A Triple Aspect Theory

 

Does pain have a nature that goes beyond the feeling of pain? Pain has a phenomenology, which we experience internally, but does it have any other properties? Apparently it does, since it has a functional role—a way it functions in the mind and in relation to the body. This functional role forms part of what pain is. It is the same with other mental states such as desire: desire has an introspective appearance but it also functions in the organism’s psychophysical life. This is fairly uncontroversial. Much the same could be said about water and other natural kinds: they have a phenomenological appearance but they also have a causal role in the world—a set of causal powers. But is that all—does pain have no further intrinsic nature? Well, what does it have its functional role in virtue of? We might say in virtue of its phenomenology: it functions as it does because of the way it feels. But this is not plausible for the following two reasons: (a) the functional role of pain includes its bodily causes and effects, which are not themselves phenomenological, but physical; and (b) states of the brain are the de facto causal basis of these bodily phenomena. It is hard to see how phenomenology alone could give rise to physical functional role, and anyway the brain already has that job covered. So the natural assumption is that brain states are the basis of the functional role of pain, not the phenomenology of pain. But given that functional role is partly constitutive of pain, it follows that the necessary conditions of functional role are too: that is, states of the brain are also part of the nature of pain. So pain has three aspects (as do other mental states): its phenomenology, its functional role, and its neural correlate. In fact its neural correlate is not a correlate at all, any more than phenomenology and functional role are correlates of pain; it is part of what pain is. Pain isn’t just correlated with the feeling of pain, and it isn’t just correlated with its neural basis either—any more than water is just correlated with H2O. Water comprises three sorts of property: appearance properties, underlying molecular properties, and causal properties. But so does pain: its appearance to introspection, its functional role, and its neural basis. It is thus more than its first-person appearance as a feeling; it has another type of reality altogether. Pain is partly made of brain stuff.

            This is not some sort of generalized materialism (whatever that means); it is a point specifically about the nature of pain and other mental states. Because mental states have functional roles as part of their intrinsic nature they also have neural states as part of their nature, since the latter are the basis of the former. The best hypothesis is that the brain, as we now conceive it, forms part of the essence of the mind. Neurons are really part of the inner nature of mental states. This doesn’t mean for all conceivable types of mental states—Martians may not have neurons in their “brains” but some other type of unit. The point is just that terrestrial animals have minds whose nature includes the nature of their neural brains. The brain is not extrinsic to the mind, located somewhere outside of the mind. Brain states form the hidden machinery of the mind in much the way that molecular states form the hidden machinery of water, and for essentially the same reason, namely to ground the causal properties of the things in question. Mental natural kinds are partly constituted by neural natural kinds (here on earth)—but only partly because they also have a phenomenology. This is not some sort of reductionism about phenomenology, just the pedestrian (but important) point that the reality of the mind is not confined to its appearance to introspection—the brain is also an aspect of the mind (as molecules are an aspect of water). Maybe the phenomenological aspect is irreducible to anything else; maybe it is a complete mystery how anything can have both phenomenological and physical aspects; maybe the whole thing is pure magic: but still, mental states have a physical aspect existing in the brain. To repeat, not a correlate (as in traditional dualism) but an intrinsic dimension of their being: states of mind actually are partly composed of states of the brain physically described. There need be no necessary connection between phenomenology and a specific brain physiology; it is just that functioning mental states must needs be partly constituted by brain states of some sort. In the case of terrestrial animals brains have a certain sort of physiology, so the minds of these animals are partly constituted by that physiology. They don’t float above the brain, as “nomological danglers”, but are intimately enmeshed in the brain. Brain states don’t merely correlate with mental states; they constitute them. Just as H2O molecules are intrinsically involved when you wash your hands, so neurons are intrinsically involved when you think your thoughts or feel your pains (with the emphasis on “intrinsically”). They aren’t somehow removed, existing in another parallel place; they are right there in the thoughts or pains. They are as much in your mind as its phenomenology is. Perhaps we have a bias in favor of phenomenology because that is the way our minds strike us internally, but from a more objective perspective our minds are equally brain involving. The mind is just as steeped in the brain as it is steeped in its own subjectivity, i.e. its own introspective appearance. To put it bluntly, mental states have a neural architecture existing alongside their phenomenological character.  [1]

            I introduced the brain directly into pain via the functional role of pain, but once we have taken that step we can probably limit ourselves to just the brain combined with phenomenology; for the brain’s states can substitute for functional roles, given that they determine functional roles. It is not customary to say that water is H2O plus the causal role of H2O, since the former determines the latter; likewise we can say, not that pain is (partly) C-fiber firing plus the causal role of C-fiber firing, but just the C-fiber firing itself, since that determines causal role. Strictly speaking, we have a trio of aspects in both cases, but to all intents and purposes the physical basis makes mention of the causal-functional role redundant. So we could simplify and say that pain is constituted by the feeling of pain combined with the neural basis of pain, with causal role entailed by neural basis. The essential point is that the brain is just as integral to pain as its phenomenology is. This gives us a good deal of what the classic identity theory proposed (token or type), but not all. Mind and brain are inextricably intertwined, which is not to say identical.

