An Immaterial Philosophy of Mind

Metaphysics & Epistemology
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But are such judgments, like the nature of abstractions generally, dependent on or derived from physical states? Put bluntly, if number is real but not material, then materialism is false, as it says that only material things and states are real. This is really a very long–standing debate in philosophy of mathematics: at least some mathematicians are platonist. Mathematical platonism holds that the natural numbers are real independently of the individual act of thought. (See What is Math? Smithsonian Institute Magazine.)

But it’s not a valid analogy. Remember that the subject of discussion is the nature of mind. The materialist contention is the mind can be reduced to or explained in terms of physical states of the brain. Put crudely (but then, it is a crude theory), it’s that ‘brain=mind’. So what the OP’s argument is saying, is that ‘=’ is itself not a physical state but a judgement about constitution or meaning. Furthermore, that any attempt to equate mental states or neurological data with symbolic meaning must itself rely on the very judgments which it is trying to explain. That’s where the materialist argument is circular.

1 Like
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Suppose we have a language M which has terms for mental states and their mental relations, and a language B which has terms for brain states and their relations. I offer a complete translation table, something like “x in B = y in M”.

Your objection is that “=” is itself part of M.

Thus, not only do I have to use M to define the translation table, the entries in the table cannot express B-type facts, because B cannot express “=”-relations, since “=” is not part of B.

That “because” deserves some scrutiny, but where this leaves us is that the theory cannot be expressed in B but only in M.

There are still some issues here, but I don’t think it’s want you want anyway. You want to say something like the identity of a brain state and a mental state cannot be a physical fact, but only a mental or a rational fact. It cannot be part of the natural world that mental states are brain states.

But now the question is whether it’s possible for any language or any theory to express any fact we would think of as a physical fact. “Snow is a crystalline form of water.” Hmmmm. Surely we’re trying to express something about the natural world here, but to do so we have to rely on not just words but concepts that look suspiciously non-natural—“is”, “form”, “of”.

It’s unclear to me how to proceed from here. Does your argument show something vaguely Kantian about the necessity of conceptions to cognition? Does it turn out no physical theory of the natural world is expressible at all?

On the other hand, your argument might be just another version of the irreducibility argument, which most people already accept, not just for the mental, but also for the biological, the sociological, the meteorological, …

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Yes - I accept that all of those connotations are implied by the argument in the OP. Bear in mind, the focus of the OP is narrow: it has in mind what came to be called ‘central state materialism’ which was the attitude of D M Armstrong (and several others of his ilk, all of them Australian) during the mid 20th Century. I recognise in the original post that supervenience arguments for materialism are a different matter. This argument is specifically about the identity of brain with mind. And so I’m pleased that you’ve actually recognised the subtleties involved in ‘is’ statements, of the kind that the original post discusses.

Now, I think that the basic principles can be extended - I have in mind something along the lines of the ‘argument from reason’, although not directed in any sense towards Christian apologetics as it originally was. There are also resonances with Husserl’s critique of naturalism. But the basic point is the absence of insight in materialist philosophy into the epistemological implications of its own principles.

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Your description of these things being “real” leaves a lot to the imagination:

This vague description is what I was saying is consistent with materialism.

No one would suggest numbers are physical objects. But we CAN recognize a certain quality that groups of objects have that is consistent with the characteristics we associate with numbers. Arguably, we’re recognizing a very real aspect of these groups.

If this is inconsistent with your understanding of materialism, you can either adjust your understanding of materialism or coin a new name for a theory that includes this.

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It is not vague. Materialism is the thesis that everything can be explained in terms of, or reduced to, material or energetic entities. Numbers are real, but cannot be thus reduced. It is not my understanding that is vague.

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The sun and the distance from the earth could be a greater seed. Seeds contingent on seeds. It may only be the perspective given by our own conscious entity that appears to recognise one teleology over another.

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It’s vague because you haven’t defined what means to be “real”.

A group of 5 marbles exhibits a property, one that a group of 5 apples also exhibits. There is something real about this property: it is actually present in the groups of objects. IOW it exists. You choose to define such property as non-physical, and then pronounce materialism- thus defined- as falsified. But I consider the properties of objects to be a real aspect of the object- and therefore consistent with materialism. Your definition is a strawman.

Your strawman materialism is falsified. Fine. But my materialism is not.

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The idea that energy is a material thing is a mistake which gives materialism traction. Energy is a concept with a mathematical formulation.

How about energy? It’s not the property of an object, but something produced from applying a mathematical formula to the values given from the measurements of a number of properties, mass and velocity for example.

How could you justify calling something like this “material”? Take the body mass index of a human being, as another example, it’s produced from applying a formula to the weight and height of an individual. Do you think that a person’s body mass index has material existence?

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As a matter of interest, had you heard the expression ‘mathematical platonism’ prior to this discussion?

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Yes.This section of the SEP article on Philosophy of Mathematics addresses it: Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)

Here’s my view. We can interpret aspects of the world in a way that leads to mathematics: abstracting observations, organizing these abstractions, and developing coherent theories (in the philosophical sense of theory) which we call a mathematical system. Some, but not all, mathematical systems reflect aspects of the world (e.g. peano arithmetic, calculus). Not so with the groups, rings, and fields of abstract algebra.

