The Cogito

There have been many criticisms of the Cogito and many versions of it (some preceding Descartes’ version). Lichtenberg’s criticism has been influential: all we know with certainty is that there are thoughts occurring, not that there exists someone having those thoughts. We introspect our thoughts and thereby come to know that they exist, but we don’t introspect any subject that has those thoughts. Maybe there are thoughts without thinkers. We cannot with certainty infer a substantial self from the mere occurrence of thoughts. To this objection it can be replied (following Frege) that there cannot be thoughts without a bearer of thoughts: it logically follows from the existence of thoughts that someone has those thoughts. Descartes might argue that thoughts are “accidents” and that all accidents need substances in which to inhere; so if thoughts are occurring they must be occurring insomething. There is no thinking without a subject that thinks—there are no “free-floating” thoughts (doubts, pains, etc).

            I am sympathetic to this kind of reply to Lichtenberg, but I think there is another gap in the argument that I have not seen addressed. Descartes does not conclude from the Cogito that someone exists; he concludes that heexists. The Cogito is not, “There are thoughts, so someone exists” or “I know that thoughts exist, so someone exists”; it is “I think, therefore I exist” or “I know that thoughts exist, so I exist”. If we eliminate the question-begging occurrence of “I” in the premise, the proper form of the Cogito should be: “There are thoughts, therefore I exist”. But now that looks like a patent non sequitur, because those thoughts might not belong to me. It is true that for Descartes’ purposes the impersonal form of the Cogito is good enough, since he can still prove that there are things other than thoughts, viz. selves; but he cannot prove his own existence this way, because the bearer of the thoughts he knows to exist might be someone else. He knows that thoughts exist but he doesn’t know whose thoughts they are. So he can’t prove that he exists by this form of argument. The skeptic will ask how he knows that it is him that is thinking, i.e. how he knows that the thinker of the thoughts he knows to exist is identical to himself. There is a logical gap here that needs to be plugged, however strange the gap may sound.

            I can imagine a reply to this point along these lines: if the thoughts belonged to someone else I couldn’t know with certainty that they exist, because I can’t know other minds with certainty; so they must belong to me, given that I know of their existence with certainty. I can rule out the possibility that the thoughts belong to someone else by observing that I am certain of their existence, which I couldn’t be if they belonged to someone else. That is, I use my certainty of the existence of thoughts as a premise in the argument to my own existence: “I am certain that thoughts exist, so it must be me that is their bearer, since I can’t be certain of the existence of other people’s thought”. It is not the known existence of thoughts that leads to the conclusion that I exist—that only proves that someone exists—but the certainty I have in my knowledge of their existence, since this is incompatible with the possibility that the thoughts belong to someone else.

This, however, is not the Cogito as we have come to know and love it, in all its simplicity and straightforwardness; we now need to build in some assumptions about knowledge of other minds and how it differs from knowledge of one’s own mind. The skeptic can then ask us to justify these assumptions: Is it really inconceivable that I could know another’s mind with the certainty I know my own mind? Couldn’t God have hooked my introspective faculty up to another mind so that I directly know the thoughts in that other mind? If so, I could know of the existence of thoughts with certainty but it is false that those thoughts belong to me—it just seems to me that they do (or perhaps it doesn’t even seem that way). The mere fact of certainty about the existence of thoughts isn’t enough to justify the claim that it is my thoughts that I know about. Still, it may be that this hidden assumption is what enabled Descartes (and others) to overlook the possibility to which I am drawing attention. He just assumed that any thoughts he could know about with certainty had to be his, but the resourceful skeptic sees a gap here—how can Descartes be so sure that those thoughts don’t belong to someone else? The Cogito therefore only gives us certainty that someone exists (pace Lichtenberg) not that we ourselves exist. My existence remains unproven.

            This suggests that the basis of my knowledge that I exist is not the Cogito or anything like it. I do know with certainty that I exist, but the Cogito cannot yield such first-person knowledge; so I must have this knowledge in some other way. It is not an inference from the existence of thoughts.