 

  [1] This doesn’t solve the mind-body problem, nor is it intended to; it simply tells us how the problem is shaped.

 

 

Addition and the Origin of the Human Mind

 

How did language and arithmetic evolve?  [1] It is natural to ask about both in the same breath because of certain broad similarities between the two, particularly regarding discrete infinity, recursive rules, and computation. It would be nice if a common feature could be revealed allowing both to have the same origin. This would also provide an identical explanation for the learnability of arithmetic and language: the same basic cognitive mechanism is responsible for acquiring both sorts of competence, suitably specialized. The idea is that a single mutation, occurring around 200,000 years ago, provided the human brain with the cognitive machinery to grasp both the syntactic structure of language and the structure of arithmetic. No doubt this basic machinery got supplemented and shaped by the demands of externalization and other factors, but the core principle evolved in a single genetic mutation encoding an instruction for the construction of human brains. A new brain circuit implementing a cognitive trick or trait sufficed to permit the arrival of arithmetic and language. Thus the specifically human mind evolved as an upshot of this remarkable mutation; and the rest is history. The question is what this magical mutation might be. It needs to be both simple enough to evolve in the standard manner and yet rich enough to encompass the essence of the competences it permits. This is no doubt a daunting question, but presumably it has an answer—and we might as well set about trying to answer it. So: what structural, operational principle lies behind both arithmetic and language?

            The answer I will propose is: addition. We should first rid our minds of the usual connotations of that word, namely school sums written with the plus sign. The OED gives this for “add”: “join to or put with something else”. Notice this does not even mention numbers specifically; it is a very general operation of joining or combining different things. The mathematical sense of “add”, as we now understand it, is given by the OED as “put together (two or more numbers or amounts) to calculate their total value”. Roughly, then, addition is an operation of joining different things to form a whole—as in joining 3 and 5 to get 8. What is the analogue in the case of language? Conjunction, of course—in the narrow logician’s sense and in the wider grammatical sense. In the logician’s sense the word “and” works to conjoin two sentences to deliver a certain truth table: one sentence is added to another to produce a larger sentence true if and only of both conjoined sentences are true. The truth-value of the whole may be said to incorporate the truth-values of the conjoined sentences, rather as 8 incorporates 5 and 3. In the grammarian’s sense conjunction is not limited to “and” and its synonyms: the OED gives “a word used to connect clauses or sentences or to coordinate words in the same clause (e.g. and, if)”. So disjunction is a type of conjunction: it is a way to add sentences to other sentences. In fact, the concatenation operation is itself just another type of addition: in a sentence or phrase words are joined together by an operation of addition (“concatenate”: “link together in a chain or series”, OED). This operation has infinite potential. It is clearly part of our linguistic competence, even though it may be unconscious and automatic. But the same is true of arithmetical addition: our mathematical competence is likewise predicated on a grasp of numerical addition, which may also be unconscious and automatic. So there is a factor in common here: a principle of addition that takes us from one set of elements to another—a joining together of parts into wholes. The hypothesis, then, is that mastery of this operation lies behind the origins of our human mastery of language and arithmetic. In short, there was a mutation for addition (the cognitive competence) and this is what allowed arithmetic and language to get off the ground. It was like the development of an aerodynamic wing (in both biological evolution and aircraft technology).

            There cannot be much doubt that addition is fundamental to arithmetic. As the mathematics textbooks say, subtraction is just the inverse operation to addition (it “undoes” addition), and any subtraction formula can be rewritten as an addition formula. Multiplication and division calculations likewise involve addition. When someone grasps the concept of addition he or she grasps the concept of subtraction: what can be added can also be taken away. If you can add 3 to 5 to get 8, you can also subtract 3 from 8 to get 5: the two concepts are intertwined. Also, each number can be viewed as the continued addition of 1 to 1, or some other type of addition of integers. Isn’t arithmetic really the systematic study of addition? The natural number series is just one long addition; the successor function simply adds 1 to the preceding number taken as argument. There is no need to labor the point: addition is the lifeblood of arithmetic. In the case of language, we are not adding numbers, but we are adding another type of unit—what we call a word, a unit of meaning. This is not just a matter of uttering words in temporal sequence; it is a more abstract mental operation, often carried out entirely inside the mind. It is a compositional process analogous to numerical addition (which may involve adding amounts of stuff not merely numbers). The suggestion, then, is that this additive compositional process might be the foundation on which mature language and arithmetic are based. In order to evaluate this proposal I will now list the defining features of addition in the intended sense; it will emerge that addition has specific formal features that suit it to performing such a role. It is a more refined and structured operation that might at first appear: it is both rich and yet primordial—exactly what we need to solve the problem of origins for language and arithmetic.

