Mind-Body Identity

tl;dr
Inferring from the reliable correlation of certain brain events, on the one hand, and certain mental events on the other, to their being identical, has long seemed an attractive solution to the mind-body problem. Its attraction lurks as a challenge to the Model's quite different solution. Kripke rejected the validity of such inferences on the basis of conclusions about the character of scientific identity claims in general, which follow from his semantic theory. Kripke's argument is unavailable in the Model. It turns out that the Model yields the same result more directly and modestly.
 
Two Insights
I have reviewed elsewhere two insights which the Model gives us about consciousness. The first was about how, if we can see our way through to its moral that our talk is invested with meaning and truth only in virtue of being used in interpersonal exchange (so, not through solitary reflection) , then what we imagine to be our thoughts about dreams and phenomenal experiences or qualia are sapped of all content. This first insight approached the Model, so to speak, from the outside, deferring the relevance of its specifics to more detailed investigation.
The second insight emerged considering the Model from the inside. It was noticed that it naturally lends itself to categorizing classes of sentences such as observation sentences or theory sentences. The noteworthy thought was that, without making any special assumptions about the speakers who people the Model, a class of sentences naturally arises within it which closely correlate to the sentences which exercise consciousness theorists (sentences immediately valued only by the speakers uttering them). Investigation of these sentences' semantics, in the Model's terms, leads directly to the conclusion that the key expressions figuring in them have meaning at most in a highly limited, degenerate sense, deflating the problem of consciousness.
In both of these cases we reached the conclusion that statements reporting dreams or so-called 'qualia' are true at best in a degenerate, anodyne sense (this was acknowledged to be counter-intuitive). But this is possibly not the end of the story.
The Challenge
Let's consider again sentences about dreams or experiencing sensations:
S1: I dreamt there was an orange platypus on my desk.
S2: I feel an ache in one of my molars.
Nothing in either of those insights above was meant to cast doubt on the possibility that natural science might one day find systematic correlations between the occurence of unproblematic neural events, on one hand, and the people undergoing them reporting specific types of dreams or having certain sensations such as these, on the other. Let's take inspiration from Kripke and suppose that scientific study finds that consistently, whenever a person feels a molar-ache, specific neurons of a certain type, we'll call them 'mc-fibres', are found to be actuated. If, now, a person reports the sensation of an ache in one of their molars but we find their mc-fibres are quiescent, do we not have grounds to say that what they said is false in a robust, non-degenerate sense? Wouldn't such a correlation -whose possibility, again, is not being doubted here- refute the model, on this point?
Let's step back. Scientific theorizing gives us, among other things, an understanding of what stuffs are made of. A familiar example is water:
P1: Water is H2O.
The thought we are considering here is whether, if scientific study were to find a correlation such as we just hypothesized, we'd be licensed to say something like,
P2: Molar aches (molar-ache 'qualia') are mc-fibre firings.
... and that we could then close up our laptops and go out for a pint, content in knowing that the problem of consciousness was definitively done and dusted.
Many of us will be apt to protest that matters are not so simple. Our objective here is to say precisely, why.
Kripke
In his Naming and Necessity, Saul Kripke spells out a theory of the meanings of proper names and in part also of what are called 'natural kind' terms, like 'water'. I won't go into the details here. The take-aways are first, that the theory implies that phenomenal experience terms like 'pain' (as we are understanding it in this context, referring to qualia), and terms like 'water', are importantly different in the natures of what they refer to, and that this would break the analogy and preclude the truth of P2. Secondly, the theory relies, by its own admission, on non-trivial assumptions about the 'essential' properties of things, making its claims less easily defensible than those of a theory which makes no such assumptions. Lastly, for my purposes, setting all of this aside, Kripke's theory is firmly rooted in traditional thinking with which the Model has no truck .
The Model
The Model assumes the 4-dimensional world to be fixed and opaque apart from the speakers who visit it. It then sets out to capture the parameters relevant to the valuation of a sentence by someone hearing it . These are found to be,
  • s: the sentence voiced - the sounds or ink-marks produced (the sentence *type*)
  • t: the time of utterance
  • x: the place of utterance
  • ξ: the point of focus of the hearer's attention
  • u: the utterer of the sentence
  • C: the context of utterance, being just the set of token sentences recently heard by the hearer
  • B: the set of token sentences hitherto appraised to be valuable by the hearer (the hearer's *beliefs*)
We can think of these parameters as determining a kind of input → output mapping or function. This value function, V, maps combinations of these parameters onto a 'yea' or 'nay' measure, which it's convenient to think of as ranging from 0 (flat 'No') to 1 (unqualified 'Yes'):
Vi: s, t, x, ξ, u, C, B → v
(where lower-case 'v' is that 0-1 output).