                                                Metamorphosis and the Self

It is not implausible to maintain that the caterpillar and the butterfly it becomes are the same organism, but it is another question whether they are the same self. The caterpillar crawls on tiny feet and munches leaves: it has the sensations and motivations that go with these activities. The butterfly has delicate wings and dines on nectar: its sensations and motivations are tailored accordingly. Are these the same conscious subject? If you don’t like attributing mental characteristics to caterpillars and butterflies, then imagine a similar type of creature stipulated to possess such traits. Suppose these creatures have personality as well as consciousness: do they have the same personality at the two stages of their life cycle? Are they the same person? Let us suppose that the psychological lives of the caterpillar and the butterfly are sufficiently different that we would not want to say that they are the same person or self. When the creature leaves its larval stage behind it also leaves its larval self behind, becoming a quite new self with its metamorphosis into a butterfly. This means that the earlier self ceases to exist, to be replaced by a new self in a body also considerably transformed (though biologically continuous). That new self will also eventually die, so that there is a double death in the life of every butterfly: the caterpillar self dies when it is replaced by the butterfly self, and then the butterfly self dies too.

            If we imagine intelligent, reflective, and cultured butterflies, there will be a question about how they understand their own life cycle. Do they grieve over the death of larval selves? Do larval selves fear their impending death? We can imagine that some of them believe that larval selves have an afterlife, maybe even a heaven and hell, while others believe that these selves simply pass out of existence (they may or may not believe that butterfly selves survive bodily death). Some may find the juvenile selves to be morally superior to the adult selves, less vain and flighty; others may find the juveniles to be more psychologically rigid than the adults. But they will all agree that reaching the chrysalis stage is tantamount to the death of the larval self. Nor do they take this death lightly: they don’t suppose that the onset of a new butterfly self somehow expunges the significance of the earlier death.

            How would their predicament affect their view of the death of an adult? When the adult butterfly is contemplating its death how does the prior death of the caterpillar self figure in its emotions? The butterfly knows that its childhood self is already dead, which was not good news for that self; but death has already been endured once, and yet life went on. You can only reach the adult self by going through the caterpillar stage, so you lose one self to gain another. True, the eventual death of the adult self is a bad thing—just like the death of the juvenile self—but it doesn’t have quite the same sting as if there had been no death before. It makes it easier to accept death if you have already been through it once (or your larval predecessor has)–if it is simply part of life. You have been there before and you can go there again.  [1] The butterfly thinks: “I have already died once, I can do it a second time”. Not that its death isn’t a bad thing, but it doesn’t seem as bad—its badness is more bearable.

            Compare your attitude to death if you believe that you are already dead (a self-conscious zombie). If you believe that you are already dead, you will not fear being dead again, or not as much. Likewise, if you think you have no self to be alive, then the prospect of that self ceasing to exist will not bother you too much.  [2] Death has little sting for the already dead or already non-existent. Similarly, if you have already died once and emerged from it none the worse for wear, then the prospect of dying again loses its novelty and fearsomeness. Been there, done that. You are not exactly consoled in the face of death by your earlier demise, but it is recognized as part of your overall life: the first death, though admittedly bad, wasn’t that bad, so why should the second death be? Do we grieve over caterpillars knowing that butterflies will succeed them?  If not, can’t we grieve less over the death of butterflies knowing that other butterflies will succeed them? Why should the death of a butterfly self be worse than the death of a caterpillar self? And that death wasn’t all that terrible, was it?

            Why am I speculating about the death of butterflies? Because of a possible analogy with humans: for don’t we also go through the equivalent of a self-annihilating metamorphosis? I am thinking particularly of adolescence—that time of transformation and upheaval. It is a familiar thought that a single human life might house a succession of distinct selves according to the psychological changes undergone.  [3] We say, “I am not the same person as I was thirty years ago”. Some illnesses, physical or mental, are thought to destroy the self that once was, possibly leading to the formation of a new self. Psychological trauma can make a person feel like someone else entirely. But adolescence affects everyone and the changes are plain to see: the body changes dramatically, but so does the mind. People put away childish things and embark on a new mode of living, priorities reverse, and new motivations take over. A child can transform into another psychological being entirely (from obedient angel to rebellious lout, say). Is it an exaggeration to say that a new self takes root? Given that it does, what happens to the old self? It dies. It is no more. It goes out of existence. It buys the farm. We may regret this passing, even mourn for that lost child, with its sweetness and innocence; but we recognize that it could not persist if an adult self is to take over the premises. Maybe we should grieve more than we do, but the change seems relatively seamless, the body soldiers on, and a brand new self rises up to greet the dawn. We take it in stride—as butterflies do.

