PhronesisThe true core
Grant the word first, in full. Infinite is right, in one exact sense — the sense that has a name.
Humboldt fixed it in 1836. Language, he wrote, "must therefore make infinite use of finite means" — von endlichen Mitteln einen unendlichen Gebrauch machen. The means are finite: a fixed stock of sounds, a fixed stock of words. The use is not. A grammar is a recursive rule for combining the stock, and a recursive rule has no ceiling — sentences nest inside sentences, and no longest sentence exists.
Chomsky adopted the phrase and later named the property. In Aspects (1965) he takes up Humboldt's line directly; the term discrete infinity comes later (Hauser, Chomsky and Fitch, 2002). Chomsky put it plainly in The Architecture of Language (2000): "you have six-word sentences, seven-word sentences but you don't have six-and-a-half-word sentences … there is no limit." Discrete, because the units are whole and countable. Infinite, because the combining never has to stop. The alphabet is finite; the grammar is not. The infinity lives in the combination, not in the primitives.
Any sound language
The seed's strong half is nearly literal. Any sound language — yes, from a small set.
Jakobson, Fant and Halle drew the map in 1952 (Preliminaries to Speech Analysis, MIT Acoustics Laboratory Technical Report No. 13). Every spoken language draws its phonemes from one universal pool of distinctive features — in that report, twelve binary oppositions: vocalic/non-vocalic, consonantal/non-consonantal, voiced/unvoiced, nasal/oral, and so on. And the load-bearing line: "No language contains all of these features." The pool is finite. Each language selects a subset of it, adds its own phonotactics — its rules for which sounds may sit beside which — and stops there. (The exact feature set was revised later, by Chomsky and Halle in 1968; the twelve are the 1952 count, not a permanent standard. What holds across the revisions is the shape: a finite pool, sampled.)
The sampling is small, and the range is wide. Maddieson's survey (Patterns of Sounds, 1984; the UPSID database) puts the smallest inventories near eleven segments — Rotokas at six consonants and five vowels, one of the two smallest UPSID records — and the largest past a hundred: Taa (ǃXóõ) with clicks, where the exact count is not well defined and runs from roughly 58 consonants to over 120 depending on whether click accompaniments and phonation contrasts are counted as separate phonemes or as clusters. Consonant inventories across languages range from about 6 to 95, mean near 23; vowels from 3 to 46, mean near 9. A living language is a finite sampling of the finite feature-space. So a small primitive set does generate any sound language — the strong half of the seed stands.
Where it over-reaches
The seed's other half is the reason to write, because as stated it does not hold. Evolve from those primitives — the visual glyphs — no.
The glyphs are real and old. Klüver catalogued them from mescaline self-experiments in the 1920s and named them form constants: lattices and honeycombs, cobwebs, tunnels and funnels, spirals (Mescal, and Mechanisms of Hallucinations, 1966). Many people see these same four classes in altered states; Allyson Grey's "secret writing" notates one such vision. They are not arbitrary. Ermentrout and Cowan (1979) and then Bressloff, Cowan, Golubitsky, Thomas and Wiener (2001) traced them to the visual cortex reading its own geometry — the retino-cortical map turns rings and rays in the eye into the stripes and lattices seen in the mind. The glyphs are the visual system's signature: what a patch of cortex draws when it samples the space it is built on.
There is no established derivation of spoken phonology from those glyphs. The visual cortex samples its own map. The auditory and vocal system samples a different space — the feature inventory, set by what the mouth can shape and the ear can tell apart. Two organs, two spaces, two signatures. They are parallel samplings in different modalities, not one grown from the other. Nothing in the record runs a line from the spiral to the phoneme.
The corrected claim
The seed points at something true, and it can be repaired. Here is the line, offered as a proposal.
Any sound language is a finite sampling of a finite feature-space, made unbounded by recursive combination — the same abstract form the visual glyphs instantiate in another modality. What is shared, and what is infinite, is the generative principle: finite means, infinite use. The primitives themselves stay finite, few, and modality-specific — the phonemes belong to the mouth, the glyphs to the eye. The two rhyme because both are small closed primitive sets under combination, not because one descends from the other.
Language must make infinite use of finite means.
Cousins, not lineage. The infinity is in the rule, held in common; the primitives are separate, each drawn from its own organ's geometry. That is the whole correction: keep the shared principle, drop the shared ancestry.
A fair aside
One question sits to the side, honest and worth a line: do the primitives carry any meaning of their own, or are they blank until combined?
Mostly blank. Saussure fixed the default in 1916 — l'arbitraire du signe, the arbitrariness of the sign: no natural reason ties a given sound to a given meaning. But not perfectly blank. Köhler's takete/baluma pairing (Gestalt Psychology, 1929), later maluma/takete, revived as bouba/kiki by Ramachandran and Hubbard (2001), shows people match rounded sounds to rounded shapes and sharp sounds to sharp ones, above chance and across many languages. The effect is real and it is limited — iconicity at the margins, a gradient bias layered on an arbitrary lexicon, appearing late in development rather than from the start. It does not overturn Saussure, and it does not rescue the causal claim. It only shows the primitives are not quite meaningless — which changes nothing about whether one modality grew from the other.
A finite alphabet sits at /field/alphabet: finite letters, and the count of what they spell refuses to stay finite.
Kin to The Introspection Ceiling, Perception Minus, Tacit Knowledge, and When Thought Becomes Artificial — with the generator at /field/alphabet.
Rests on: Humboldt, Über die Verschiedenheit des menschlichen Sprachbaues (1836; posthumous), "make infinite use of finite means," Heath trans. (Cambridge, 1988), p. 91; Chomsky, Aspects of the Theory of Syntax (MIT Press, 1965), p. 8, for the Humboldt adoption; Hauser, Chomsky & Fitch, "The Faculty of Language," Science 298 (2002): 1569–1579, for the term discrete infinity; Chomsky, The Architecture of Language (Oxford University Press, 2000), for the "six-word sentences … there is no limit" quotation; Jakobson, Fant & Halle, Preliminaries to Speech Analysis, MIT Acoustics Laboratory Technical Report No. 13 (1952) — twelve binary features, "No language contains all of these features"; Maddieson, Patterns of Sounds (Cambridge, 1984) and UPSID/WALS for inventory ranges (Rotokas ~11, Taa/ǃXóõ 100+ with the count analysis-dependent, consonants 6–95 mean ~23, vowels 3–46 mean ~9); Klüver, Mescal, and Mechanisms of Hallucinations (1966, from 1920s experiments) for the four form constants; Ermentrout & Cowan, "A mathematical theory of visual hallucination patterns," Biological Cybernetics 34 (1979): 137–150, and Bressloff, Cowan, Golubitsky, Thomas & Wiener, "Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex," Phil. Trans. R. Soc. B 356 (2001): 299–330, for the retino-cortical account; Saussure, Cours de linguistique générale (1916), for l'arbitraire du signe; Köhler, Gestalt Psychology (1929), and Ramachandran & Hubbard, "Synaesthesia — A Window Into Perception, Thought and Language," Journal of Consciousness Studies 8 (2001): 3–34, for takete/baluma (standardized to maluma/takete in the 1947 edition) and bouba/kiki — a real but limited effect (Ćwiek et al. 2022; Fort et al. 2023). Discrete infinity, distinctive features, and the form constants are all long established, cited as such. The corrected claim — that any sound language and the visual glyphs are cousins under one generative principle, not ancestor and descendant — is the proposal, offered to be argued with.