Infinity: An Essay in MetaphysicsClarendon Press, 1964 - 289 pagina's |
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Pagina 55
... Brouwer and the Paradoxes If the names of Aristotle , Leibniz , Gauss and Cantor may be allowed to mark four of the five phases in our abridged history of the infinite in mathematics , then it is the name of Brouwer that looms largest ...
... Brouwer and the Paradoxes If the names of Aristotle , Leibniz , Gauss and Cantor may be allowed to mark four of the five phases in our abridged history of the infinite in mathematics , then it is the name of Brouwer that looms largest ...
Pagina 56
... Brouwer ] that its theorems lack a real meaning in terms of which they are true.1 Hilbert is thus seen to be in essential agreement with Brouwer on the ontological issue . Ontologically speaking , Hilbert is no less a finitist than Brouwer ...
... Brouwer ] that its theorems lack a real meaning in terms of which they are true.1 Hilbert is thus seen to be in essential agreement with Brouwer on the ontological issue . Ontologically speaking , Hilbert is no less a finitist than Brouwer ...
Pagina 129
... Brouwer is to mathematics . Brouwer is indeed the Kant of mathematics , an almost identical strategy being employed by both . Nevertheless , I believe that there may be some special justification for Brouwer's refusal to acquiesce in ...
... Brouwer is to mathematics . Brouwer is indeed the Kant of mathematics , an almost identical strategy being employed by both . Nevertheless , I believe that there may be some special justification for Brouwer's refusal to acquiesce in ...
Inhoudsopgave
INFINITY | 1 |
HYPERMATHEMATICS | 72 |
COSMOLOGY I | 102 |
Copyright | |
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absolutely actual infinite actual infinitesimal aleph-null argument Aristotle Brouwer Cantor certainly code number concept of number convergent series cosmological count countable decimal expansion denumerable discourse divergent series earth empirical entails equal exist fact falsifiable finite proof finitist follows formula geometry Grandi's series Hence Hyperboreans hypothesis inch infinite distance infinite number infinite sequence infinite series infinitesimal infinitum infinity insist integers intelligible interval Kant Leibniz logical Löwenheim-Skolem theorem mathe mathematician mathematics matics mean merely metaphysical minim minute natural numbers non-denumerable number of stars object ontological open end order-type paradox Peano postulates philosophy physics pluriverse possible potential infinite precisely predicates prime twin principle priori proof number proto-concept prove punct question random numbers rational real numbers rule seen sense serrated continuum Space spatial speaking standard concept straight line sum-total suppose Swahilis theorem thesis things transfinite tropological uncountable vulgar concept whole Wittgenstein word Z-series Zeno procedure