Omnipresence, multipresence and ubiquity: kinds of generality in and around mathematics and logics
type: Item
instance of: scholarly article
title: Omnipresence, multipresence and ubiquity: kinds of generality in and around mathematics and logics
zbMATH Open document ID: 1261.00004
published in: Logica Universalis
publication date: 2013-03-19T00:00:00Z
review text: The author claims that three kinds of generality are to be found in mathematics and logic: omnipresent and multipresent theories and ``ubiquitous'' notions. The role of diagrams and notations in these two disciplines is stressed. Various consequences are explored -- one says about means of developing applied mathematics and about ways of elaborating or appraising theories. The problem of monism vs. pluralism in mathematics and in logic is considered. Some suggestions about the special character of mathematical and logical knowledge are made. Several historical examples are given and case studies are described.
reviewed by: Roman Murawski
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 01A85
Mathematics Subject Classification ID: 00A35
zbMATH DE Number: 6146089
zbMATH Keywords: history and philosophy of pure and applied mathematics
zbMATH Keywords: history and philosophy of symbolic logics
zbMATH Keywords: parts and moments
zbMATH Keywords: generality of theories
zbMATH Keywords: theory change
zbMATH Keywords: monism and pluralism
zbMATH Keywords: sets and multisets
zbMATH Keywords: abstract algebras
zbMATH Keywords: metamathematics
zbMATH Keywords: model theory
author: Ivor Grattan-Guinness
MaRDI profile type: Publication
full work available at URL: s11787-010-0023-0
OpenAlex ID: W2039988951
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Omnipresence, multipresence and ubiquity: kinds of generality in and around mathematics and logics (DOI)
DOI: 10.1007/S11787-010-0023-0