Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'On Platonism in Mathematics' and 'Nietzsche, Genealogy, History'

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8 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.

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

10304	Very few things in set theory remain valid in intuitionist mathematics [Bernays]
	Full Idea: Very few things in set theory remain valid in intuitionist mathematics.
	From: Paul Bernays (On Platonism in Mathematics [1934])

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 / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

10303	Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
	Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought.
	From: Paul Bernays (On Platonism in Mathematics [1934], p.261)
	A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

10306	Mathematical abstraction just goes in a different direction from logic [Bernays]
	Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction.
	From: Paul Bernays (On Platonism in Mathematics [1934], p.268)
	A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic.

18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions

22235	Feelings are not unchanging, but have a history (especially if they are noble) [Foucault]
	Full Idea: We believe that feelings are immutable, but every sentiment, particularly the most noble and disinterested, has a history.
	From: Michel Foucault (Nietzsche, Genealogy, History [1971], p.86), quoted by Johanna Oksala - How to Read Foucault 5
	A reaction: This is the sort of remark that makes me think Foucault is worth reading. Aristotle thought you could teach correct feelings. That implies that you can also teach incorrect feelings.

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.