Jump to ContentJump to Main Navigation
Enlightening SymbolsA Short History of Mathematical Notation and Its Hidden Powers$
Users without a subscription are not able to see the full content.

Joseph Mazur

Print publication date: 2016

Print ISBN-13: 9780691173375

Published to Princeton Scholarship Online: January 2018

DOI: 10.23943/princeton/9780691173375.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see http://www.universitypressscholarship.com/page/privacy-policy).date: 24 June 2018

Mental Pictures

Mental Pictures

Chapter:
(p.210) Chapter 23 Mental Pictures
Source:
Enlightening Symbols
Author(s):

Joseph Mazur

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691173375.003.0023

This chapter considers the mental pictures of thought and images in relation to algebraic symbols. According to Ludwig Wittgenstein, “We make to ourselves pictures of facts.” For Wittgenstein, the picture is a model of what we take to be real. The geneticist Francis Galton claimed that his thoughts almost never suggested words, and when those rare moments did suggest words, they were nonsense words like “the notes of a song might accompany thought.” As for words, the French mathematician Jacques Hadamard suggested that words are neither followed by thoughts, nor thoughts by words. He goes on to say that this is also the case when he is thinking about algebraic symbols. More revealing is Hadamard's presentation of his mental pictures of the steps in a proof that there are an unlimited number of prime numbers. The chapter also discusses thought without verbal language and in relation to proofs.

Keywords:   mental pictures, thought, images, algebraic symbols, Ludwig Wittgenstein, words, Jacques Hadamard, prime numbers, verbal language, proofs

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.