---
title: "The Concept of Truth in Formalized Languages"
authors:
  - "Alfred Tarski"
year: 1933
venue: "Polish original 1933; German 1935; English in Logic, Semantics, Metamathematics"
arxiv: null
doi: null
source: "https://hackettpublishing.com/logic-semantics-metamathematics"
topics:
  - tarski
  - truth
  - semantics
  - metamathematics
seed_rank: 631
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 9
lineage: foundations-of-computing
cites:
  - title: "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I"
    url: "https://doi.org/10.1007/BF01700692"
    year: 1931
    arxiv: null
    doi: "10.1007/BF01700692"
  - title: "Die Vollständigkeit der Axiome des logischen Funktionenkalküls"
    url: "https://doi.org/10.1007/BF01692469"
    year: 1930
    arxiv: null
    doi: "10.1007/BF01692469"
  - title: "Grundzüge der theoretischen Logik"
    url: "https://doi.org/10.1007/978-3-642-86848-1"
    year: 1928
    arxiv: null
    doi: "10.1007/978-3-642-86848-1"
see:
  - "500-uber-formal-unentscheidbare-satze-der-principia-mathematica-"
  - "499-die-vollstandigkeit-der-axiome-des-logischen-funktionenkalku"
  - "491-grundzuge-der-theoretischen-logik"
---

# The Concept of Truth in Formalized Languages

## One-sentence takeaway

Tarski defines a materially adequate, formally correct truth predicate for a formalized object language inside a stronger metalanguage, and proves that a language cannot define its own truth.

## Why it matters here

Semantic counterpart to Gödel incompleteness and the charter of model theory. Any claim that an ano program, a GRID COMMAND order, or a Broadside card is “true” has to live in a metalanguage — Convention T is why.

## Key ideas

- Convention T / T-schema: a truth definition must yield every instance of “‘P’ is true iff P”.
- Object language vs metalanguage: the truth predicate for L is not expressible in L if L is rich enough for arithmetic.
- Undefinability of truth (Tarski’s theorem) is the semantic twin of Gödel’s incompleteness.
- Polish 1933, German 1935 (*Studia Philosophica*); complete English text is Woodger/Corcoran in *Logic, Semantics, Metamathematics* (Hackett 2nd ed.).

## Caveats

## Links

- Hackett English edition: https://hackettpublishing.com/logic-semantics-metamathematics