---
title: "Grundzüge der theoretischen Logik"
authors:
  - "David Hilbert"
  - "Wilhelm Ackermann"
year: 1928
venue: "Springer"
arxiv: null
doi: "10.1007/978-3-642-86848-1"
source: "https://link.springer.com/book/10.1007/978-3-642-86848-1"
topics:
  - first-order-logic
  - entscheidungsproblem
  - hilbert-program
seed_rank: 491
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 10
lineage: foundations-of-computing
cites:
  - title: "Mathematical Problems (Hilbert's Problems)"
    url: "https://www.ams.org/bull/1902-08-10/S0002-9904-1902-00923-3/S0002-9904-1902-00923-3.pdf"
    year: 1900
    doi: "10.1090/S0002-9904-1902-00923-3"
see:
  - "487-mathematical-problems-hilbert-s-problems"
---

# Grundzüge der theoretischen Logik

## One-sentence takeaway

Hilbert and Ackermann give the textbook axiomatization of first-order logic and state the Entscheidungsproblem — find a finite procedure that decides validity of any FOL formula — that Church and Turing prove unsolvable.

## Why it matters here

The named source Turing cites when he reduces the Entscheidungsproblem to the halting problem; Broadside's logic cards start here, not from later popularizations.

## Key ideas

- Clean axiomatic propositional and first-order calculi, with the now-standard distinction between validity and provability.
- Explicit Entscheidungsproblem: a general decision method for the *engere Funktionenkalkül* (first-order logic).
- Hilbert-school proof-theory pedagogy that later editions (1938, 1949) revise; quote the 1928 first edition for the historical problem statement.
- Companion to Hilbert's consistency program: logic is the instrument, arithmetic the intended application.

## Caveats

## Links

- DOI: [10.1007/978-3-642-86848-1](https://doi.org/10.1007/978-3-642-86848-1)
- Springer: https://link.springer.com/book/10.1007/978-3-642-86848-1