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All the ideas for 'Precis of 'Limits of Abstraction'', 'Letters to Antoine Arnauld' and 'Space, Knowledge and Power (interview)'

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6 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy

15045	The big issue since the eighteenth century has been: what is Reason? Its effect, limits and dangers? [Foucault]
	Full Idea: I think the central issue of philosophy and critical thought since the eighteenth century has always been, still is, and will, I hope, remain the question: What is this Reason that we use? What are its historical effects? What are its limits and dangers?
	From: Michel Foucault (Space, Knowledge and Power (interview) [1982], p.358)
	A reaction: One can hardly deny the fairness of the question, but I hope that won't prevent us from trying to be rational. Maybe logicians do a better job of clarifying reason than the political and historical speculations of Foucault?

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.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

21963	It is possible that an omnipotent God might make one and two fail to equal three [Descartes]
	Full Idea: Since every basic truth depends on God's omnipotence, I would not dare to say that God cannot make it....that one and two should not be three.
	From: René Descartes (Letters to Antoine Arnauld [1645]), quoted by A.W. Moore - The Evolution of Modern Metaphysics 01.3
	A reaction: An unusual view. Most people would say that if Descartes can doubt something that simple, he should also doubt his reasons for believing in God's existence.

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.