Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Difficulties of Transfinite Numbers and Types' and 'Good and Evil'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17447	Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
	Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
	From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
	A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism

21558	'Predicative' norms are those which define a class [Russell]
	Full Idea: Norms (containing one variable) which do not define classes I propose to call 'non-predicative'; those which do define classes I shall call 'predicative'.
	From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141)

21559	We need rules for deciding which norms are predicative (unless none of them are) [Russell]
	Full Idea: We need rules for deciding what norms are predicative and what are not, unless we adopt the view (which has much to recommend it) that no norms are predicative. ...[146] A predative propositional function is one which determines a class.
	From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141)
	A reaction: He is referring to his 'no class' theory, which he favoured at that time.

22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good

22489	'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot]
	Full Idea: Geach puts 'good' in the class of attributive adjectives, such as 'large' and 'small', contrasting such adjectives with 'predicative' adjectives such as 'red'.
	From: report of Peter Geach (Good and Evil [1956]) by Philippa Foot - Natural Goodness Intro
	A reaction: [In Analysis 17, and 'Theories of Ethics' ed Foot] Thus any object can simply be red, but something can only be large or small 'for a rat' or 'for a car'. Hence nothing is just good, but always a good so-and-so. This is Aristotelian, and Foot loves it.