Combining Texts

All the ideas for 'works', 'A Puzzle Concerning Matter and Form' and 'Rechnungsmethoden (dissertation)'

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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.
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
16755 The possible Aristotelian view that forms are real and active principles is clearly wrong [Fine,K, by Pasnau]
     Full Idea: Aristotle seems to have a possible basis for the belief [in individual forms], namely that forms are real and active principles in the world, which is denied by any right-minded modern.
     From: report of Kit Fine (A Puzzle Concerning Matter and Form [1994], p.19) by Robert Pasnau - Metaphysical Themes 1274-1671 24.3 n8
     A reaction: Pasnau says this is the view of forms promoted by the scholastics, whereas Aristotle's own view should be understood as 'metaphysical'.
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
     Full Idea: Philosophers are the forefathers of heretics.
     From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
6610 I believe because it is absurd [Tertullian]
     Full Idea: I believe because it is absurd ('Credo quia absurdum est').
     From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2
     A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though.