in a drought. And, for that matter, a cliff face that has collapsed in a great storm; tectonic plates grinding together; a meteor burning up in the atmosphere.
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I don't like the expression "carve reality at the joints", I think it's very vague and hard to verify if a concept carves it there or not. The best way I can imagine this is that you have lots of events or 'things' in some description space and you can notice some clusterings, and you pick those clusters as concepts. But a lot depends on which subspace you choose and on what scale you're working... 'Good' may form a cluster or may not, I just don't even know how you could give evidence either way. It's unclear how you could formalize this in practice.
My thoughts on pleasure and the concept of good is that your problem is that you're trying to discover the sharp edges of these categories, whereas concepts don't work like that. Take a look at this LW post and this one from Slatestarcodex. From the second one, the concept of a behemah/dag exists because fishing and hunting exist.
Try to make it clearer what you're trying to ask. "What is pleasure really?" is a useless question. You may ask "what is going on in my body when I feel pleasure?" or "how could I induce that state again?"
You seem to be looking for some mathematical description of the pattern of pleasure that would unify pleasure in humans and aliens with totally unknown properties (that may be based on fundamentally different chemistry or maybe instead of electomagnetism-based chemistry their processes work over the strong nuclear force or whatever). What do you really have in mind here? A formula, like a part of space giving off pulses at the rate of X and another part of space at 1 cm distance pulsating with rate Y?
You may just as well ask how we would detect alien life at all. And then I'd say "life" is a human concept, not a divine platonic object out there that you can go to and see what it really is. We even have edge cases here on Earth, like viruses or prions. But the importance of these sorts of questions disappears if you think about what you'd do with the answer. If it's "I just want to know how it really is, I can't imagine doing anything practical with the answer" then it's too vague to be answered.
I think we're still not seeing eye-to-eye on the possibility that valence, i.e., whatever pattern within conscious systems innately feels good, can be described crisply.
If it's clear a priori that it can't, then yes, this whole question is necessarily confused. But I see no argument to that effect, just an assertion. From your perspective, my question takes the form: "what's the thing that all dogs have in common?"- and you're trying to tell me it's misguided to look for some platonic 'essence of dogness'. Concepts don't work like that. I do get that, and I agree that most concepts are like that. But from my perspective, your assertion sounds like, "all concepts pertaining to this topic are necessarily vague, so it's no use trying to even hypothesize that a crisp mathematical relationship could exist." I.e., you're assuming your conclusion. Now, we can point to other contexts where rather crisp mathematical models do exist: electromagnetism, for instance. How do you know the concept of valence is more like 'dogness' than electromagnetism?
Ultimately, the details, or mathematics, behind any 'universal' or 'rigorous' theory of valence would depend on having a well-supported, formal theory of consciousness to start from. It's no use talking about patterns within conscious systems when we don't have a clear idea of what constitutes a conscious system. A quantitative approach to valence needs a clear ontology, which we don't have yet (Tononi's IIT is a good start, but hardly a final answer). But let's not mistake the difficulty in answering these questions with them being inherently unanswerable.
We can imagine someone making similar critiques a few centuries ago regarding whether electromagnetism was a sharply-defined concept, or whether understanding it matters. It turned out electromagnetism was a relatively sharply-defined concept: there was something to get, and getting it did matter. I suspect a similar relationship holds with valence in conscious systems. I'm not sure it does, but I think it's more reasonable to accept the possibility than not at this point.