Combining Texts

All the ideas for 'fragments/reports', 'Capitalism and Community' and 'Replies on 'Limits of Abstraction''

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20 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Concern for rigour can get in the way of understanding phenomena [Fine,K]
     Full Idea: It is often the case that the concern for rigor gets in the way of a true understanding of the phenomena to be explained.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)
     A reaction: This is a counter to Timothy Williamson's love affair with rigour in philosophy. It strikes me as the big current question for analytical philosophy - of whether the intense pursuit of 'rigour' will actually deliver the wisdom we all seek.
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
There is no stage at which we can take all the sets to have been generated [Fine,K]
     Full Idea: There is no stage at which we can take all the sets to have been generated, since the set of all those sets which have been generated at a given stage will itself give us something new.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
We might combine the axioms of set theory with the axioms of mereology [Fine,K]
     Full Idea: We might combine the standard axioms of set theory with the standard axioms of mereology.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K]
     Full Idea: We are tempted to ask of second-order quantifiers 'what are you quantifying over?', or 'when you say "for some F" then what is the F?', but these questions already presuppose that the quantifiers are first-order.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005])
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K]
     Full Idea: In doing semantics we normally assign some appropriate entity to each predicate, but this is largely for technical convenience.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K]
     Full Idea: Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)
     A reaction: See Idea 10572.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
Why should a Dedekind cut correspond to a number? [Fine,K]
     Full Idea: By what right can Dedekind suppose that there is a number corresponding to any pair of irrationals that constitute an irrational cut?
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]
     Full Idea: What is the union of the singleton {0}, of zero, and the singleton {φ}, of the null set? Is it the one-element set {0}, or the two-element set {0, φ}? Unless the question of identity between 0 and φ is resolved, we cannot say.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]
     Full Idea: Set-theoretic imperialists think that it must be possible to represent every mathematical object as a set.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K]
     Full Idea: Logicists traditionally claim that the theorems of mathematics can be derived by logical means from the relevant definitions of the terms, and that these theorems are epistemically innocent (knowable without Kantian intuition or empirical confirmation).
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K]
     Full Idea: It is natural to have a generative conception of abstracts (like the iterative conception of sets). The abstracts are formed at stages, with the abstracts formed at any given stage being the abstracts of those concepts of objects formed at prior stages.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)
     A reaction: See 10567 for Fine's later modification. This may not guarantee 'levels', but it implies some sort of conceptual priority between abstract entities.
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K]
     Full Idea: Abstraction-theoretic imperialists think that it must be possible to represent every mathematical object as a Fregean abstract.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)
We can combine ZF sets with abstracts as urelements [Fine,K]
     Full Idea: I propose a unified theory which is a version of ZF or ZFC with urelements, where the urelements are taken to be the abstracts.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)
We can create objects from conditions, rather than from concepts [Fine,K]
     Full Idea: Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects.
     From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)
     A reaction: The point is that no particular object is now required to make the abstraction.
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
     Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
     From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?
24. Political Theory / D. Ideologies / 11. Capitalism
Capitalism may actually be the best way to foster community [Conway,D]
     Full Idea: Not only is there no good reason for supposing capitalism inimical to community, but there is reason to think it more conducive to community than the feasible alternatives to it.
     From: David Conway (Capitalism and Community [1996], I)
     A reaction: Conway is defending an obviously unorthodox view, while attacking the hopes of communitarians.
Capitalism is just the market, with optional limited government, and perhaps democracy [Conway,D]
     Full Idea: There are three types of capitalism: 1) the market - private ownership, labor contracts and profit, 2) limited government - the state provides goods the market cannot do, 3) limited government with democracy - with political freedom and elections.
     From: David Conway (Capitalism and Community [1996], II)
     A reaction: [compressed] I would have thought that capitalism is compatible with a fair degree of workplace democracy, which would make a fourth type.
Capitalism prefers representative democracy, which avoids community decision-making [Conway,D]
     Full Idea: By opting for representative rather than direct democracy, capitalism is said to preclude political community, for which the citizens of a state must possess a common will, which needs their direct participation in decisions.
     From: David Conway (Capitalism and Community [1996], V)
     A reaction: Conway does not accept this claim. I'm beginning to wonder whether the famous British electoral system is actually a capitalist conspiracy against the people.
Capitalism breaks up extended families, and must then provide welfare for the lonely people [Conway,D]
     Full Idea: It is said that capitalism encourages the breakup of extended families, which creates the need for extensive state welfare for those indigent members of society who can no longer rely on their own family to take care of them.
     From: David Conway (Capitalism and Community [1996], V)
     A reaction: Conway does not accept this claim. It seems to simplistic to say that capitalism is the sole culprit. Any rise of mechanisation in agriculture would break up rural extended families.
Capitalism is anti-community, by only valuing individuals, and breaking up families [Conway,D]
     Full Idea: Communitarns say capitalism is inimical to family community, because it encourages an individualistic mentality which only values self-fulfilment, and because it demands labour mobility which is disruptive of families.
     From: David Conway (Capitalism and Community [1996], VI)
     A reaction: Chicken-and-egg with the first one. Small entrepreneurs are individualists who seek their own gain. It is big capitalism that sucks in the others. Traditional community is based on labour-intensive agriculture.