9 ideas
3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
Full Idea: Dedekind and Peano define the number series as the series of successors to the number zero, according to five postulates. | |
From: report of Giuseppe Peano (works [1890]) by Simon Blackburn - Oxford Dictionary of Philosophy p.279 |
5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
Full Idea: 1) 0 is a number; 2) The successor of any number is a number; 3) No two numbers have the same successor; 4) 0 is not the successor of any number; 5) If P is true of 0, and if P is true of any number n and of its successor, P is true of every number. | |
From: report of Giuseppe Peano (works [1890]) by Antony Flew - Pan Dictionary of Philosophy 'Peano' | |
A reaction: Devised by Dedekind and proposed by Peano, these postulates were intended to avoid references to intuition in specifying the natural numbers. I wonder if they could define 'successor' without reference to 'number'. |
15645 | Nominal essence are the observable properties of things [Eagle] |
Full Idea: It is clear the nominal essences really are the properties of the things which have them: they are (a subset of) the observable properties of the things. | |
From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
A reaction: I think this is wrong. The surface characteristics are all that is available to us, so our classifications must be based on those, but it is on the ideas of them, not their intrinsic natures. That is empiricsm! What makes the properties 'essential'? |
15642 | If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle] |
Full Idea: If the kinds there are depend not on the essences of the objects but on their observed distinguishing particulars, ...then for any kind that we think there is, it is possible that there are many underlying essences which are observably indistinguishable. | |
From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
A reaction: Eagle is commenting on Locke's reliance on nominal essences. This seems to be the genuine problem with jadeite and nephrite (both taken to be 'jade'), or with 'fool's gold'. This isn't an objection to Locke; it just explains the role of science. |
15643 | Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle] |
Full Idea: Nominal essence does not allow for gradations in significance for the underlying properties. Those are all essential for the object behaving as it observably does, and they must all be given equal weight when deciding what the object does. | |
From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
A reaction: This is where 'scientific' essentialism comes in. If we take one object, or one kind of object, in isolation, Eagle is right. When we start to compare, and to set up controlled conditions tests, we can dig into the 'gradations' he cares about. |
8070 | It would be better to point to failings of character, than to moral wrongness of actions [Anscombe] |
Full Idea: It would be a great improvement if, instead of 'morally wrong', one always named a genus such as 'untruthful', 'unchaste', or 'unjust'. | |
From: G.E.M. Anscombe (Modern Moral Philosophy [1958], p.183) | |
A reaction: People are indeed much more struck by the suggestion that they have a weakness of character, rather than that they have just done something wrong. This is Anscombe's first great appeal for a return to virtue as the basis of ethics. |
8065 | 'Ought' and 'right' are survivals from earlier ethics, and should be jettisoned [Anscombe] |
Full Idea: The moral sense of 'ought' and of what is right should be jettisoned, if possible, because they are survivals from an earlier conception of ethics, and are only harmful without it. | |
From: G.E.M. Anscombe (Modern Moral Philosophy [1958], p.175) | |
A reaction: This is part of a revolutionary proposal to return to virtue theory, and has had a great influence (e.g. on me). Richard Taylor gives a good account of how duty lost its social and religious underpinnings. Our duties now seem to be purely contractual. |
8069 | Between Aristotle and us, a Judaeo-Christian legal conception of ethics was developed [Anscombe] |
Full Idea: Between Aristotle and us came Christianity, with its law conception of ethics, and Christianity derived its ethical notions from the Torah. | |
From: G.E.M. Anscombe (Modern Moral Philosophy [1958], p.179) | |
A reaction: While I am a fan of the primacy of the virtues in ethical thinking, I am doubtful about the complete elimination of laws (e.g. by Particularists). The law teaches us the virtues, and reminds us of them (like speed-limit signs). |
15641 | Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle] |
Full Idea: The natural thought is to think that real kinds are given only by classification on the basis of essential properties: properties that make an object the kind of thing that it is. | |
From: Antony Eagle (Locke on Essences and Kinds [2005], II) | |
A reaction: Circularity alert! Circularity alert! Essence gives a thing its kind - and hence we can see what the kind is? Test for a trivial property! Eagle is not unaware of these issues. Does he mean 'necessary' rather than 'essential'? |