Combining Texts

All the ideas for 'Concerning the Trinity', 'Rechnungsmethoden (dissertation)' and 'Entity and Identity'

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 / 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
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
16980 We need a logical use of 'object' as predicate-worthy, and an 'ontological' use [Strawson,P]
     Full Idea: There is a good case for a conservative reform of the word 'object'. Objects in the 'logical' sense would be all predicate-worthy identifiabilia whatever. Objects in the 'ontological' sense would form one ontological category among many others.
     From: Peter F. Strawson (Entity and Identity [1978], I n4)
     A reaction: This ambiguity has caused me no end of confusion (and irritation!). I wish philosophers wouldn't hijack perfectly good English words and give them weird meanings. Nice to have a distinguished fellow like Strawson make this suggestion.
9. Objects / D. Essence of Objects / 3. Individual Essences
16979 It makes no sense to ask of some individual thing what it is that makes it that individual [Strawson,P]
     Full Idea: For no object is there a unique character or relation by which it must be identified if it is to be identified at all. This is why it makes no sense to ask, impersonally and in general, of some individual object what makes it the individual object it is.
     From: Peter F. Strawson (Entity and Identity [1978], I)
     A reaction: He links this remark with the claim that there is no individual essence, but he seems to view an individual essence as indispensable to recognition or individuation of the object, which I don't see. Recognise it first, work out its essence later.