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. |
| 6175 | External identification doesn't mean external location, as with sunburn [Davidson, by Rowlands] |
| Full Idea: Davidson observes that the inference from a thought being identified by a relation to something outside the head does not entail that the thought is not wholly in the head, just as sunburn is identified by external factors, but is still in the skin. | |
| From: report of Donald Davidson (Knowing One's Own Mind [1987]) by Mark Rowlands - Externalism Ch.8 | |
| A reaction: Rowlands (an externalist) agrees, and this strikes me as correct, and it needs to be one of the fixed points in any assessment of externalism. |
| 14409 | I am a presentist, and all language and common sense supports my view [Bigelow] |
| Full Idea: I am a presentist: nothing exists which is not present. Everyone believed this until the nineteenth century; it is writing into the grammar of natural languages; it is still assumed in everyday life, even by philosophers who deny it. | |
| From: John Bigelow (Presentism and Properties [1996], p.36), quoted by Trenton Merricks - Truth and Ontology | |
| A reaction: The most likely deniers of presentism seem to be physicists and cosmologists who have overdosed on Einstein. On the whole I vote for presentism, but what justifies truths about the past and future. Traces existing in the present? |