            First, addition is infinitely productive: you can keep on doing it ad infinitum. You can keep on adding numbers to numbers to get further numbers, and you can keep on adding words to words to get more words. The word “and” by itself has infinite productivity: you can conjoin sentences and predicates to infinity, but you can also conjoin singular terms, as in “gin and tonic” or “strawberries and cream”. The concatenation function likewise has infinite range, as does our grasp of it (logically it is just like the function expressed by “plus” in arithmetic). In both cases addition operates over discrete entities, thus generating discrete infinities (as opposed to continuous magnitudes). It is no small matter to acquire a capacity to handle such an infinitely productive operation. Connectedly, addition is generative: it generates one thing from another. It isn’t passive or static but active and dynamic. Thus we have generative grammar and generative arithmetic—rules that produce something from something else. Third, addition is combinatorial in the sense that it brings things together to produce something new: it isn’t just a brute process of sequencing but the production of a new entity considered as a whole. Adding 5 and 3 produces the number 8, which is not just a sequence (ordered pair) consisting of 5 and 3. Likewise a sentence is a new whole derived by combining parts; it is not just a list of words but a new type of linguistic unit. So the agent of such construction must be able to grasp the whole that results from the operation of combination as a whole. It isn’t just setting elements side by side but combining them. Fourth, and consequently, addition is ampliative (Kant’s word) in the sense that it generates something not already present in what is added together; it produces not just arbitrary strings but organic unities (to use the old-fashioned term). New phrases and sentences are unities in their own right, just as numbers are: addition has the power to confer such unity on its outputs. Fifth, this ability is reflected in the creativity of addition: that is, mathematical and linguistic competences consist in a capacity to create brand new wholes, new unities. Even a simple conjunction (“grass is green and the sky is blue”) exhibits this kind of creativity—rather like the production of a number no one has ever thought of before. Addition is not merely “mechanical”: it involves breaking new ground, going where no man has gone before. It might even intersect with creation in the usual sense of exceptional human production—as in writing poetry or discovering a new type of number. Without the ability to “put things together” mentally human creativity in the usual sense would not be possible. It is actually quite a feat to add 5 and 3, and likewise a feat to produce even a simple sentence like “the sky is blue” (adding one word to another till we get the desired result). Sixth, and important, addition is hierarchical: you can add what has previously been added. You can add 3 to 5 and then add the resulting number to another number. The addition operation can be applied cyclically and recursively: this would include adding to the result of a subtraction in order to get a further number. Bracketing becomes necessary for depicting such computations. In the same way language allows for hierarchical structure: we can, for example, conjoin conjunctions (as well as disjunctions etc.). In this respect addition is like Chomsky’s Merge operation, which also applies to its own outputs in a hierarchical manner.  [2] Indeed Merge may be seen to incorporate Add, since it involves joining or combining elements to produce a new element: merging X and Y into Z is adding X and Y to get Z. In both operations we have the ability to apply the operation to its own outputs generated at a lower level. Seventh, addition has scope in the logical sense: there is always a question as to what the scope of the addition operation is supposed to be. It is like the scope of quantifiers: not every variable to the right of a quantifier is bound by it, just as not every number following a given one is automatically included within the addition operation. We have conventions, generally expressed by brackets, for indicating scope, and addition needs such conventions in order to avoid ambiguities. Addition is thus selective in its intended scope, not all-inclusive. Eighth, and worth emphasizing, addition is notably liberal in its domain of operation: you can add quite disparate things to each other; similarity is not required. Any number can be added to any number (not just even numbers to even numbers, say), just as any sentences can be conjoined regardless of subject matter. This enables us to transcend natural associations between things: things don’t have to be conjoined in nature to be conjoined in thought. That is how set formation works: a set may contain the Eiffel tower and your favorite aunt and that dog over there. There is a certain freedom to the addition operation: it is not too choosy about what it will combine. This gives it enormous creative power; it liberates thought from the tyranny of nature. A mind possessing it thereby possesses considerable freedom of expression. We should not underestimate the power to put things together ad libitum (as well as ad infinitum). Finally, addition has an inverse: what can be added can be taken away. Addition is a reversible operation. You can add 3 to 5 but you can also subtract it from 8; you can conjoin two sentences but you can also de-conjoin them (as in conjunction elimination in logic). This gives addition flexibility—it isn’t stuck with the wholes it has produced. You can form ever more complex sentences, but you can also simplify sentences by removing parts of them; indeed, this is just the other side of what addition is. Adding and subtracting are parts of the same package.