            Let us accept that our childhood selves do indeed die (if you can’t accept that, then imagine a species where we stipulate it to be so). My question is how that fact should affect our attitudes towards death. We can also frame the question by supposing that a single human life contains many personal deaths—childhood, young adulthood, middle age, and old age (or even that we die every time we go to sleep). We are not already (finally) dead, but we have already died. But to focus the issue just consider the death of the childhood self—a death we have all been through (I vaguely remember bidding adieu to my childhood self during adolescence and feeling some sadness at his departure). If we let this fact sink in, will it affect our attitude to our later death? I think it will. I have already died once—my first self went the way of all mortal things. That is sad, but life went on; it wasn’t the end of the world (though it was the end of his world). Suppose that at the age of 13 children went into a genetically programmed coma, only to emerge three months later with new bodies and new minds—with different things onthese bodies and minds. Suppose the psychological changes were drastic enough to make us say that these are new persons, tenuously related to the old ones (maybe different parts of the brain are involved pre- and post-coma). We might feel some sadness at the departure of the previous person, but we have to accept it as part of our natural life cycle. We may have rituals surrounding it, softening the blow, reconciling us to the facts of life. Would we then not have a different attitude to later adult death? The coma involved an organically driven loss of consciousness and personality that everyone experiences at age 13: this is the actual death of the juvenile self. But this death, though real enough, is viewed as a rite of passage, nothing to get too worked up about, nothing to despair over.

Then what is so terrible about our final death (though that first death was also final for the self undergoing it)? True, we will no more ever experience the wonderful things of life—but the same is true of the dead juvenile self: she will never again experience the wonderful things of life either. It’s easier to live with future death if you have already died in your life once before. New selves will arrive to replace you, as you replaced your erstwhile childhood self: that’s just the way nature works. No doubt death is tragic for all the selves concerned, but there is tragedy and tragedy. You already died once and it wasn’t the end of the world; some good came of it—the mature you. True, the self that called itself “I” did not make it—a new self came to utter “I” using the same mouth. But that death wasn’t as bad as we are inclined to think when we contemplate death; so maybe we should calm down about our later death too. Maybe we should temper the hysteria.

            There might be a similar death towards the end of life. What if there was a genetically programmed depletion of the self at age 60 that made us say that the previous self was no more? That would no doubt be bad, but not allthat bad. Wouldn’t this make the final biological death a little more bearable? Not because the last self has little intrinsic value but because it will be the third death in a line of previous deaths. Death would not be that one-off catastrophic event that fills us with cold dread, but a predictable alteration in human psychology—the phasing out of selves when they reach their expiration date. They are all real deaths, terminations of a self, and so exact their proper measure of fear and grief; but none is intrinsically worse than any of the others, since all involve the cessation of a self. If you reply that the final death has no natural replacement, as the previous deaths do, then consider that another self can come along to replace my final self—say, the self of my child. These are all brand new selves, stepping into the shoes of other departed selves—just like the caterpillar and the butterfly. No one is returning from death, so every death counts: but they all count equally—and some don’t seem all that appalling. So maybe we can dial it back a bit, this dread of death. It’s bad, yes, undeniably bad: but it’s not super-bad–not weeping-and-wailing bad, not can’t-get-out-of-bed-in-the-morning bad. Maybe indeed the end of that sweet innocent self at age 13 is more to be lamented than the end of that crabby old codger self at age of 80.

            Selves come and go more easily than bodies, with less in the way of injury or illness; they depend on psychology not physiology. The end of a self is not the end of a body—though the end of a body is the end of a self (under current technology). Maybe selves are even more perishable than we generally realize, lasting no more than a decade or so, depending upon contingency. A human life contains not just a single permanent self from womb to tomb but a succession of distinct temporary selves. The living body itself has no intrinsic value—there is no tragedy in terminating a living body that doesn’t house a person—but the value of selves might be less than we customarily suppose, if they come and go so frequently and naturally. Maybe the death of selves isn’t quite as horrifying as we tend to suppose.  We can never be reconciled to death, certainly, but perhaps we can learn to face it more coolly.         

  [1] Strictly, of course, you have not been through it, since you are not identical to the larval self that preceded you. But you are both part of the same life cycle and are clearly closely related.

  [2] This is a simple statement of the Buddhist view of death and the self: there is no substantial self to be the subject of death, so no such self is lost at the point of bodily extinction. Derek Parfit holds the same kind of view, as he notes.

  [3] It might be helpful to distinguish two notions of the self that we operate with: first, there is the notion of a subject of consciousness; second, there is the notion of sameness of person where that requires some coincidence of psychological traits. The first is not logically sufficient for the second, since the bare subject of consciousness could change dramatically in its associated psychology (it might just be the brain). I am discussing here the second notion, which brings in character and personality as well as memory, intelligence, desires, ambitions, etc. If I change too much psychologically, I cease to be the same self in the second sense; but the individual subject of consciousness might be the same throughout (that single continuous brain organ or the “transcendental ego”).

