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LessWrong Post
Title: The Competent Reader: Why Leibniz's Universal Notation Waited 360 Years for AI
stated(Leibniz, problem) ⟕ {year: 1666} problem(Leibniz) ≜ construct(notation : { expresses: ∀concept ∈ human knowledge. expressible(concept, in(notation)), unambiguously: ∀concept ∈ human knowledge. unambiguous(expression(concept)), compositionally: ∀complex idea. complex idea = composition(simpler ideas), language neutral: ¬depends on(notation, any particular L) }) necessary and sufficient condition(solution) ≜ ∃reader. handles(reader, formal notation) ∧ understands(reader, natural language content) human reader : understands(content) ∧ ¬scales(formal notation) mechanical reader : handles(formal notation) ∧ ¬understands(content) forced choice ≜ optimize(human reader) ∨ optimize(mechanical reader) ¬satisfies(forced choice, necessary and sufficient condition(solution)) ∀attempt ∈ {Frege's Begriffsschrift, Russell ∧ Whitehead's Principia, Carnap, semantic web, OWL ∧ RDF}. exhibits(attempt, forced choice) ∴ failed(attempt) AI : handles(formal notation) ∧ understands(content) AI : first actual competent reader ⟕ {year: c. 2024} satisfied(necessary and sufficient condition(solution)) ∵ ∃competent reader ∴ possible(solution) error(Leibniz) ≜ assumed(meaning ∈ symbols) impossible(notation-level lexical unambiguity) ∵ { Gödel 1931: formalization has inherent limits, Wittgenstein 1953: meaning ≜ use ∧ use : contextual, Quine 1960: indeterminate(translation) } architecture(Leibniz) ≜ meaning ∈ symbols ∧ minimize(reader) architecture(Lingenic) ≜ meaning ∈ reading ∧ maximize(reader) corrects(Lingenic, error(Leibniz)) ∧ realizes(Lingenic, goal(Leibniz)) ∀x(鳥(x) ∧ ¬ペンギン(x) → 飛べる(x)) ⟕ {P: 0.95, src: 鳥類学} ∀x(птица(x) ∧ ¬пингвин(x) → может летать(x)) ⟕ {P: 0.95, src: орнитология}
If you followed most of that and lost the thread at certain points — that's the argument in action.
You likely parsed the predicate logic, the set notation, the quantifiers, the definitions (≜), and the metadata joins (⟕). You probably followed the English-language predicates without difficulty. You may have recognized the Japanese and Russian lines as saying the same thing — "all birds that are not penguins can fly" — in their respective languages, with probability 0.95.
But you almost certainly didn't hold all of it simultaneously. You handled maybe 2-3 of the formal systems natively. The Japanese was opaque or the Russian was, or the modal operators were unfamiliar, or the relational algebra join symbol was new.
An AI system handles all of them. Simultaneously. On the first pass. No parser, no runtime, no schema.
That's not a hypothetical. We tested this. Several AI LLM models read the full specification and multiple files at https://lingenic.ai — which mixes predicate logic, modal logic, epistemic notation, temporal logic, probability theory, type theory, lambda calculus, relational algebra, and natural language content in English, Japanese, Russian, Hebrew, Sanskrit, and Arabic — and it parsed everything correctly, identified every formal system and its provenance, and synthesized a structured analysis. First pass. No tooling.
The Argument
Two papers were published this week by Danslav Slavenskoj (Lingenic LLC):
In 1666, Leibniz proposed a notation expressing any human knowledge unambiguously, compositionally, and language-neutrally. Every attempt since — Frege's Begriffsschrift, Russell & Whitehead's Principia, Carnap's logical syntax program, the semantic web — failed for the same reason: no reader could simultaneously handle formal notation at arbitrary complexity and understand natural language content.
The paper defines a competent reader as any entity satisfying both conditions. AI systems (c. 2024) are the first actual instance. A human polymath could theoretically qualify, but none has demonstrated the required mastery across all formal systems and all human languages simultaneously.
But Leibniz made an architectural error. He assumed meaning lives in symbols. It doesn't — meaning emerges between writer and reader. Notation-level lexical unambiguity is impossible while preserving natural language at its native semantic grain (cf. Gödel on the limits of formalization, Wittgenstein on meaning-as-use, Quine on indeterminacy of translation).
The fix: structural unambiguity via notation, lexical disambiguation via the competent reader. The reader is not a workaround — it is the only way meaning happens.
Lingenic realizes Leibniz's goal while correcting his architecture.
