Skip to main content
Springer Nature Link
Log in
Menu
Find a journal Publish with us Track your research
Search
Saved research
Cart
  1. Home
  2. The bulletin of mathematical biophysics
  3. Article

A logical calculus of the ideas immanent in nervous activity

  • Published: December 1943
  • Volume 5, pages 115–133 (1943)
  • Cite this article

Access provided by Institution of Civil Engineers Library

Download PDF
Save article
View saved research
The bulletin of mathematical biophysics Aims and scope Submit manuscript
A logical calculus of the ideas immanent in nervous activity
Download PDF
  • Warren S. McCulloch1 &
  • Walter Pitts2 
  • 59k Accesses

  • 15k Citations

  • 628 Altmetric

  • 141 Mentions

  • Explore all metrics

Abstract

Because of the “all-or-none” character of nervous activity, neural events and the relations among them can be treated by means of propositional logic. It is found that the behavior of every net can be described in these terms, with the addition of more complicated logical means for nets containing circles; and that for any logical expression satisfying certain conditions, one can find a net behaving in the fashion it describes. It is shown that many particular choices among possible neurophysiological assumptions are equivalent, in the sense that for every net behaving under one assumption, there exists another net which behaves under the other and gives the same results, although perhaps not in the same time. Various applications of the calculus are discussed.

Article PDF

Download to read the full article text

Similar content being viewed by others

A Self-Similarity Logic May Shape the Organization of the Nervous System

Chapter ÂĐ 2024

Analysis of oscillating processes in spiking neural networks

Article 02 March 2023

Optimal time lags from causal prediction model help stratify and forecast nervous system pathology

Article Open access 22 October 2021

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.
  • Logic in AI
  • Logical Analysis
  • Mathematical Models of Cognitive Processes and Neural Networks
  • Neural Circuits
  • Neural Induction
  • Symbolic AI

Literature

  • Carnap, R. 1938.The Logical Syntax of Language. New York: Harcourt, Brace and Company.

    Google Scholar 

  • Hilbert, D., und Ackermann, W. 1927.GrundÞge der Theoretischen Logik. Berlin: J. Springer.

    Google Scholar 

  • Russell, B., and Whitehead, A. N. 1925.Principa Mathematica. Cambridge: Cambridge University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Medicine, Department of Psychiatry at the Illinois Neuropsychiatric Institute, University of Illinois, Illinois, USA

    Warren S. McCulloch

  2. The University of Chicago, Chicago, USA

    Walter Pitts

Authors
  1. Warren S. McCulloch
    View author publications

    Search author on:PubMed Google Scholar

  2. Walter Pitts
    View author publications

    Search author on:PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

McCulloch, W.S., Pitts, W. A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5, 115–133 (1943). https://doi.org/10.1007/BF02478259

Download citation

  • Issue date: December 1943

  • DOI: https://doi.org/10.1007/BF02478259

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Nervous Activity
  • Excitatory Synapse
  • Inhibitory Synapse
  • Temporal Summation
  • Spatial Summation

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us
  • Track your research

Footer Navigation

Discover content

  • Journals A-Z
  • Books A-Z
  • Subjects A-Z

Publish with us

  • Journal finder
  • Publish your research
  • Language editing
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our brands

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Discover

Corporate Navigation

  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support
  • Legal notice
  • Cancel contracts here

172.71.28.185

ICE Institution of Civil Engineers (3000167333) - Institution of Civil Engineers Library (2000027800)

Springer Nature

© 2026 Springer Nature