Quantum Semantics

The so-called quantum revolution, initiated by Planck and Einstein in the first decade of the twentieth century, was just that: an overturning of entrenched earlier theory. Light (radiation) had been conceived as continuous and wavelike not as having a particulate structure. Much of the experimentally observed behavior of light confirmed this picture (interference and diffraction), and light didn’t look as if it was a swarm of discrete particles. The quantum theory was thus counter to common sense and previous science. But this is not the situation with regard to language: we don’t need to be persuaded that language consists of an array of discrete entities (words) that combine to form ensembles. It isn’t as if language looks to be continuous or that previous linguistics had good theoretical reasons for favoring continuity; it is just part of common sense that language has a particulate structure, as well as a tenet of the science of linguistics.  [1] No one needs to be converted to quantum semantics: meaning is obviously quantized (unlike energy), consisting of discrete semantic units (as well as syntactic and phonetic units). Meanings are not values of continuous variables, and they are either present or not (there are no degrees of meaning). The structure of meaning is evidently a quantum structure. As a consequence, the infinity of language is a discrete infinity not a continuous infinity—an infinity of combinations not of mathematical points. We don’t speak of “point meanings”: meanings are not loci on a continuum. Meaningful words are block-like entities: granular not graded.

I don’t intend to question this assumption—quantum semantics is clearly the correct view—but I do want to raise some questions about it, because it is not a trivial assumption and has important theoretical consequences. First, why exactly do we believe it—what is our evidence for supposing that language has a quantum structure? Why do we think that language is made up of discrete units of meaning—the things we call words? It is important to see that a natural answer to this question is wrong, namely that spoken language is divided into discrete acoustic elements strung together in time. As Chomsky would point out, speech is but the externalization of language not language itself: it is the joint product of an internal cognitive system (language proper) and a sensory-motor system that forms its contingent outer expression (which precedes language in evolutionary history and was not designed to mirror the structure of language itself).  [2] It simply does not follow from the fact that this external vehicle has a discrete digital structure that the underlying cognitive system does. Compare musical notation: just because written sheet music has a discrete digital structure it doesn’t follow that music itself does (it is a continuous medium). Musical notation is designed to be read, and hence must be suitable for the eye—just as speech is designed to be heard, and hence must be suitable for the ear. But music and language are not in themselves visual and auditory, respectively. Language, for Chomsky, is primarily a tool of thought not of communication and as such it need not mirror the structure of spoken language. In fact, it is more plausible to suppose that we impose a quantum structure on speech, based on our prior acceptance of language as discrete, than that we derive the discreteness of language from the observed discreteness of speech. Speech is actually not as discrete acoustically we as tend to imagine, as is revealed by a speech spectrograph; and it has a continuous nature that is irrelevant to its function as a vehicle of meaning. Volume, pitch, and duration have no semantic significance—loud high-pitched fast speech doesn’t have a different meaning from quiet low-pitched slow speech. So it can’t be that our reason for believing that language is discrete is that speech is discrete: that would be a non sequitur given the relation between language proper and vocalization, and anyway it doesn’t deliver the kind of discreteness we attribute to language. We can’t derive quantum semantics from quantum acoustics (or quantum gestural language for that matter).

If language is more a mental thing than its physical externalization, perhaps our evidence for discreteness comes from introspection: we arrive at the idea of quantum semantics by noticing the structure of our innerspeech. Bu this is no more plausible than the first suggestion: inner speech is at least partly silent outer speech (a sensory-motor system) and hence is not guaranteed to reveal the structure of language as a cognitive system (the language faculty); but also it is implausible to suppose that we can read semantic structure off the form of internal acts of speech. Are such conscious acts really as segmented as we take language to be? Is awareness of the (phenomenological) structure of inner speech the reason we so readily acquiesce to the quantum theory of language? What if the introspective system is as misleading as the sensory-motor system when it comes to the intrinsic character of language? The truth is that we do not perceive the quantum structure of language, either outwardly or inwardly—that is, our evidence for that conception is not acquired through perception (though our perception might be conditioned by a prior knowledge of semantic structure).

