Combining Texts

Ideas for 'Parmenides', 'On Eternal and Immutable Morality' and 'On What There Is'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

5 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
16150 One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
     Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it.
     From: Plato (Parmenides [c.364 BCE], 144a)
     A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
1613 Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine]
     Full Idea: The logicism of Frege, Russell, Whitehead, Church and Carnap condones the use of bound variables or reference to abstract entities known and unknown, specifiable and unspecifiable, indiscriminately.
     From: Willard Quine (On What There Is [1948], p.14)
6. Mathematics / C. Sources of Mathematics / 7. Formalism
1616 Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine]
     Full Idea: The formalism of Hilbert keeps classical maths as a play of insignificant notations. Agreement is found among the rules which, unlike the notations, are quite significant and intelligible.
     From: Willard Quine (On What There Is [1948], p.15)
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
1615 Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine]
     Full Idea: The intuitionism of Poincaré, Brouwer, Weyl and others holds that classes are invented, and accepts reference to abstract entities only if they are constructed from pre-specified ingredients.
     From: Willard Quine (On What There Is [1948], p.14)
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
1614 Conceptualism holds that there are universals but they are mind-made [Quine]
     Full Idea: Conceptualism holds that there are universals but they are mind-made.
     From: Willard Quine (On What There Is [1948], p.14)