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All the ideas for 'fragments/reports', 'Philosophy of Mathematics' and 'Religion and Respect'

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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)

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]
	Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
	From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?

23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect

23223	The word 'respect' ranges from mere non-interference to the highest levels of reverence [Blackburn]
	Full Idea: The word 'respect' seems to span a spectrum from simply not interfering, passing by on the other side, through admiration, right up to reverence and deference. This makes it uniquely well placed for ideological purposes.
	From: Simon Blackburn (Religion and Respect [2005], p.2)
	A reaction: Most people understand the world perfectly well, but only when they fully understand the context. I've taken to distinguishing conditional from unconditional forms of respect. Everyone is entitled to the unconditional form, which has limits.