5 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. |
16007 | I assume existence, rather than reasoning towards it [Kierkegaard] |
Full Idea: I always reason from existence, not towards existence. | |
From: Søren Kierkegaard (Philosophical Fragments [1844], p.40) | |
A reaction: Kierkegaard's important premise to help show that theistic proofs for God's existence don't actually prove existence, but develop the content of a conception. [SY] |
16013 | Nothing necessary can come into existence, since it already 'is' [Kierkegaard] |
Full Idea: Can the necessary come into existence? That is a change, and everything that comes into existence demonstrates that it is not necessary. The necessary already 'is'. | |
From: Søren Kierkegaard (Philosophical Fragments [1844], p.74) | |
A reaction: [SY] |
12702 | Causes can be inferred from perfect knowledge of their effects [Leibniz] |
Full Idea: Whoever understands some effect perfectly will also arrive at the knowledge of its cause. | |
From: Gottfried Leibniz (Meditatio de principio individui [1676], A6.3.490), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 2 | |
A reaction: This sounds highly improbable, given that you would have thought that there could be lots of ways to bring about the same effect. Predicting effects is rather more plausible. I suppose if you can record all the ripples in the pond before they fade... |