This doesn’t imply some direct correspondence from abstraction to aspect of the world (nor does it preclude it). But it does imply a coherent framing of these aspects of the world. So “1+1=2” isn’t residing in a 3rd realm. Rather, it’s just a semantic description of an aspect the world that we perceive and make sense of- formalizing into a coherent theory. The aspect of the world is “real”, but it’s not “out there”; rather, it’s in there: within things.

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Thanks, I can see you have considered the question deeply. I note the scare quotes around “real”. And indeed I think that is where the question lies - real in what sense? I say, not just in a manner of speaking or derivatively, but actually real. If it were simply semantics - just a way of ordering signs - then it can’t account for the fact that mathematical reasoning underlies the progress in physics and many other sciences since the 17th century. In other words, mathematics enables discovery. And these are discoveries which in turn enable inventions (including the one you’re looking at.) This is the fact that inspired Eugene Wigner’s essay on the unreasonable effectiveness of mathematics in the natural sciences (one of the first articles I encountered on joining philosophy forums!)

As regards the ‘third realm’. I think there is such a realm, but that it’s important not to reify it as any kind of place or location. After all, the expression ‘the domain of natural numbers’ is unexceptionable, but again, it doesn’t imply an actual place. Why? Because mathematical facts are independent of space and time. Which is why empiricism has such a hard time accepting their reality!

I notice many of the arguments in both the article you cite, and a companion article Platonism in the Philosophy of Mathematics are intended to defuse the claim that we have rational insight into non–empirical facts. An article on the so-called ‘indispensability theory of mathematics’ says that:

Some philosophers, called rationalists, claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. But, the rationalist’s claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.

Perish the thought! Should that prove to be so, then Socrates was right all along!

(P.S. - you might also be interested in Frege on Knowing the Third Realm, Tyler Burge (pdf file)).

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In fact, progress depends on the ability to communicate through signs, generally written ones. The question is how a child learns so much from such simple signs. They learn to handle and manipulate them. What can a child derive from signs beyond their manipulation? There are certainly certain intuitive concepts to which symbols correspond, such as natural numbers, but there is also a manipulation of signs that cannot be assumed or found in such intuition.

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Can’t we put the description of the life of a star in intentional, teleological terms - as seeking to maximise entropy, or to produce as many heavy elements as it can? So isn’t a teleological account just another way of saying much the same thing as a physical description?

I don’t see that you have shown that the teleological account of a cell’s function adds something that is irreducible to the physical account.

So I don’t see that this change of track works for you.

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All throughout the Platonic corpus, there are reflections on the idea that these abilities are something we’re born with. As noted before, Socrates (and presumably Plato) ascribe this to the idea that the soul had such knowledge ‘before birth’. I don’t know if we need to accept that mythological account to agree that humans indeed possess an innate capacity for language acquisition. Besides, Noam Chomsky has been quite open about the fact that his ‘nativist’ account of language acquisition presupposes innate cognitive structures that are not derived from experience. The poverty of the stimulus argument — that children acquire grammatical competence far exceeding what their linguistic exposure could account for — is structurally similar to ‘the argument from equals’. The capacity is innate. Experience triggers it but doesn’t generate it.

But the point about all living systems, as Schrödinger pointed out, is that they are negentropic. All of the ‘energy gradients’ of stars are dictated by, and explicable in terms of, the laws of physics. But even the simplest of life-forms seem to defy entropy in this respect. They harness energy to increase their degree of order. So this is where the Aristotelian account still holds: that organisms possess an intrinsic drive to actualize and preserve themselves which is absent in the non-organic realm.

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I’m not sure whether innateness is a good answer to this question. It seems like an easy way out. There may well be a cognitive proto-structure, but it seems to me that this structure cannot account for the number of operations and manipulations carried out with mathematical symbols. I would say that, to a large extent, these manipulations and operations are learnt through school practice. In this sense, the written sign is essential, as it allows us to build on what has already been achieved. I also don’t know how ‘the argument of equals’ might fit in here. Perhaps equality belongs to a proto-cognitive structure, but this still seems like a vague intuition. An intuition which, it seems to me, is solidified by the recurrence of the written sign. Here we return to a point I discussed earlier: what Husserl calls written ‘sedimentation’ or ‘historic idealization’ would function as a necessary supplement to a deficiency inherent in the vague intuition of equality.

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Naturalism and empiricism hate the idea of innateness. That’s why so many people take delight in pointing out the cleverness of Caledonian crows — ‘See! We’re not so special after all!’ The ancient idea of rationality as the faculty which distinguishes man from beast is politically incorrect. But have a look at the sad, sad story of Nim Chimpsky.

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Perhaps. But it’s just so simplistic. It’s like saying we’re born with all mathematical knowledge stored in our heads (or in our souls, whatever) and that we just need to unlock it.

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Seems…

It’s just bad physics.

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It’s simplistic if you put it like that. But it’s really not so simple. The meaning of ‘education’ is derived from the latin ‘educare’ , to bring up, rear, draw out, and human education typically occupies about 18 years. Also notice there is huge variability amongst individuals in regard to capacity to learn and understand maths. I don’t hold to a literal reading of Plato, in which the ‘slave boy’ is said to already possess the knowledge of maths that Socrates draws out of him through dialectic, but it seems impossible to deny that humans have at least some innate ability to learn such things, which other animals certainly lack.

Other than that, I’m not quite sure what you’re arguing for, or against.

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I am arguing against the idea that ideality can be established once and for all through a single subjective act. What I mean is that ideality is constituted through history.