Nicolas Bourbaki and the concept of mathematical structure

@article{Corry1992NicolasBA,
  title={Nicolas Bourbaki and the concept of mathematical structure},
  author={Leo Corry},
  journal={Synthese},
  year={1992},
  volume={92},
  pages={315-348}
}
  • L. Corry
  • Published 1 September 1992
  • Philosophy
  • Synthese
In the present article two possible meanings of the term “mathematical structure” are discussed: a formal and a nonformal one. It is claimed that contemporary mathematics is structural only in the nonformal sense of the term. Bourbaki's definition of structure is presented as one among several attempts to elucidate the meaning of that nonformal idea by developing a formal theory which allegedly accounts for it. It is shown that Bourbaki's concept of structure was, from a mathematical point of… 

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References

SHOWING 1-10 OF 71 REFERENCES

Linearity and Reflexivity in the Growth of Mathematical Knowledge

  • L. Corry
  • Mathematics
    Science in Context
  • 1989
The Argument Recent studies in the philosophy of mathematics have increasingly stressed the social and historical dimensions of mathematical practice. Although this new emphasis has fathered

Mathematics and Reality

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the

The Genesis of the Abstract Group Concept: A Contribution to the History of the Origin of Abstract Group Theory

In this book, Hans Wussing sets out to trace the process of abstraction that led finally to the axiomatic formulation of the abstract notion of group. His main thesis is that the roots of the

The Architecture of Mathematics

1. Mathematic or mathematics? To present a view of the entire field of mathematical science as it exists,-this is an enterprise which presents, at first sight, almost insurmountable difficulties, on

Bourbaki N.. Théorie des ensembles. Éléments de Mathématique, Première partie, Livre I, Chapitres I, II. Actualités scientifiques et industrielles 1212. Hermann & Cie, Paris 1954, title pages + 136 pp.

  • R. Gandy
  • Mathematics
    Journal of Symbolic Logic
  • 1959
The second part is devoted to the deductive organization of the theories that were propounded before. A first basis of about forty theorems of the propositional calculus is constructed with

Perception and mathematical intuition

S ET theoretic realism is a view whose main tenets are that sets exist independently of human thought, and that set theory is the science of these entities.1 The foremost advocate of this position,

122. Free Topological Groups and Infinite Direct Product Topological Groups

1. The notion of a free topological group was introduced by A. Markoff1), and the existence of a free topological group for any completely regular topological space was established by him. Recently,

On universal mappings and free topological groups

It has been observed that constructions so apparently different as Kronecker products, extension of the ring of operators of a module, field of quotients of an integral domain, free groups, free

Foundations of mathematics for the working mathematician

It is doubtful whether extant documents will ever enable us to draw valid conclusions about those decisive centuries in early Greek science when the need for proofs first reached the level of consciousness and a technique was slowly and laboriously worked out to satisfy that need.

Theory of sets

The theory of sets is a theory which contains the relational signs =, ∈ and the substantific sign ⊃ (all these signs being of weight 2); in addition to the schemes S1 to S7 given in Chapter I, it
...