Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Intro to Oxford Hndbk of Metaphysics' and 'The Foundations of Mathematics (2nd ed)'

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6 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual

9217	Modern empirical metaphysics focuses on ontological commitments of discourse, or on presuppositions [Loux/Zimmerman]
	Full Idea: The empiricist revival of metaphysics came with Quine, who focused on ontological commitments associated with accepting a body of discourse, and Strawson, asking about the presuppositions of our conceptual practices.
	From: M Loux / D Zimmerman (Intro to Oxford Hndbk of Metaphysics [2003])
	A reaction: I find myself preferring the British approach. I can discourse about things without ontological commitment, and utter truths about non-existent things. I really yearn, though, for the third way - actually reasoning towards knowing what's out there.

2. Reason / D. Definition / 2. Aims of Definition

10528	Definitions concern how we should speak, not how things are [Fine,K]
	Full Idea: Our concern in giving a definition is not to say how things are by to say how we wish to speak
	From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)
	A reaction: This sounds like an acceptable piece of wisdom which arises out of analytical and linguistic philosophy. It puts a damper on the Socratic dream of using definition of reveal the nature of reality.

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle

10529	If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
	Full Idea: Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth.
	From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)
	A reaction: This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers.

10530	Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
	Full Idea: The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition.
	From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312)
	A reaction: I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition.

8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation

18465	An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen]
	Full Idea: R is an equivalence relation on A iff R is reflexive, symmetric and transitive on A.
	From: Kenneth Kunen (The Foundations of Mathematics (2nd ed) [2012], I.7.1)

18. Thought / E. Abstraction / 7. Abstracta by Equivalence

10527	An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
	Full Idea: If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not.
	From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307)
	A reaction: I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects.