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All the ideas for 'Super Epistolam Pauli Apostoli', 'Philosophy of Mathematics' and 'Second Commentary on 'Isagoge''

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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)

8. Modes of Existence / D. Universals / 5. Universals as Concepts

15035	If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio]
	Full Idea: Boethius argued that universals can be successfully isolated by abstraction, even if they do not exist as separate entities in the world.
	From: report of Boethius (Second Commentary on 'Isagoge' [c.517]) by Claude Panaccio - Medieval Problem of Universals 'Sources'
	A reaction: Personally I rather like this unfashionable view. I can't think of any other plausible explanation, unless it is a less conscious psychological process of labelling. Boethius's idea led to medieval 'immanent realism'.

29. Religion / D. Religious Issues / 2. Immortality / a. Immortality

1863	If the soul achieves well-being in another life, it doesn't follow that I do [Aquinas]
	Full Idea: Even if soul achieves well-being in another life, that doesn't mean I do or any other human being does.
	From: Thomas Aquinas (Super Epistolam Pauli Apostoli [1272])