---
title: "Introduction to a General Theory of Elementary Propositions"
authors:
  - "Emil L. Post"
year: 1921
venue: "American Journal of Mathematics"
arxiv: null
doi: "10.2307/2370324"
source: "https://doi.org/10.2307/2370324"
topics:
  - propositional-logic
  - post
  - completeness
  - truth-tables
seed_rank: 537
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 9
lineage: foundations-of-computing
cites:
  - title: "Grundzüge der theoretischen Logik"
    url: "https://link.springer.com/book/10.1007/978-3-642-86848-1"
    year: 1928
    arxiv: null
    doi: "10.1007/978-3-642-86848-1"
  - title: "Investigations into Logical Deduction"
    url: "https://doi.org/10.1007/BF01201353"
    year: 1935
    arxiv: null
    doi: "10.1007/BF01201353"
  - title: "The Two-Valued Iterative Systems of Mathematical Logic"
    url: "https://press.princeton.edu/books/paperback/9780691095707/the-two-valued-iterative-systems-of-mathematical-logic"
    year: 1941
    arxiv: null
    doi: null
see:
  - "491-grundzuge-der-theoretischen-logik"
  - "632-investigations-into-logical-deduction"
  - "538-the-two-valued-iterative-systems-of-mathematical-logic"
---

# Introduction to a General Theory of Elementary Propositions

## One-sentence takeaway

Post's 1920 doctoral work, published 1921, proves classical propositional logic complete via truth tables and simultaneously introduces the many-valued systems that later become Post algebras.

## Why it matters here

Early completeness result, before Gödel's FOL completeness. Anoptic standing rules and ano boolean columns are two-valued by default; this paper is why that default is a *complete* calculus, and why non-classical many-valued variants are a designed generalization rather than a bug.

## Key ideas

- Truth-table method decides every propositional tautology and shows the usual axioms are complete for classical two-valued logic.
- Generalizes the same table method to \(m\)-valued systems, seeding the lattice of clones developed in the 1941 monograph.
- 1920 Columbia dissertation published in *American Journal of Mathematics* 43 (1921).
- Completeness here is propositional only; first-order completeness is Gödel 1930.

## Caveats

## Links

- DOI: [10.2307/2370324](https://doi.org/10.2307/2370324)
- JSTOR: https://www.jstor.org/stable/2370324