14234
|
If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
|
|
Full Idea:
A 'singularist', who refers to objects one at a time, must resort to the language of sets in order to replace plural reference to members ('Henry VIII's wives') by singular reference to a set ('the set of Henry VIII's wives').
|
|
From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro)
|
|
A reaction:
A simple and illuminating point about the motivation for plural reference. Null sets and singletons give me the creeps, so I would personally prefer to avoid set theory when dealing with ontology.
|
14237
|
We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
|
|
Full Idea:
Plurals earn their keep in set theory, to answer Skolem's remark that 'in order to treat of 'sets', we must begin with 'domains' that are constituted in a certain way'. We can speak in the plural of 'the objects', not a 'domain' of objects.
|
|
From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro)
|
|
A reaction:
[Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it.
|
14246
|
If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
|
|
Full Idea:
If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics.
|
|
From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1)
|
|
A reaction:
Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application.
|
14247
|
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
|
|
Full Idea:
Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers.
|
|
From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2)
|
|
A reaction:
Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated.
|
8326
|
Science has shown that causal relations are just transfers of energy or momentum [Fair, by Sosa/Tooley]
|
|
Full Idea:
Basic causal relations can, as a consequence of our scientific knowledge, be identified with certain physicalistic [sic] relations between objects that can be characterized in terms of transference of either energy or momentum between objects.
|
|
From:
report of David Fair (Causation and the Flow of Energy [1979]) by E Sosa / M Tooley - Introduction to 'Causation' §1
|
|
A reaction:
Presumably a transfer of momentum is a transfer of energy. If only anyone had the foggiest idea what energy actually is, we'd be doing well. What is energy made of? 'No identity without substance', I say. I like Fair's idea.
|
10379
|
Fair shifted his view to talk of counterfactuals about energy flow [Fair, by Schaffer,J]
|
|
Full Idea:
Fair, who originated the energy flow view of causation, moved to a view that understands connection in terms of counterfactuals about energy flow.
|
|
From:
report of David Fair (Causation and the Flow of Energy [1979]) by Jonathan Schaffer - The Metaphysics of Causation 2.1.2
|
|
A reaction:
David Fair was a pupil of David Lewis, the king of the counterfactual view. To me that sounds like a disappointing move, but it is hard to think that a mere flow of energy through space would amount to causation. Cause must work back from an effect.
|