Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'The Myth of the Aesthetic Attitude' and 'Philosophy of Mathematics'

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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 / B. Unity of Objects / 2. Substance / d. Substance defined

19347	Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
	Full Idea: For individuation, substance needs three properties: independence, to separate it from other things; unity, to call it one thing, rather than an aggregate; and permanence or stability over time. Its other role is as subject for predicates.
	From: Franklin Perkins (Leibniz: Guide for the Perplexed [2007], 3.1)
	A reaction: Perkins is describing the Aristotelian view, which is taken up by Leibniz. 'Substance' is not a controversial idea, if we see that it only means that the world is full of 'things'. It is an unusual philosopher wholly totally denies that.

21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude

20443	The aesthetic attitude is nothing more than paying close attention [Dickie, by Giovannelli]
	Full Idea: Once analysed, Dickie claimed, the so-called aesthetic attitude is not special at all, but is rather just a matter of close attention and focus on the subject.
	From: report of George Dickie (The Myth of the Aesthetic Attitude [1964]) by Alessandro Giovannelli - Some contemporary developments (aesthetics) 1
	A reaction: Sounds wrong. If a paint specialist gives close attention to a painting, they do not necessarily have an aesthetic view of it. You need to know the aim of the activity, just as when you watch a game.