Combining Texts

All the ideas for 'Explaining the A Priori', 'Precis of 'Limits of Abstraction'' and 'Structure and Ontology'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

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.

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 / D. Concepts / 2. Origin of Concepts / a. Origin of concepts

17722	The concept 'red' is tied to what actually individuates red things [Peacocke]
	Full Idea: The possession conditions for the concept 'red' of the colour red are tied to those very conditions which individuate the colour red.
	From: Christopher Peacocke (Explaining the A Priori [2000], p.267), quoted by Carrie Jenkins - Grounding Concepts 2.5
	A reaction: Jenkins reports that he therefore argues that we can learn something about the word 'red' from thinking about the concept 'red', which is his new theory of the a priori. I find 'possession conditions' and 'individuation' to be very woolly concepts.

18. Thought / E. Abstraction / 3. Abstracta by Ignoring

9626	A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro]
	Full Idea: A structure is the abstract form of a system, focussing on the interrelationships among the objects, and ignoring any features of them that do not affect how they relate to other objects in the system.
	From: Stewart Shapiro (Structure and Ontology [1989], 146), quoted by James Robert Brown - Philosophy of Mathematics Ch.4
	A reaction: I find this account very attractive, even though it appeals to supposedly outmoded psychological abstractionism. It seems pretty close to Aristotle's view of things. Shapiro's account must face up to Frege's worries about these matters.

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.