Quantum Semantics





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

  [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. 

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