4 ideas
| 18256 | Quantity is inconceivable without the idea of addition [Frege] |
| Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former. | |
| From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit' | |
| A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree. |
| 9831 | Geometry appeals to intuition as the source of its axioms [Frege] |
| Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms. | |
| From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged. |
| 16661 | There are two sorts of category - referring to things, and to circumstances of things [Boethius] |
| Full Idea: Is it not now clear what the difference is between items in the categories? Some serve to refer to a thing, whereas others serve to refer to the circumstances of a thing. | |
| From: Boethius (Concerning the Trinity [c.518], Ch. 4), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.5 |
| 16668 | Modes of things exist in some way, without being full-blown substances [Gassendi] |
| Full Idea: Modes are not nothing but something more than mere nothing; they are therefore 'res' of some kind, not substantial of course, but at least modal. | |
| From: Pierre Gassendi (Disquisitions [1644], II.3.4), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 260 | |
| A reaction: This is the great modern atomist talking pure scholastic metaphysics. He's been reading Suárez. Gassendi seems to accept more than one type of existence. |