Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Interview with Baggini and Stangroom' and 'Introduction to Russell's Theory of Types'

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7 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason

6851	We overvalue whether arguments are valid, and undervalue whether they are interesting [Monk]
	Full Idea: We encourage students to be concerned with whether an argument is valid or not, and we don't encourage them much to consider the question of whether the argument is interesting or not.
	From: Ray Monk (Interview with Baggini and Stangroom [2001], p.16)
	A reaction: What do you make of arguments which are very interesting, but (unfortunately) totally invalid? That said, this is a nice comment. A philosopher cannot contemplate too long or too deeply on the question of what is really 'interesting'.

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.

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility

18170	The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine]
	Full Idea: The Axiom of Reducibility is self-effacing: if it is true, the ramification it is meant to cope with was pointless to begin with.
	From: Willard Quine (Introduction to Russell's Theory of Types [1967], p.152), quoted by Penelope Maddy - Naturalism in Mathematics I.1
	A reaction: Maddy says the rejection of Reducibility collapsed the ramified theory of types into the simple theory.

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.

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.

22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics

6850	Wittgenstein pared his life down in his search for decency [Monk]
	Full Idea: One of the most conspicuous things about Wittgenstein is that, on the ethics side, he pared his life down to the minimum, so as to make as central as possible his search for decency, the drive to be a decent person.
	From: Ray Monk (Interview with Baggini and Stangroom [2001], p.14)
	A reaction: It rather looks as if decency was quite an effort for him, as he had a rather waspish temperament, and people found it hard to get close to him. On the whole, though, he sounds like good company, as do nearly all the great philosophers.