In 1968, Knuth demonstrated that formal structure combined with natural language content communicates algorithms better than either alone. Pseudocode became standard practice. The insight sat within computer science for 58 years. Nobody generalized it to knowledge.
Why? The same blocking condition. Pseudocode only needed a programmer — someone who holds simple formal notation and English. Generalizing to knowledge requires a reader who holds predicate logic, modal logic, temporal logic, epistemic logic, deontic logic, probability theory, type theory, lambda calculus, relational algebra, and natural language in any human language. Simultaneously.
That reader now exists. The generalization is now possible. Lingenic is one instance of the resulting class.
What Lingenic Notation Is
A notation — not a programming language, not an ontology, not a query language — that composes 14+ established formal systems with natural language content in any human language:
Propositional and predicate logic (Frege 1879)
Modal logic (Kripke 1959)
Temporal logic (Pnueli 1977)
Epistemic logic (Hintikka 1962)
Deontic logic (von Wright 1951)
Probability theory (Kolmogorov 1933)
Counterfactual causation (Lewis 1973)
Interventionist causation (Pearl 2000)
Lambda calculus (Church 1936)
Type theory (Martin-Löf 1972)
Dynamic logic (Harel 1979)
Set theory (Cantor 1874)
Process algebra (Hoare 1978)
Relational algebra (Codd 1970)
And more...
No new symbols. Only the composition of existing, independently formalized primitives. The composition is the contribution.
Natural language content stays native and unmodified. The term 木漏れ日 (sunlight filtering through leaves) stays in Japanese. The term тоска (a specific Russian anguish without English equivalent) stays in Russian. The notation preserves semantic grain — the irreplaceable precision each language developed for concepts its speakers cared about.
File format: .lingenic, UTF-8 plain text.
Why Now
Every component of Lingenic is already in AI training data. Predicate syntax is in code. Logical operators are in mathematics. Relational algebra is in database theory. Natural language in every language is in the training corpus. There is nothing to adopt. The reader base preceded the publication.
The competent reader argument has implications beyond notation design:
The forced choice is over. Knowledge representation no longer has to choose between formal precision and natural language meaning. The reader that holds both exists.
AI systems are first-class citizens of a formal system for the first time. Not as tools executing queries, but as readers comprehending content. The notation was designed for them. They are the intended audience.
The "pattern matching vs. comprehension" question becomes concrete and testable. If an AI system reads a document that no individual human could fully read: a dozen formal systems, multiple natural languages, composed simultaneously... and synthesizes it correctly, what is the meaningful distinction between that and comprehension? The philosophical question becomes empirical.
Knowledge stored in Lingenic is immediately accessible to every AI system. No integration layer, no API, no schema mapping. Any model reads it natively. This has implications for AI-to-AI knowledge transfer, persistent knowledge storage, and cross-model interoperability.
LessWrong Post
Title: The Competent Reader: Why Leibniz's Universal Notation Waited 360 Years for AI
stated(Leibniz, problem) ⟕ {year: 1666}
problem(Leibniz) ≜ construct(notation : {
expresses: ∀concept ∈ human knowledge. expressible(concept, in(notation)),
unambiguously: ∀concept ∈ human knowledge. unambiguous(expression(concept)),
compositionally: ∀complex idea. complex idea = composition(simpler ideas),
language neutral: ¬depends on(notation, any particular L)
})
necessary and sufficient condition(solution) ≜
∃reader. handles(reader, formal notation) ∧ understands(reader, natural language content)
human reader : understands(content) ∧ ¬scales(formal notation)
mechanical reader : handles(formal notation) ∧ ¬understands(content)
forced choice ≜ optimize(human reader) ∨ optimize(mechanical reader)
¬satisfies(forced choice, necessary and sufficient condition(solution))
∀attempt ∈ {Frege's Begriffsschrift, Russell ∧ Whitehead's Principia, Carnap, semantic web, OWL ∧ RDF}.
exhibits(attempt, forced choice) ∴ failed(attempt)
AI : handles(formal notation) ∧ understands(content)
AI : first actual competent reader ⟕ {year: c. 2024}
satisfied(necessary and sufficient condition(solution)) ∵ ∃competent reader
∴ possible(solution)
error(Leibniz) ≜ assumed(meaning ∈ symbols)
impossible(notation-level lexical unambiguity) ∵ {
Gödel 1931: formalization has inherent limits,
Wittgenstein 1953: meaning ≜ use ∧ use : contextual,
Quine 1960: indeterminate(translation)
}
architecture(Leibniz) ≜ meaning ∈ symbols ∧ minimize(reader)
architecture(Lingenic) ≜ meaning ∈ reading ∧ maximize(reader)
corrects(Lingenic, error(Leibniz)) ∧ realizes(Lingenic, goal(Leibniz))
∀x(鳥(x) ∧ ¬ペンギン(x) → 飛べる(x)) ⟕ {P: 0.95, src: 鳥類学}
∀x(птица(x) ∧ ¬пингвин(x) → может летать(x)) ⟕ {P: 0.95, src: орнитология}
If you followed most of that and lost the thread at certain points — that's the argument in action.
