Combining Texts

Ideas for 'Meaning and the Moral Sciences', 'To be is to be the value of a variable..' and 'The Structure of Appearance'

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5 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing

15510	Classes are a host of ethereal, platonic, pseudo entities [Goodman]
	Full Idea: I will not willingly use apparatus that peoples the world with a host of ethereal, platonic, pseudo entities.
	From: Nelson Goodman (The Structure of Appearance [1951], II.2), quoted by David Lewis - Parts of Classes 2.1
	A reaction: This represents the big gap that opened up with Goodman's former comrade in arms, Quine. Lewis quotes it in order to ask whether he means ethereal or platonic, as they are very different. I sympathise with Goodman.

7785	The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos]
	Full Idea: We should abandon the idea that the use of plural forms commits us to the existence of sets/classes… Entities are not to be multiplied beyond necessity. There are not two sorts of things in the world, individuals and collections.
	From: George Boolos (To be is to be the value of a variable.. [1984]), quoted by Henry Laycock - Object
	A reaction: The problem of quantifying over sets is notoriously difficult. Try http://plato.stanford.edu/entries/object/index.html.

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

9920	Two objects can apparently make up quite distinct arrangements in sets [Goodman, by Burgess/Rosen]
	Full Idea: Goodman argues that the set or class {{a}},{a,b}} is supposed to be distinct from the set or class {{b},{a,b}}, even though both are ultimately constituted from the same a and b.
	From: report of Nelson Goodman (The Structure of Appearance [1951]) by JP Burgess / G Rosen - A Subject with No Object I.A.2.a
	A reaction: I'm with Goodman all the way here, even though it is deeply unfashionable, particularly in the circles I move in. If there are trillion grains of sand on a beach, how many sets are we supposed to be committed to?

10699	Does a bowl of Cheerios contain all its sets and subsets? [Boolos]
	Full Idea: Is there, in addition to the 200 Cheerios in a bowl, also a set of them all? And what about the vast number of subsets of Cheerios? It is haywire to think that when you have some Cheerios you are eating a set. What you are doing is: eating the Cheerios.
	From: George Boolos (To be is to be the value of a variable.. [1984], p.72)
	A reaction: In my case Boolos is preaching to the converted. I am particularly bewildered by someone (i.e. Quine) who believes that innumerable sets exist while 'having a taste for desert landscapes' in their ontology.

4. Formal Logic / G. Formal Mereology / 1. Mereology

10657	The counties of Utah, and the state, and its acres, are in no way different [Goodman]
	Full Idea: A class (counties of Utah) is different neither from the individual (state of Utah) that contains its members, nor from any other class (acres of Utah) whose members exhaust the whole. For nominalists, distinction of entity means distinction of content.
	From: Nelson Goodman (The Structure of Appearance [1951], p.26), quoted by Achille Varzi - Mereology 3.1
	A reaction: This is a nice credo for the nominalist version of mereology. You can still have a mereology that commits you to the wholes as well as the parts. Cf. Lewis in Idea 10660.