            Putting all these properties together, we can see that addition is by no means a simple matter of setting things side by side like marbles in a drawer. It has subtlety and structure, a rich cognitive profile. Yet it is conceivable that it arose by a relatively localized mutation, producing a distinctive piece of neural rewiring. It might have arisen much like the cornea or the eyelash. But it also has the power to carry us a long way in the manufacture (the engineering) of arithmetic and language (i.e. syntax). A great deal of these two cognitive faculties can be fitted into the framework of addition—that mental operation has considerable power to produce what is characteristic of arithmetic and language. Perhaps not all—other factors no doubt joined with his basic factor—but as a fundamental cognitive principle it is capable of a lot of work. Certainly other animals are lacking in its productive power: they may have primitive communication systems and an elementary grasp of counting, but they don’t have the full structure generated by addition in its abstract form. They have not yet reached the stage of unlimited mental conjunction. What the human mind is particularly good at is forming new wholes by means of addition (composition, conjunction, putting together)—where this is to be understood by reference to the ensemble of features enumerated above. Once this operation evolved in the human brain it was available for use in various worthwhile endeavors such as calculating, thinking, and talking. It arose by chance but it was soon exploited and promoted by natural selection. Thus we became the adding species, the dedicated conjoiners, the arithmeticians and grammarians. Now we add up all the time, constantly using our capacity to put things together, always creating sums. This theory seems like the optimal combination of simplicity and fecundity necessary in any proposal for explaining the evolution and learning of arithmetic and language, with the bonus that both areas fall under the same theoretical framework. Both are offshoots of a primordial ability, arriving a couple of hundred thousand years ago, to perform acts of addition. Arithmetic is the application of addition to numbers, and language (syntax) is the application of addition to words.  [3]

 

  [1] This paper was stimulated by things Chomsky has said in various places. It presupposes a lot and is very compressed.

  [2] See Why Only Us by Robert Berwick and Noam Chomsky (2016), especially 72-4. My suggestion might be viewed as complementary to this but with a different emphasis.

  [3] We should note that the theory is not intended to explain the origin of words (lexical elements) or concepts of numbers. It doesn’t even explain the existence of standard grammatical categories. It is solely concerned to explain the most abstract features of language and arithmetic (as the Merge operation is supposed to). It tells us how certain structural properties of the two domains may have come into existence. It is basically a theory of the origins of the human combinatorial capacity. Much would need to be added to it to reach arithmetic and language as they now exist in the human species. Still, we do need a theory of the basic cognitive architecture of these two domains that is consistent with their having evolved in the usual way. We need a theory of the basic form of the innate program for acquiring these capacities. 

 

 

Metaphysical Pluralism

 

I will discuss a question at the outer edge of human comprehension. Some metaphysical views are monist, some dualist, and some pluralist. Monist views include materialism and idealism; dualist views typically divide reality into the mental and the material; and pluralist views include a variety of disparate types of being. A standard form of pluralism would list matter, space, time, mind, value, and number—with possible subdivisions within these broad categories. The question I want to discuss concerns pluralism of this type—the view that reality divides into several distinct categories and is not unified by any overarching category (or pair of categories). Thus matter is not the same as space, time is a distinct dimension of reality, mind is separate from matter, value is not reducible to any of the aforementioned, and mathematics deals with its own sphere of existence. We might further allow that matter and mind allow for subdivisions and are not themselves homogeneous categories. The picture is that reality comes intrinsically divided up into several types of being with no unifying ontological structure. The components may be connected in various ways, causally and otherwise, but there is no unity at a basic level: reality is fundamentally a list.  [1] Alternatively, reality is disjunctively defined: to be real is to be either matter or space or time or mind or value or mathematics. Reality is a mixed bag, a jumble, a heterogeneous collection. Hopes of unification are therefore misplaced.

