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All the ideas for 'Actualism and Thisness', 'The Evolution of Modern Metaphysics' and 'Philosophy of Mathematics'

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7 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics

21959	Metaphysics is the most general attempt to make sense of things [Moore,AW]
	Full Idea: Metaphysics is the most general attempt to make sense of things.
	From: A.W. Moore (The Evolution of Modern Metaphysics [2012], Intro)
	A reaction: This is the first sentence of Moore's book, and a touchstone idea all the way through. It stands up well, because it says enough without committing to too much. I have to agree with it. It implies explanation as the key. I like generality too.

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 / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity

16463	Adams says actual things have haecceities, but not things that only might exist [Adams,RM, by Stalnaker]
	Full Idea: Adams favours haecceitism about actual things but no haecceities for things that might exist but don't.
	From: report of Robert Merrihew Adams (Actualism and Thisness [1981]) by Robert C. Stalnaker - Mere Possibilities 4.2
	A reaction: This contrasts with Plantinga, who proposes necessary essences for everything, even for what might exist. Plantinga sounds crazy to me, Adams merely interesting but not too plausible.

11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism

21958	Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW]
	Full Idea: Appearances in general are nothing outside our representations, which is just what we mean by transcendental ideality.
	From: A.W. Moore (The Evolution of Modern Metaphysics [2012], B535/A507)