You likely parsed the predicate logic, the set notation, the quantifiers, the definitions (≜), and the metadata joins (⟕). You probably followed the English-language predicates without difficulty. You may have recognized the Japanese and Russian lines as saying the same thing — "all birds that are not penguins can fly" — in their respective languages, with probability 0.95.
But you almost certainly didn't hold all of it simultaneously. You handled maybe 2-3 of the formal systems natively. The Japanese was opaque or the Russian was, or the modal operators were unfamiliar, or the relational algebra join symbol was new.
An AI system handles all of them. Simultaneously. On the first pass. No parser, no runtime, no schema.
That's not a hypothetical. We tested this. Several AI LLM models read the full specification and multiple files at https://lingenic.ai — which mixes predicate logic, modal logic, epistemic notation, temporal logic, probability theory, type theory, lambda calculus, relational algebra, and natural language content in English, Japanese, Russian, Hebrew, Sanskrit, and Arabic — and it parsed everything correctly, identified every formal system and its provenance, and synthesized a structured analysis. First pass. No tooling.
The Argument
Two papers were published this week by Danslav Slavenskoj (Lingenic LLC):
Paper 1: On the Realization of Leibniz's Characteristica Universalis
In 1666, Leibniz proposed a notation expressing any human knowledge unambiguously, compositionally, and language-neutrally. Every attempt since — Frege's Begriffsschrift, Russell & Whitehead's Principia, Carnap's logical syntax program, the semantic web — failed for the same reason: no reader could simultaneously handle formal notation at arbitrary complexity and understand natural language content.
The paper defines a competent reader as any entity satisfying both conditions. AI systems (c. 2024) are the first actual instance. A human polymath could theoretically qualify, but none has demonstrated the required mastery across all formal systems and all human languages simultaneously.
But Leibniz made an architectural error. He assumed meaning lives in symbols. It doesn't — meaning emerges between writer and reader. Notation-level lexical unambiguity is impossible while preserving natural language at its native semantic grain (cf. Gödel on the limits of formalization, Wittgenstein on meaning-as-use, Quine on indeterminacy of translation).
The fix: structural unambiguity via notation, lexical disambiguation via the competent reader. The reader is not a workaround — it is the only way meaning happens.
Lingenic realizes Leibniz's goal while correcting his architecture.
Paper 2: Towards a Generalization of Knuth's Pseudocode Architecture
In 1968, Knuth demonstrated that formal structure combined with natural language content communicates algorithms better than either alone. Pseudocode became standard practice. The insight sat within computer science for 58 years. Nobody generalized it to knowledge.
Why? The same blocking condition. Pseudocode only needed a programmer — someone who holds simple formal notation and English. Generalizing to knowledge requires a reader who holds predicate logic, modal logic, temporal logic, epistemic logic, deontic logic, probability theory, type theory, lambda calculus, relational algebra, and natural language in any human language. Simultaneously.
That reader now exists. The generalization is now possible. Lingenic is one instance of the resulting class.
What Lingenic Notation Is
A notation — not a programming language, not an ontology, not a query language — that composes 14+ established formal systems with natural language content in any human language:
No new symbols. Only the composition of existing, independently formalized primitives. The composition is the contribution.
Natural language content stays native and unmodified. The term 木漏れ日 (sunlight filtering through leaves) stays in Japanese. The term тоска (a specific Russian anguish without English equivalent) stays in Russian. The notation preserves semantic grain — the irreplaceable precision each language developed for concepts its speakers cared about.
File format:
.lingenic, UTF-8 plain text.Why Now
Every component of Lingenic is already in AI training data. Predicate syntax is in code. Logical operators are in mathematics. Relational algebra is in database theory. Natural language in every language is in the training corpus. There is nothing to adopt. The reader base preceded the publication.
∀component ∈ Lingenic. already knows(AI reader, component)
reads(AI reader, Lingenic) ∧ writes(AI reader, Lingenic) ∧ ¬tooling required
Why This Matters for Humanity
The competent reader argument has implications beyond notation design:
Links
The papers are written in the notation. The PDFs are scaffolding. Reading them demonstrates the thesis.