            This seems unsatisfying. Why should reality be thus divided? Why should the universe be so lacking in unity? It seems thrown together, a mere assemblage, with neither rhyme nor reason. Why would God construct a universe so irreducibly diverse? Why would the laws of nature allow for such a miscellany? Monism allows for unification, and dualism at least keeps the ontological number low, but pluralism accepts arbitrary amounts of variety, gleefully so. Pluralism accepts that the inventory of what there is could go on indefinitely as a matter of principle. It all seems so chaotic and contingent—as if the universe is just a disorganized pile. The universe is really a multiverse: we might as well speak of there being as many universes as there are components of the single one. Compare games like chess or tennis: if we just listed their component parts—white and black pieces of different shapes, a board, squares; racquets, balls, a net, a court—we would be faced with a mere random assembly. It is only when we place these items in the context of a unified game that a sense of the whole emerges. Then the pluralistic universe is like the components without the game: these elements are not part of anything with a unifying theme. But why a pluralistic universe and not a unitary universe? Could there be some unknown unifying reality behind the apparent diversity? The nearest we come to unity is via mathematics: matter, space, and time all submit to mathematical description, and perhaps the mind admits of some mathematical characterization too. But value seems not to be mathematically subsumable, and the mind is not wholly mathematical. Perhaps it would be different if God were behind everything; at least then we might discern a unifying purpose to the apparently fragmentary nature of the universe. But an atheistic perspective leaves reality in a state of radical disunity: the universe just happens to jam together quite disparate elements, like an overstuffed suitcase. That is, metaphysical pluralism presents us with an unintelligible jumble of heterogeneous parts. The parts are notoriously hard to connect together (e.g. the mind-body problem and the problem of mathematical knowledge), but there is the more basic worry that they exist at all in such variety. It offends a natural desire for simplicity, or at least orderliness. If God were designing a universe, why would he impose such chaotic diversity on it? Why the desire for the new and different? Or again: if there are other universes existing alongside this one, do they all display such disunity? Surely there are non-pluralistic possible worlds, so why is the actual world condemned to unexplained plurality? It may well be that pluralist metaphysics is logically inescapable for the actual world, but that still leaves the question of why pluralism should be true to begin with. Why must we have the material and the spatial and the temporal and the mental and the normative and the mathematical? The urge towards monism becomes understandable once we appreciate that pluralism is not intellectually satisfying as a final metaphysical stance. For it leaves us with an impression of jangling meaninglessness, obdurate incoherence, and queasy randomness—the world should not be so sundered and splintered! It is as if the universe lives several different independent lives. If universal panpsychism were true, we would have the result that the universe is made up of several completely different types of mind, each alien to the other (the material mind, the spatial mind, the temporal mind, etc.). Reality, under metaphysical pluralism, is composed of far too many realities, if I may put it so. And this is not a point about the types of reality making up Reality, but about the sheer number of them. What if pluralism said that reality as a whole is made up of 283 basic types of reality? Why is 6 the magic number?

            Compare biological and astronomical reality. The biological world contains many types of animal—zoological pluralism is the norm—but this variety is underlain by a unifying theory, viz. the theory of evolution. So there is a fundamental unity to the variety we observe: the plurality isn’t just brute and inexplicable. Similarly, astronomy has discovered a plurality of galaxies where once we suppose unity, but this plurality is explained by the origin of the universe in the big bang (combined with the laws of nature)—it isn’t just a brute fact. But the plurality of the universe, as conceived by metaphysical pluralism, does seem like a brute fact (and is so intended by the metaphysical outlook in question). It seems distinctly arbitrary, surplus to requirements, and suspiciously de trop. It is not a plurality we can comfortably live with; it makes the universe seem casually put together, a mere congeries of qualitatively diverse elements. If we suppose (plausibly) that time is the original reality preceding all others, then the question time would have is why someone saw fit to keep introducing new realities in addition to time itself. It would be different if the additions were just modifications of time, but evidently they are completely different orders of being. Pleasing unity gave way to pointless disunity, gratuitous division. The universe became a mere bunch of sui generis elements. Metaphysical pluralism seems a bit too much like metaphysical anarchism. It may be true but it is hardly aesthetically pleasing or theoretically satisfying. Where was Occam’s razor when the universe needed it? Why the ontological multiplication for multiplication’s sake? And it is not as if the pieces fit snugly together, like pieces in a jigsaw; the pluralistic universe is by no means a harmonious universe. The architect of the universe was just making trouble for himself by insisting on irreducible plurality. The plural universe is a puzzling universe. Why Many instead of One?  [2]

 

  [1] I don’t of course mean that reality consists of words; the point is that reality is thought to be specified by a list of disparate elements each with its own nature.  

  [2] The question I am asking is not one I have seen addressed before, so it may seem odd or eccentric. I have tried to home in on the intuition in question, but it isn’t easy to do that. It might help if I say that the many types of reality envisaged by the pluralist look like so many types of stuff—and then the question is why so many types of stuff.