Combining Texts

All the ideas for 'fragments/reports', 'Philosophy of Mathematics' and 'Power/Knowledge'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

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?

24. Political Theory / C. Ruling a State / 1. Social Power

8991	Foucault can't accept that power is sometimes decent and benign [Foucault, by Scruton]
	Full Idea: It became impossible for Foucault to accept that power is sometimes decent and benign.
	From: report of Michel Foucault (Power/Knowledge [1980]) by Roger Scruton - Upon Nothing: Swansea lecture p.12
	A reaction: Actually Idea 7425 suggests that Foucault has no dream of eliminating power, but he does seem to be utterly in favour of maximum autonomy, and to regard paternalism as inherently evil. What sort of parent would Foucault have been?