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All the ideas for 'Precis of 'Limits of Abstraction'', 'Positions' and 'Is Hume's Principle analytic?'

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7 ideas

1. Philosophy / H. Continental Philosophy / 6. Deconstruction
Deconstruction is not neutral; it intervenes [Derrida]
     Full Idea: Deconstruction, I have insisted, is not neutral. It intervenes.
     From: Jacques Derrida (Positions [1971], p.76)
     A reaction: This, I think, is because there is in Derrida, as in most French philosophers, a strong streak of Marxism, and a desire to change the world, rather than merely understanding it. Idea 8213 shows the sort of thing he wants to change.
2. Reason / C. Styles of Reason / 1. Dialectic
I try to analyse certain verbal concepts which block and confuse the dialectical process [Derrida]
     Full Idea: I have tried to analyse certain marks in writing which are undecidables, false verbal properties, which inhabit philosophical opposition, resisting and disorganising it, without ever constituting a third term, withour ever leaving room for a solution.
     From: Jacques Derrida (Positions [1971], p.40)
     A reaction: [I have simplified his sentence!] Much of Derrida seems to be a commentary on the Hegelian dialectic, and the project is presumably to figure out why philosophy is not advancing in the way we would like. Interesting...
2. Reason / D. Definition / 2. Aims of Definition
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
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.
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
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.
An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos]
     Full Idea: Hume's Principle has a structure Boolos calls an 'abstraction principle'. Within the scope of two universal quantifiers, a biconditional connects an identity between two things and an equivalence relation. It says we don't care about other differences.
     From: George Boolos (Is Hume's Principle analytic? [1997]), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 3.7
     A reaction: This seems to be the traditional principle of abstraction by ignoring some properties, but dressed up in the clothes of formal logic. Frege tries to eliminate psychology, but Boolos implies that what we 'care about' is relevant.