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All the ideas for 'poems', 'Philosophy of Mathematics' and 'Commentary on the Sentences'

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6 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10882 Predicative definitions only refer to entities outside the defined collection [Horsten]
     Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.4)
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10884 A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
     Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.2)
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10885 Computer proofs don't provide explanations [Horsten]
     Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.3)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10881 The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
     Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.3)
9. Objects / D. Essence of Objects / 12. Essential Parts
16792 If parts change, the whole changes [William of Ockham]
     Full Idea: That is not the same whole that does not have the same parts.
     From: William of Ockham (Commentary on the Sentences [1320], IV.13), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 29.2
     A reaction: In isolation, this is mereological essentialism (as Pasnau confirms), which is incredibly implausible, if I cease to be the same person when I cut one of my fingernails.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
6017 Nomos is king [Pindar]
     Full Idea: Nomos is king.
     From: Pindar (poems [c.478 BCE], S 169), quoted by Thomas Nagel - The Philosophical Culture
     A reaction: This seems to be the earliest recorded shot in the nomos-physis wars (the debate among sophists about moral relativism). It sounds as if it carries the full relativist burden - that all that matters is what has been locally decreed.