6 ideas
17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
Full Idea: Cantor gives informal versions of the axioms of ZF as ways of getting from one set to another. | |
From: report of George Cantor (Later Letters to Dedekind [1899]) by John Lake - Approaches to Set Theory 1.6 | |
A reaction: Lake suggests that it should therefore be called CZF. |
5637 | Nowadays logic is seen as the science of extensions, not intensions [Scruton] |
Full Idea: Logicians have come increasingly to realise that logic is the science not of the intension, but of the extension of terms. | |
From: Roger Scruton (Short History of Modern Philosophy [1981], Ch.4) | |
A reaction: I take this to be because the notion of a 'set' is basic, which is defined strictly in terms of its members. This move is probably because we can be clear about extensions, but not intensions. Tidiness is no substitute for complex truth. |
5636 | Cartesian 'ideas' confuse concepts and propositions [Scruton] |
Full Idea: Cartesian 'ideas' seem to be both concepts and propositions at once. | |
From: Roger Scruton (Short History of Modern Philosophy [1981], Ch.4) | |
A reaction: This seems to be the simple reason why modern philosophers don't like this seventeenth century notion. There is something slightly too tidy about the modern notion of propositions built out of concepts. Animals see propositions in a flash. |
468 | 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? |
5660 | Allegiance is prior to the recognition of individual rights [Scruton] |
Full Idea: Personally I regard allegiance, in the manner of Hegel, as prior to the recognition of individual rights. | |
From: Roger Scruton (Short History of Modern Philosophy [1981], Bibliog) | |
A reaction: Scruton notoriously generates rather right-wing views from this basis, but it is also the basis of communitarianism, which can take a softer form. It seems to me self-evident that rights cannot be the prime concept in a society. What society? |
5653 | A right is a power which is enforced in the name of justice [Scruton] |
Full Idea: Rights are enforced in the name of justice, whereas power is enforced come what may. | |
From: Roger Scruton (Short History of Modern Philosophy [1981], Ch.14) | |
A reaction: Presumably rights can be claimed as well as enforced, and the notion of a natural right is at least a discussable concept, as in the 'right' of self-defence. Scruton offers us a very right-wing definition of rights. |