Distinctions
The value mapping/function immediately enables us to mark some distinctions. We may allow that the value of a sentence type, together with the time, position, focus, context, and utterer parameters, is mostly independent of B, or alternately, significantly dependent on it . If the value remains constant, regardless for the most part of what B happens to contain, we may call s an 'observation sentence'. Alternately, if the contents of B can change the valuation of s, then it is a 'theory sentence':
Observation sentence: s is an observation sentence just in case Vi(s, t, x, ξ, u, C, B) is the same mostly regardless of the contents of B.
Theory sentence: s is a theory sentence just in case Vi(s, t, x, ξ, u, C, B) depends importantly on the contents of B.
The distinction is real, but not sharp. Sentences can vary in their 'observationality' or 'theoreticality' - a point which will become relevant.
The last, related category of sentences is what I have called 'Q-sentences'. These are sentences which, first, are completely independent of B, and second, which are only ever valued by their utterer:
Q-sentence: s is a Q-sentence just in case Vi(s, t, x, ξ, u, C, B) is the same regardless of the contents of B, and only agent i values s differently than 0.5.
This category of sentences is meant to capture what we commonly think of as consciousness or qualia reports such as our s1 or s2 above. The idea is that nothing one might come to believe (or cease to believe) would change one's valuation of s1 or s2, and also that no-one would come to value either, apart from their experiencer having made the reports.
Meaning in the Model
Although it's not especially difficult, summarizing this topic methodically here would require an unwieldy digression - details are here. The relevant highlights are as follows. First, the primary bearers of truth in the model are token sentences (specific utterances of sentences), and the primary bearers of meaning, token words -or, more properly, token phrases. The meaning of a token phrase ph is just the set of all other token phrases with the same meaning as ph. And two phrases ph1 and ph2 having the same meaning is just a matter, very roughly, of every token sentence containing ph1 which is true at the moment of its utterance having a counterpart sentence just like it but with ph2 swapped-in for ph1, and vice-versa. For example, if a token of 'H2O' has the same meaning as 'water', then (roughly) for every token sentence containing 'H2O' which true at the moment in question, there is a counterpart sentence with 'water' swapped-in for 'H2O'.
Scientific claims
Our ultimate goal is to be able relevantly to distinguish statements like P1 from those like P2.
The first point to make is that identity claims like these imply that the terms used to make them have the same meaning: P1 tells us that 'water' means the same as 'H2O' (has the same reference, in the usual terminology). This is a direct consequence of how the model specifies the concept of samenesss of meaning.
The second, key point is that the effect of accepting -coming to believe- an identity claim such as this is to change the observationality of sentences in which the terms figure. Having in one's belief set B the sentence 'Water is H2O' and coming to value 'This is H2O' at a moment ought, and generally will, coincide with one's coming to value 'This is water' - even if one might not have valued this absent the other two beliefs . This is the substance of accepting the scientific theory.
Pains and Dreams
The problem for P2 is now apparent. The parallel point in the pain case would be that having P2 in one's belief set B and coming to believe 'There is a case of mc-fibre firing in my brain' at a moment ought, and generally will, coincide with one's coming to value S2 - even if one might not have valued S2 absent the other two beliefs. For this to be the case, one's valuation of S2 would have to be dependent on B. This straight-forwardly violates our hypothesis that S2 is a Q-sentence. The only solution would be to reject the valuability of P2.
The upshot
This is all well and good, but it's fair still to ask what we ought to say in the scenario we opened with, where scientific research uncovers a reliable correlation between neural events of a certain type (mc-fibre actuations) and reports of subjective qualia experiences (molar-aches), and we're confronted in the face of this with someone reporting a molar-ache with no mc-fibres active.
The moral in this case has mundane parallels. Consider the soccer player who, after a tackle, collapses to the ground, clutching his ankle, apparently in agony. Is he really in pain, or is this just theatrics to elicit a free kick? The whole mind-body problem we are contemplating here gets its grip with a certain understanding of what's at issue with questions like this. The conviction that pain experiences can be intelligibly factored into purely subjectively and objectively available dimensions is what philosophers the likes of Wittgenstein and Ryle inveighed against. It is the thought which animates the discomfort, here. What we potentially have in both cases (the molar and the writhing midfielder) is a conflict between what we can objectively see and our belief in the sincerity of the subject's reports. In both cases, the Model shows, it's a mistake to think that there's some objectively unavailable thing which decides the matter. There is only the subject's sincerity.