Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Summa quaestionum super Sententias' and 'Reply to Richards'

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5 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
The greatest philosophers are methodical; it is what makes them great [Grice]
     Full Idea: The greatest philosophers have been the greatest, and most self-conscious, methodologists; indeed, I am tempted to regard the fact as primarily accounting for their greatness as philosophers.
     From: H. Paul Grice (Reply to Richards [1986], p.66), quoted by Stephen Boulter - Why Medieval Philosophy Matters 3
     A reaction: I agree. Philosophy is nothing if it is not devoted to the attempt to be fully rational, and that implies consistency and coherence. If a thinker doesn't even try to be systematic, I would not consider them to be a philosopher.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
8. Modes of Existence / A. Relations / 1. Nature of Relations
Relations do not add anything to reality, though they are real aspects of the world [Olivi]
     Full Idea: It does not seem that a relation adds anything real to that on which it is founded, but only makes for another real aspect belonging to the same thing. It is real since an aspect exists in re, not solely in the intellect, but it is not another thing.
     From: Peter John Olivi (Summa quaestionum super Sententias [1290], II.54), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.4
9. Objects / C. Structure of Objects / 4. Quantity of an Object
Quantity just adds union and location to the extension of parts [Olivi]
     Full Idea: Quantity or extension adds absolutely nothing really distinct to the quantified matter or to the extended and quantified form, except perhaps the union and location and position of those parts.
     From: Peter John Olivi (Summa quaestionum super Sententias [1290], II:58,II:440), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.1
     A reaction: Other views seem to say that the Quantity provides the extension, but he seems to take that as given.
27. Natural Reality / G. Biology / 5. Species
Things are limited by the species to certain modes of being [Olivi]
     Full Idea: A subject is limited by its species to certain modes of being.
     From: Peter John Olivi (Summa quaestionum super Sententias [1290], I:586-7), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.2
     A reaction: I think this is so very the wrong way round. Species characteristics are generalisations about similar individual creatures. The 'species' doesn't do anything at all. It is a classification. See ring species, for example.