10243
|
My ontology is quarks etc., classes of such things, classes of such classes etc. [Quine]
|
|
Full Idea:
My tentative ontology continues to consist of quarks and their compounds, also classes of such things, classes of such classes, and so on.
|
|
From:
Willard Quine (Structure and Nature [1992], p.9), quoted by Stewart Shapiro - Philosophy of Mathematics 4.9
|
|
A reaction:
I would call this the Hierarchy of Abstraction (just coined it - what do you think?). Unlike Quine, I don't see why its ontology should include things called 'sets' in addition to the things that make them up.
|
8954
|
Geometrical circles cannot identify a circular paint patch, presumably because they lack something [Szabó]
|
|
Full Idea:
The vocabulary of geometry is sufficient to identify the circle, but could not be used to identify any circular paint patch. The reason must be that the circle lacks certain properties that can distinguish paint patches from one another.
|
|
From:
Zoltán Gendler Szabó (Nominalism [2003], 2.2)
|
|
A reaction:
I take this to be support for the traditional view, that abstractions are created by omitting some of the properties of physical objects. I take them to be fictional creations, reified by language, and not actual hidden entities that have been observed.
|
8955
|
Abstractions are imperceptible, non-causal, and non-spatiotemporal (the third explaining the others) [Szabó]
|
|
Full Idea:
In current discussions, abstract entities are usually distinguished as 1) in principle imperceptible, 2) incapable of causal interaction, 3) not located in space-time. The first is often explained by the second, which is in turn explained by the third.
|
|
From:
Zoltán Gendler Szabó (Nominalism [2003], 2.2)
|
|
A reaction:
Szabó concludes by offering 3 as the sole criterion of abstraction. As Lewis points out, the Way of Negation for defining abstracta doesn't tell us very much. Courage may be non-spatiotemporal, but what about Alexander the Great's courage?
|