Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Replies to Critics' and 'Frege on Knowing the Third Realm'

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6 ideas

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.

3. Truth / C. Correspondence Truth / 1. Correspondence Truth

18702	Names, descriptions and predicates refer to things; without that, language and thought are baffling [Davidson]
	Full Idea: The simple thesis that names and descriptions often refer to things, and that predicates often have an extension in the world of things, is obvious, and essential to the most elementary appreciation of both language and the thoughts we express.
	From: Donald Davidson (Replies to Critics [1998], p.323)
	A reaction: In 1983 Davidson had been a rare modern champion of the coherence theory of truth, but this is his clearest later renunciation of that view (and quite right too).

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic

13479	Given that thinking aims at truth, logic gives universal rules for how to do it [Burge]
	Full Idea: The laws of logic - which are constituted by atemporal thoughts and atemporal subject matter - provide universal prescriptions of how one ought to think, given that one's thinking has the function of attaining truth.
	From: Tyler Burge (Frege on Knowing the Third Realm [1992], p.316)
	A reaction: Burge is giving, and endorsing, Frege's view. Burge is fighting a rearguard action, when logical systems keep proliferating. See Idea 10282. I sympathise with the dream of Burge and Frege.

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.