Semantic Discreteness as a Logical Defect
It used to be said that natural languages are logically defective in one respect or another: quantifiers look like names, definite descriptions look like names, names look like names, vagueness is pervasive, no distinction is made between object language and meta-language, and so on. But I have never heard it alleged that the very discreteness of words is a logical defect. Words are individual units of meaning that combine with other such units to produce composite sentences—they are digital not analogue. The meanings they carry are also discrete and digital: meanings combine as self-enclosed units—there are no borderless meanings. Meanings don’t mix or blend or flow into each other. They are not more or less, higher or lower, weaker or stronger. They have no amplitude. Every (meaningful) expression is equally meaningful. Natural human languages are like Morse code not like a graph or a thermometer—discrete not continuous. Words and meanings are like atoms not fields: bounded, discontinuous, and combinable without loss of identity. The infinity of human languages is a discrete infinity not a continuous infinity.
It is a question why this is so: is it because of the world or the mind? Is language discrete because objective reality is discrete and language merely reflects that, or is it that the language faculty itself, as a component of mind or brain, imposes a discrete structure on language? Are words discrete because what they represent is discrete, or does their discreteness result from endogenous constraints on the language faculty? If we suppose that the language faculty evolved from a specific mutation (or set of mutations), is it that this mutation carried a preference for structural discreteness, whether the world conformed to this preference or not? And if the discreteness is endogenously based, then there is a question whether that is ideally suited to the reality that language purports to be about: the discreteness would seem to reflect us not the world. Is the world as “chunky” as language? Does it divide up in the way meaning divides up?
Certain features of reality might prompt an affirmative answer: there are distinct objects bearing distinct properties, corresponding to singular terms and predicates (this is the stuff of Logical Atomism). Meanings are segregated because objects and properties are segregated, and meanings combine into propositions in the way objects and properties combine into states of affairs. Thus the structure of language reflects the structure of reality—not our structure as psychological and biological beings. Semantic discreteness merely mirrors ontological discreteness, and so is no kind of logical defect. But this is a very partial picture, completely ignoring the continuousaspects of nature: space, time, heat and cold, colors, pitch, loudness, intensity, speed, happiness, distress, and so on. There are continuous magnitudes as well as discrete entities. But there are no magnitudes in natural language corresponding to these objective magnitudes; they are handled digitally. We don’t have symbols that vary in some magnitude to represent variations of magnitude in reality—we just use another (discrete) symbol. Wouldn’t that be better—truer to the facts? Why not have analogue components as part of the resources of the language faculty?
What would that be like? Suppose we used pitch and duration to indicate degrees of a magnitude: instead of saying, “The soup is very hot” we say, “The soup is oooooo”, where the oooooo sound is made at a high pitch and for a significant duration. This would contrast with uttering the same sound at a lower pitch and more briefly to indicate that the soup is lukewarm. We would then be availing ourselves of a representational device that permits fine continuous gradations corresponding to the gradations found in external magnitudes. We could choose different vowel sounds for different types of magnitude (distance or brightness, say), while always using pitch and duration to indicate extent or intensity. Such utterances would have truth conditions that could be stated by the standard Tarskian biconditionals, where we repeat the analogue symbol in stating the truth condition.  Thus our language would have two semantic parts: a discrete part and a continuous part, digital and analogue. It would then be capable of two sorts of infinity: discrete infinity and continuous infinity. Wouldn’t that be logically superior? The language would do justice to the continuous aspects of the world instead of digitizing everything. Bees employ continuous magnitudes to represent distance in their communicative dances—why can’t we? Should we reform language in this direction, or at least hold it out as a logical ideal? Our sensory perception of the world is already heavily analogue, so it is not as if we are unfamiliar with this type of mental representation. Yet our language seems to stick doggedly to semantic discreteness; and it does so in spite of the fact that speech already contains the resources to employ analogue representation—that is, we already have the ability to vary the pitch and duration of our vocalizations. It is not as if we would have to learn a completely new set of skills; indeed, we already sometimes use pitch and duration (as well as loudness) as semantic indicators, as when you scream a person’s name long and loud (“Ste…lla!”). We just need to incorporate this into our explicit vocabulary, replacing the clunky discrete words we use for things like degree of heat, which are typically limited to a few crude distinctions (“hot”, “very hot”, “extremely hot”). We would thereby enhance the expressive power of our language by enabling much finer distinctions of meaning: so why not upgrade to analogue?
In fact, there is a prior question: why is our language not already (partly) an analogue language? Why doesn’t our language incorporate analogue devices alongside digital devices? This seems puzzling: the human voice is capable of analogue performances, and they would enrich the expressive power of the language, yet we don’t find such devices (at least in any systematic and substantial way). Words remain discrete, yet voices are continuous. Why does spoken language eschew a resource that would enhance it? I don’t know, but here is a suggestion: the human language faculty is not in itself a vocal capacity; it is an internal cognitive system with no essential connection to the voice. We know there are visual sign languages with the same basic structure as vocally expressed languages, so the language faculty is not inherently vocal. The vocal system is just one way to externalize the internal language faculty, and that faculty is essentially discrete. The reason we don’t exploit the analogue powers of the vocal system is that the language faculty is a modality-neutral system—speech merely expresses this system, it doesn’t constitute it. Perhaps we could with an effort of will supplement our linguistic resources with analogue symbols, but then we would be stepping outside of the (innate, inherited) language system that lies beneath particular types of sensory-motor articulation. It just isn’t natural. It might be better logically or expressively, but it isn’t what the language faculty intrinsically is as a contingently evolved biological system. The mutation that led to it included no instructions for analogue sentences, though other mutations might have led to such sentences (as in bee language). In other words, our discretely structured language faculty reflects our specific biological nature more than it reflects the objective structure of the word. The world is full of continuities, but our language prefers to stick with discreteness. Thus we digitize continuous magnitudes whether they like it or not. Whether this leads to a distorted picture of reality is an interesting question.  Human language is undoubtedly a magnificent machine, but its parts are stubbornly block-like. That is just the way it evolved to be, maximally logical or not.
 In writing we could use size of letter or thickness of line to indicate degrees. What matters is that we use a medium that can vary continuously, as the height of a column of mercury does in a thermometer. In principle, we could wheel in musical instruments to fine-tune our vocal performances.
 One possibility is that perception corrects for the distortions promoted by language: we can see that the world is not totally discrete, despite the intimations of our language faculty. A creature with our type of language but no perceptual experience might be more misled about the nature of reality.