We might then opt for a strictly theoretical account of such knowledge: we infer it from observable features of language as a theoretical postulate. We know that language has infinite potential and that our vocabulary is finite, so we hypothesize that language must be made of discrete units that combine to produce more complex semantic entities—and hence we know there are such discrete units. We thus have no direct awareness of semantic quantum reality, but we know indirectly that it must be so, or else language could not have the properties we observe it to possess—specifically, infinite potential based on finite means. Combination requires units that combine. However, this kind of reasoning, cogent as it may be, does not do justice to the nature of our knowledge of language: for it is not just a matter of speculative inference that words exist—they are not like atoms or remote galaxies. So we must possess a way of knowing about language that makes non-inferential knowledge of its structure possible; and I think we do possess such a way—we know directly that meaning is quantized. We know this because we have first-person insight into the structure of our language faculty: not by deducing that structure from perception of external speech or awareness of inner speech, and not by theoretical postulation, but rather by a kind of primitive self-knowledge. We know that our thoughts are structured in a similar way—a way that is sui generis and not inferred from other types of knowledge. This basic knowledge permeates our awareness of the expressions of language, both external and internal; it is not the upshot of such awareness. It is based on an immediate intuition of linguistic structure. The epistemology of quantum semantics is therefore obscure and mysterious, and certainly worthy of further study; there is nothing trivial or transparent about it. It really isn’t at all obvious how we come to know that meaning is a discrete and divided thing—yet we do know it (short of entertaining some extreme form of skepticism). As language users, we have implicit knowledge of the structure of meaning—and we know it to be a quantum structure not a continuous structure. Other types of language user might employ a continuous non-quantum language and either know this to be the case or be in the dark about it. I suppose there might be language users for whom the quantum nature of language comes as a surprising scientific discovery, as the discovery of light quanta was for us; but we are not such beings so we are not revolutionized by the revelation that meaning comes packaged in discrete units.  [3] We suffer no paradigm shift or conceptual convulsion when linguists and philosophers announce the quantum theory of meaning (“Who could have guessed—it all looked so smooth and wavelike!”). We are all commonsense quantum theorists of meaning; no one shrilly insists that language consists of continuous variables like loudness and pitch whose values are words. How we know this–and with such certainty–remains obscure, but it is surely so: it is built into our linguistic consciousness.

Now I want to consider a different question: what should we say of the ontology of meaning, given its quantum nature? First, what is the smallest unit of semantic reality? It has been traditional to assume that the constituents of meaning correspond to the logical analysis of meaning: that microstructure and definition go hand in hand.  [4] Thus we arrive at the idea that the most basic units of meaning correspond to sensory primitives or some other definitional foundation. But this kind of correspondence is not compulsory and is not terribly plausible: for why should the microstructure of meaning be tied to what we can reflectively analyze as conscious language users? Why can’t semantic reality possess a structure that goes beyond what is accessible to conscious analysis? Why can’t it have an unconscious particulate nature geared to other concerns than our knowledge of what our words mean? The meaning of a word (morpheme) is surely too coarse to constitute semantic bedrock; it must have some hidden structure that ties it more perspicuously to underlying processes in the brain, computational and other. To suppose otherwise is like supposing that the microstructure of matter goes no deeper than what is revealed to observation by cutting things up with a knife. The meaning of a putative primitive like “red” might have a highly articulated inner constitution that links it to the brain. In other words, the basic semantic quanta might lie outside of commonsense understanding, just like physical quanta. What we call a word and think of as semantically primitive might be in reality a macro-quantum—a bigger chunk of more elementary semantic components. I can’t specify what these components look like; I can’t even promise that they will one day be discovered: I can only urge that they not be ruled out.

