Omnipresence, multipresence and ubiquity: kinds of generality in and around mathematics and logics
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.
history and philosophy of pure and applied mathematics
history and philosophy of symbolic logics
scientific article; zbMATH DE number 6146089
scientific article