There are different sorts of materialism about the mind, among them eliminative materialism, identity-materialism, and functionalism. There is also mysterian materialism. Here is a little speech by a mysterian materialist:
Look, we are just complex physical systems, and as such wholly understandable in natural-scientific terms, if not now in full, then in the future. And yet we think and are conscious. Therefore, we are wholly material beings who think and are conscious. We cannot understand how this is possible. But it is actual, hence possible, whether or not we understand or even can understand how it is possible. It's a mystery, but true nonetheless.
What motivates this mysterian view? There is first of all the deep conviction shared by many today that there is exactly one world, this physical world, that we are parts of it, that nothing in us is not part of it, and that it and us are wholly understandable in terms of the natural sciences. This naturalist conviction implies that there is nothing special about us, that we are continuous with the rest of nature. We are nothing special in that we have no higher origin or destiny. We are mortal, like everything else that lives, and anything (conscience, consciousness, ability to reason, sensus divinitatis, etc.) that suggests otherwise is susceptible of a wholly naturalistic explanation. Part of why people embrace the naturalist conviction is that it puts paid to central tenets of old-time religion: God, the soul, post-mortem rewards and punishments, the libertarian freedom of the will, man's being an image and likeness of God, etc. So hostility to religion is certainly, for some, part of the psychological (if not logical) motivation for the acceptance of the naturalist conviction.
Now take the naturalist conviction and conjoin it to the intellectually honest admission that we have no idea at all how it is so much as possible for a wholly material being to think and enjoy conscious states. The conjunction of the Conviction and the Admission generates a mysterian position according to which one affirms as true a proposition that one cannot understand as possibly true, namely, the proposition that we are wholly material beings susceptible of exhaustive natural-scientific explanation who nonetheless think, feel, love, make and feel subject to moral demands, etc.
This mysterianism is an epistemological position according to which our very make-up makes it impossible for us ever to understand how it is possible for us to think and be conscious. The claim is not that thought and consciousness are mysterious because they are non-natural phenomena; the claim is that they are wholly natural but not understandable by us.
Well, this mysterianism is certainly to be preferred to an eliminativism which argues from the unintellibility of a material thing's thinking to the nonexistence of its thinking. But eliminativism is a lunatic position best left to the exceedingly intelligent lunatics who dreamt it up.
The mysterian position cannot be so readily dismissed. But surely there is something very strange about maintaining that there are true mysteries. If a proposition either is or entails a broadly-logical contradiction, then I wouldn't know what I had before my mind if I had such a proposition before my mind. And if I didn't know exactly which proposition I had before my mind, I wouldn't know exactly which proposition I was claiming was both true and mysterious.
Before I can take a position with respect to a proposition I must know what the hell that proposition is.
I count four positions or attitudes one can take toward a proposition: accept as true, reject as false, suspend judgment as to truth-value, practice epoché , ἐποχή. Pithier still: Accept, Reject, Suspend, Withdraw. The first three are self-explanatory. By Withdraw I mean: take no position on whether or not there is even a proposition (ein Gedanke, a complete thought) before one's mind. (The notion is derived via Benson Mates from Sextus Empiricus.) Withdrawal goes farther than Suspension. To suspend is to refuse to accept or reject a well-defined proposition while accepting that there is such a proposition before one's mind. In the state of Withdrawal I take no position on whether or not there is a well-defined proposition before my mind.
Example. A Trinitarian says, 'There is exactly one God in three divine persons.' Studying the doctrine I come to the conclusion that I can attach no definite sense to it on the ground that it seems to me to entail one or more logical contradictions. That is not a case of rejection or of suspension; it is a case of epoché. I 'bracket' (to borrow a term now from Husserl) two questions: the question as to truth-value, and the more fundamental question as to whether or not there is even a proposition (a unified, coherent, sense-structure) before my mind as opposed to an incoherent, un-unified bunch of word-senses.
Suppose you say to me, "Snow is white and snow is not white." Being the charitable fellow that I am known to be, I would not churlishly jump to impute to you the assertion of a contradiction. I would take you to be using a contradictory form of words to express a non-contradictory proposition, perhaps, the proposition that snow is white where I didn't relieve myself, but not white where I did. Or something like that. The time-honored method of showing an apparent contradiction to be merely apparent is by making a distinction in respect of time, or respect, or word sense.
But if someone insists that he means literally that snow is white and snow is not white where there is no distinction in respect of time, respect, or sense of the word 'white,' then I wouldn't know what the content of the assertion was. I wouldn't know which proposition my interlocutor was trying get across to me. For if my interlocutor was otherwise rational, the principle of charity would forbid me from imputing a contradiction to him. I would have to practice withdrawal.
And so it is with the mysterian materialist. He bids me accept propositions that as far as can tell are not propositions at all. A proposition is a sense, but the 'propositions' he bids me accept make no sense. For example, he wants me to accept that my present memories of Boston are all identical to states of my brain. That makes no sense. Memory states are intentional states: they have content. No physical state has content. So no intentional state could be a physical state. The very idea is unintelligible. Where there are no thoughts one can always mouth words. So one can mouth the words, 'Memories are in the head' or 'Thoughts are literally brain states.' But one cannot attach a noncontradictory thought to the words.
No doubt there is an illusion of sense. There is nothing syntactically wrong with 'Thoughts are brain states' or 'Sensory qualia are physical features of the brain.' And the individual words have meaning. What's more, the words taken together seem to convey a coherent thought in the way in which 'Quadruplicity drinks procrastination' does not seem to convey a coherent thought. But when the meaning is made explicit, the unintelligibility becomes manifest.
My thesis is that the mysterian thesis that these unintelligible claims are true but mysterious in that they cannot be understood by us to be so much as possibly true, is itself unintelligible. For again, what is the identity of the proposition that I am supposed toaccept as both true and mysterious?
Mysterianism is the conjunction of the naturalist conviction and the intellectually honest admission that no one has any idea of how to account for consciousness in natural-scientific terms. Given that mysterianism is untenable for the reason I adduced, the reasonable thing to do is to jettison the naturalist conviction which, after all, is merely a conviction, a deep-seated belief that is just happening to to be getting a lot of play these days.
Here is a brief explanation of mysterianism with some references.
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