Combining Texts

All the ideas for 'Philosophical Fragments', 'Rechnungsmethoden (dissertation)' and 'Meditatio de principio individui'

unexpand these ideas     |    start again     |     specify just one area for these texts

5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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.
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
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.
7. Existence / A. Nature of Existence / 5. Reason for Existence
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]
10. Modality / A. Necessity / 2. Nature of Necessity
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]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
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...