---
title: "Begriffsschrift"
authors:
  - "Gottlob Frege"
year: 1879
venue: "Halle: Louis Nebert"
arxiv: null
doi: null
source: "https://gdz.sub.uni-goettingen.de/id/PPN538957069"
topics:
  - logic
  - frege
  - quantification
seed_rank: 489
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 9
lineage: foundations-of-computing
---

# Begriffsschrift

## One-sentence takeaway

Frege's 1879 ideography is the first fully formal quantificational logic: a two-dimensional notation for implication, negation, and the universal quantifier in which proofs are gapless symbol manipulations.

## Why it matters here

Without this formal language there is no clean Hilbert-program target and no precise Entscheidungsproblem; every later completeness or incompleteness theorem sits on Frege's quantifiers.

## Key ideas

- A *Begriffsschrift* (concept-script) modelled on arithmetic notation, not on subject–predicate grammar, so nested quantification is writable.
- Primitive devices: the content stroke, judgment stroke, implication (condition stroke), negation, and the concavity for generality.
- Identity of content and substitution rules let derivations be checked without leftover natural-language glue.
- Direct ancestor of the first-order language Hilbert–Ackermann axiomatize and Gödel arithmetizes.

## Caveats

## Links

- GDZ scan: https://gdz.sub.uni-goettingen.de/id/PPN538957069
- Zenodo PDF: https://zenodo.org/records/6330677