Combining Texts

All the ideas for 'Introduction to 'Virtues of Authenticity'', 'Metaphysics as a Guide to Morals' and 'What Numbers Are'

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6 ideas

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17813 Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]
     Full Idea: The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers.
     From: Nicholas P. White (What Numbers Are [1974], V)
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17812 Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
     Full Idea: Statements involving finite cardinalities can be made without treating numbers as objects at all, simply by using quantification and identity to define numerically definite quantifiers in the manner of Frege.
     From: Nicholas P. White (What Numbers Are [1974], IV)
     A reaction: [He adds Quine 1960:268 as a reference]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
17945 Forms are not a theory of universals, but an attempt to explain how predication is possible [Nehamas]
     Full Idea: The theory of Forms is not a theory of universals but a first attempt to explain how predication, the application of a single term to many objects - now considered one of the most elementary operations of language - is possible.
     From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxvii)
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
17946 Only Tallness really is tall, and other inferior tall things merely participate in the tallness [Nehamas]
     Full Idea: Only Tallness and nothing else really is tall; everything else merely participates in the Forms and, being excluded from the realm of Being, belongs to the inferior world of Becoming.
     From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxviii)
     A reaction: This is just as weird as the normal view (and puzzle of participation), but at least it makes more sense of 'metachein' (partaking).
11. Knowledge Aims / A. Knowledge / 2. Understanding
17944 'Episteme' is better translated as 'understanding' than as 'knowledge' [Nehamas]
     Full Idea: The Greek 'episteme' is usually translated as 'knowledge' but, I argue, closer to our notion of understanding.
     From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xvi)
     A reaction: He agrees with Julia Annas on this. I take it to be crucial. See the first sentence of Aristotle's 'Metaphysics'. It is explanation which leads to understanding.
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
22591 We know perfection when we see what is imperfect [Murdoch]
     Full Idea: We know of perfection as we look upon what is imperfect.
     From: Iris Murdoch (Metaphysics as a Guide to Morals [1992], 13)
     A reaction: This is in the context of a discussion of the ontological argument for God's existence, but I seize on it as a nice expression of the idealisation capacity of our minds. The alternative is that perfection is innate idea, since we aren't seeing it.