Combining Texts

All the ideas for 'Concerning the Trinity', 'Rechnungsmethoden (dissertation)' and 'The Sense of Reality'

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4 ideas

1. Philosophy / B. History of Ideas / 1. History of Ideas
7460 The great moments are the death of Aristotle, Machiavelli, and Romanticism [Berlin, by Watson]
     Full Idea: Berlin says there were three great turning points: after the death of Aristotle (when Greek schools focused on the inner life of individuals, instead of as social beings), Machiavelli's division of political and individual virtues, and Romanticism.
     From: report of Isaiah Berlin (The Sense of Reality [1996], p.168-9) by Peter Watson - Ideas Intro
     A reaction: I have the impression that Machiavelli introduced a new hard-boiled ethics, which dominated the sixteenth century, but in the seventeenth and eighteenth century they fought back, and Machiavellianism turned out to be just a phase.
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 / E. Categories / 1. Categories
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