            The second question concerns what might be called “the word-body problem”: the problem of how the brain gives rise to and implements language. Specifically, how does the quantum structure of language arise from the brain—how do we get discrete words from brain processes? That may seem like an easy problem, but it is not. It may seem easy because the brain contains discrete units of its own that can (allegedly) form the basis of discrete words: not only physical quanta, atoms, and molecules, but also cells, ganglia, and on-off neural transmission. There is plenty of particulate structure in the brain, more than enough (it will be said) to generate a lexicon of discrete elements. But this is superficial thinking, because none of this brain structure has anything to do with linguistic structure—none of it amounts to the structure that meaning exhibits. It is at the wrong level to explain the existence of semantic discreteness. Other organs of the body have the same kinds of anatomical discreteness as the brain, but no one thinks they provide an adequate basis for the structure of human language—which is a very special kind of structure. So there is a word-body problem analogous to the mind-body problem: both involve mysterious kinds of emergence. Indeed words constitute part of the mind, and they too resist reduction to brain states. In fact brain activity tends to be wavelike, which is not surprising given that it is electrical in nature; but in language we have an entity that is not wavelike (it doesn’t even have “particle-wave duality”). How can quanta of meaning arise from waves of electricity? Why doesn’t an electroencephalograph record discontinuous spikes corresponding to lexical units, as well as those wavy curves? The brain is really no more suitable, on the face of it, for producing language than the heart is when it comes to accounting for semantic discontinuity. This is an “emergent property” of the brain not a recognized aspect of its anatomy and physiology (or chemistry and physics). There is thus a non-trivial explanatory problem here—accounting for the discrete structure of language (construed as an internal mental system). We are familiar with the problem of intentionality for language, but there is also the problem of “segmentality”: the very structure of language fails to map onto underlying brain structure (in so far as we know about brain structure). Accordingly, we have a “semantic quantum problem”, as we have an “intentionality problem” and a “qualia problem”. The architecture of meaning, with its bounded discrete combinable elements, finds no counterpart in the architecture of the brain, at least as we now understand it.  [5] One can imagine someone postulating “pan-quantum-ism” as a way to explain the emergence of quanta of meaning—everything in nature has a hidden quantum structure—but such a view is clearly far from satisfying (what kind of quantum structure and how is it related to the structure of meaning?). Because we tend to take the quantum structure of meaning so much for granted, we don’t see that it produces explanatory puzzles (as it produces epistemological puzzles): but it is really not clear how this aspect of language can be fitted into what we know of the brain. In brief: semantic discreteness is not physical (physiological) discreteness. I won’t say that quantum semantics is as puzzling as quantum mechanics (no reason to postulate violations of determinism  [6]), but it is certainly not a final and finished theory; it awaits unification with the other sciences of body and brain. This most fundamental feature of human language is by no means as straightforward, epistemologically and ontologically, as has been supposed.

  [1] Genetics is somewhere between these two cases: we now know that the genome is essentially a quantum system in the sense that genes are discrete and digital, being either turned on or off; they don’t blend or mix. This is why a child whose parents have different colored eyes doesn’t have an intermediate eye color but has one or other of the two parental colors. Theorists may have been weakly committed to some kind of non-quantum theory, but the change to quantum genetics was hardly a paradigm shift, unlike the quantum theory of energy. (Let me note that I am using the word “quantum” a little loosely here, if we take physics as our guide: a quantum in physics is an amount of energy, but a word is not an amount of meaning. I am using “quantum” to capture the discontinuous nature of word meaning, not the idea of a magnitude divided into discrete steps. And I couldn’t resist the euphony of “quantum semantics”.)

  [2] See Robert C. Berwick and Noam Chomsky, Why Only Us: Language and Evolution (MIT Press, 2016).

  [3] We might date the official academic recognition of quantum semantics to Frege’s “On Sense and Reference” (1892), though no doubt there were premonitions. Frege systematized the intuitive picture of language as consisting of a finite number of discrete meaningful units combinable by rules into larger wholes—there is nothing continuous or blurry in his theory (contrast Hume’s talk of mental images and vividness). It is hard to see how Frege could not have been influenced by earlier corpuscular physics and chemistry (Planck’s and Einstein’s work on the quantum theory of light came a few years later). He does not model his theory of language on Maxwell’s theory of electromagnetism, in which the wave is supreme, because it is obvious to him that words are particle-like not wavelike. People have sometimes spoken of “semantic fields”, but no one hypothesizes that meanings are values of continuous magnitudes acting at particular points in semiotic space. Meanings are more like solid bounded objects than continuous fields of force.

  [4] Thus in Russell’s logical atomism the atom is a sentence with words as atomic constituents—quite a large unit of meaning. He is connecting logical analysis with semantic structure, not allowing for the possibility of semantic atoms at a much finer scale. Shouldn’t atoms at least be invisible?

  [5] Where in the brain do we find the neural basis for nouns and verbs? No doubt there are brain correlates, but what kind of vocabulary should we use to describe these correlates? Why should one neural correlate be noun-like and another verb-like?

  [6] Though it has been claimed that language use is an exercise of free will and as such incompatible with determinism, so there is some analogy there. No uncertainty principle, however. I can imagine a fanciful form of metaphysics that regards physical quanta as inherently semantic, so that quantum semantics underlies quantum mechanics. This would be a version of informational quantum theory, which has its adherents.