Combining Texts

All the ideas for 'Classical Cosmology (frags)', 'Realism in Mathematics' and 'Intro to 'Communitarianism and Individualism''

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10 ideas

4. Formal Logic / F. Set Theory ST / 7. Natural Sets
8755 Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
     Full Idea: Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects.
     From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3
     A reaction: This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10718 A natural number is a property of sets [Maddy, by Oliver]
     Full Idea: Maddy takes a natural number to be a certain property of sui generis sets, the property of having a certain number of members.
     From: report of Penelope Maddy (Realism in Mathematics [1990], 3 §2) by Alex Oliver - The Metaphysics of Properties
     A reaction: [I believe Maddy has shifted since then] Presumably this will make room for zero and infinities as natural numbers. Personally I want my natural numbers to count things.
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
8756 Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
     Full Idea: Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition.
     From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3
     A reaction: It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17733 We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
     Full Idea: Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience.
     From: report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5
     A reaction: Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory.
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
22808 Liberalism is minimal government, or individual rights, or equality [Avineri/De-Shalit]
     Full Idea: Liberalism has been defended as a theory of minimal government, or as a theory of basic individual rights, or as an egalitarian philosophy.
     From: Avineri,S/De-Shalit,A (Intro to 'Communitarianism and Individualism' [1992], §5)
     A reaction: Minimal government tends towards anarchist liberalism, but then what grounds the right to be free of government? Presumably any sensible theory of rights has to be egalitarian. What could ground unequal rights?
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
22803 Can individualist theories justify an obligation to fight in a war? [Avineri/De-Shalit]
     Full Idea: How can an individualist theory justify an obligation to fight for the state in the case of war?
     From: Avineri,S/De-Shalit,A (Intro to 'Communitarianism and Individualism' [1992], §4)
     A reaction: The most dramatic example of obliging citizens to contribute to the state, the notable other case being taxes. Some imagined ancient 'social contract' doesn't seem sufficient for later generations. Does being naturally sociable create such obligations?
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
22804 Autonomy is better achieved within a community [Avineri/De-Shalit]
     Full Idea: Communitarians often argue that personal autonomy is better achieved within the community.
     From: Avineri,S/De-Shalit,A (Intro to 'Communitarianism and Individualism' [1992], §4)
     A reaction: Hegel is the source of this view. The simplest version of the point is that autonomy can only be asserted if a person has rights, which can be asserted and defended, and only a society can provide that. That is plausible.
22806 Communitarians avoid oppression for the common good, by means of small mediating communities [Avineri/De-Shalit]
     Full Idea: Because of the mediating structures of small communities, communitarians are less fearful [than liberals] of the emergence of an oppressive government as a result of the politics of the common good.
     From: Avineri,S/De-Shalit,A (Intro to 'Communitarianism and Individualism' [1992], §5)
     A reaction: A politics of the common good has an obvious implicit conservatism because the central consensus is always likely to disapprove of errant individuals, of all sorts. Only individual rights can block an oppressive government.
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
22807 If our values are given to us by society then we have no grounds to criticise them [Avineri/De-Shalit]
     Full Idea: If communitarians are right that we are not free to choose, but rather that our values are determined by our community, the individualists say, then there is no reason to criticise the values of one's society.
     From: Avineri,S/De-Shalit,A (Intro to 'Communitarianism and Individualism' [1992], §5)
     A reaction: This is an obvious challenge, but if one's concept of community is a forum for free debate then it can be overcome. There is no avoiding the fact, though, that a good community always needs a high degree of consensus.
27. Natural Reality / E. Cosmology / 1. Cosmology
5994 Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG]
     Full Idea: The four major disputes in classical cosmology were whether the cosmos is 'open' or 'closed', whether it is explained mechanistically or teleologically, whether it is alive or mere matter, and whether or not it has a beginning.
     From: report of T.M. Robinson (Classical Cosmology (frags) [1997]) by PG - Db (ideas)
     A reaction: A nice summary. The standard modern view is closed, mechanistic, inanimate and non-eternal. But philosophers can ask deeper questions than physicists, and I say we are entitled to speculate when the evidence runs out.