Proof of the Reducibility of Some Qualia
Here is a proof that some qualia are reducible. If the very notion of this is so disgusting that you are dissuaded from even looking at the proof, go right to the explanation after the proof, which accounts for (and reconciles) your sentiment.
From four completely intuitive premises, we derive a contradiction.
P1. An experience is not reducible.
P2. The essence of an irreducible event is no different from the event itself; something irreducible has no accidental properties.
P3. Where there can be told a difference, there is non-identity.
P4. My first experience tasting saltiness is different than my second experience tasting saltiness (in fact it was much saltier, much more intense).
1. An experience cannot be reduced to its essence combined with its accidental properties. (from P1 and P2)
2. If two irreducible events differ, they can have no similarities. (from P2 & P3)
3. The tasting experiences differ only in essence, they have no accidental properties of which they could differ. (from P2 & P4)
4. The tasting experiences have no similarities. (from 2 & 3)
5. The two experiences are similar in that they are both are salty. (from P4)
Since P2 and P3 are necessary and P4 is a fact, P1 must be the false the premise that allows us to derive a contradiction, 4 & 5.
As an aside, this topic seems to frequently include an equivocation of quantifiability, where quantifiability can be relative or absolute. While it is clear to most that qualities cannot be quantified absolutely, we can certainly quantify qualities relatively, such as in saying that one dish is sweeter than another, or sweeter than two other dishes put together. Saying that a third dish is as sweet as the first two dishes put together quantifies the sweetness of the third dish, even if in relative sense. The arbitrariness of these units of quality should not deter us from a belief in them anymore than the arbitrariness of abstract numerical units should dissuade us from a belief in them (using integer variables, x=a+b is relative quantification of integers). The personal nature of using a qualitative experience to relatively quantify another experience does not invalidate the belief that that qualitative experience is a unit anymore than the personal nature of choosing an arbitrary number to relatively quantify another number does not invalidate the belief that numbers are units. What principle may be given to justify the correctness of saying that 2 is a permutation of the number 1 over the numbers of 1.01, e, the square root of -1, 5, or the like? None, and yet these things are quantities. Consider that there is no principle that we should say one dish is saltier than the other rather than saying the other dish is less salty than the one dish. So, we should not be deterred in thinking that a lack of principle for stating one experience in terms of another should not deter us from saying that qualities are relative quantities. This explains why "reducibility of qualia" is so offensive to some - they assume it to mean "reducibility of qualia to numbers" rather than "reducibility of qualia to other qualia".
From four completely intuitive premises, we derive a contradiction.
P1. An experience is not reducible.
P2. The essence of an irreducible event is no different from the event itself; something irreducible has no accidental properties.
P3. Where there can be told a difference, there is non-identity.
P4. My first experience tasting saltiness is different than my second experience tasting saltiness (in fact it was much saltier, much more intense).
1. An experience cannot be reduced to its essence combined with its accidental properties. (from P1 and P2)
2. If two irreducible events differ, they can have no similarities. (from P2 & P3)
3. The tasting experiences differ only in essence, they have no accidental properties of which they could differ. (from P2 & P4)
4. The tasting experiences have no similarities. (from 2 & 3)
5. The two experiences are similar in that they are both are salty. (from P4)
Since P2 and P3 are necessary and P4 is a fact, P1 must be the false the premise that allows us to derive a contradiction, 4 & 5.
As an aside, this topic seems to frequently include an equivocation of quantifiability, where quantifiability can be relative or absolute. While it is clear to most that qualities cannot be quantified absolutely, we can certainly quantify qualities relatively, such as in saying that one dish is sweeter than another, or sweeter than two other dishes put together. Saying that a third dish is as sweet as the first two dishes put together quantifies the sweetness of the third dish, even if in relative sense. The arbitrariness of these units of quality should not deter us from a belief in them anymore than the arbitrariness of abstract numerical units should dissuade us from a belief in them (using integer variables, x=a+b is relative quantification of integers). The personal nature of using a qualitative experience to relatively quantify another experience does not invalidate the belief that that qualitative experience is a unit anymore than the personal nature of choosing an arbitrary number to relatively quantify another number does not invalidate the belief that numbers are units. What principle may be given to justify the correctness of saying that 2 is a permutation of the number 1 over the numbers of 1.01, e, the square root of -1, 5, or the like? None, and yet these things are quantities. Consider that there is no principle that we should say one dish is saltier than the other rather than saying the other dish is less salty than the one dish. So, we should not be deterred in thinking that a lack of principle for stating one experience in terms of another should not deter us from saying that qualities are relative quantities. This explains why "reducibility of qualia" is so offensive to some - they assume it to mean "reducibility of qualia to numbers" rather than "reducibility of qualia to other qualia".