Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'The Architecture of Mathematics' and 'on Goodman's 'Ways of Worldmaking''

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.

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

10190	From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]
	Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures.
	From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79
	A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s.

7. Existence / D. Theories of Reality / 6. Physicalism

18438	Every worldly event, without exception, is a redistribution of microphysical states [Quine]
	Full Idea: Nothing happens in the world, not the flutter of an eyelid, not the flicker of a thought, without some redistribution of microphysical states.
	From: Willard Quine (on Goodman's 'Ways of Worldmaking' [1978], p.98)
	A reaction: Is this causation, identity, or baffling supervenience?

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.