## Samenvatting

Most philosophers of mathematics only mention Whitehead as Russell's co-author of Principia Mathematica, and simply assume that, at least during their collaboration, both men shared the foundationist view on mathematics we nowadays call logicism. However, a closer look at Whitehead reveals that his ultimate motivation did not coincide with Russell's urge for certainty and mathematical foundations. Whitehead - as first manifest in his Universal Algebra - was striving for unification and mathematical synthesis. At the root of his enthusiasm, first for Grassmann's algebra of extensions, then for Russell's symbolic logic of relations, lay their potential to develop into unification-tools, enabling to think together various mathematical disciplines as diverse as non-metrical and metrical, Euclidean and non-Euclidean geometry. On top of that, Whitehead sensed the potential of the logic of relations to bridge the gap between the rough-edged world of sense-experiences and the smooth world of mathematical concepts.

So instead of accepting only two possible functions for one and the same logical apparatus - the Russellian reduction to atoms of certainty and the Wittgensteinian purification of language - we'd better consider a third option: the Whiteheadian unification of experience. Instead of calling Whitehead a logicist and identifying his approach with Russell's analytic search for the indubitable logical atoms to which the entire mathematical universe can be reduced, we'd better call Whitehead a relationist and value his continual attempts to tie all mathematical concepts, as well as the underlying processes and experiences, together by means of patterns, be they algebraic structures or logical relations. Instead of conceiving Whitehead as a happy inhabitant of the paradise of logical atomism, created by the vigour of Russell's conversion to anti-idealism, we'd better listen to Russell's statement that 'it was Whitehead who was the serpent in this paradise of Mediterranean clarity.'

So instead of accepting only two possible functions for one and the same logical apparatus - the Russellian reduction to atoms of certainty and the Wittgensteinian purification of language - we'd better consider a third option: the Whiteheadian unification of experience. Instead of calling Whitehead a logicist and identifying his approach with Russell's analytic search for the indubitable logical atoms to which the entire mathematical universe can be reduced, we'd better call Whitehead a relationist and value his continual attempts to tie all mathematical concepts, as well as the underlying processes and experiences, together by means of patterns, be they algebraic structures or logical relations. Instead of conceiving Whitehead as a happy inhabitant of the paradise of logical atomism, created by the vigour of Russell's conversion to anti-idealism, we'd better listen to Russell's statement that 'it was Whitehead who was the serpent in this paradise of Mediterranean clarity.'

Originele taal-2 | English |
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Titel | New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics |

Redacteuren | Bart Van Kerkhove |

Uitgeverij | World Scientific Publishing |

Pagina's | 207-221 |

Aantal pagina's | 15 |

ISBN van geprinte versie | 978-981-281-222-3 |

Status | Published - 2009 |

### Publicatie series

Naam | New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics |
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