Ideas of Zoltán Gendler Szabó, by Theme

[American, fl. 2003, Professor at Cornell University.]

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4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
What is a singleton set, if a set is meant to be a collection of objects?
     Full Idea: The relationship between an object and its singleton is puzzling. Our intuitive conception of a set is a collection of objects - what are we to make of a collection of a single object?
     From: Zoltán Gendler Szabó (Nominalism [2003], 4.1)
     A reaction: The ontological problem seems to be the same as that of the empty set, and indeed the claim that a pair of entities is three things. For logicians the empty set is as real as a pet dog, but not for me.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things
     Full Idea: It is better not to include in the definition of abstract entities that they ontologically depend on their concrete correlates. Note: ..but they may depend on the totality of concreta; maybe 'the supervenience of the abstract' is part of ordinary thought.
     From: Zoltán Gendler Szabó (Nominalism [2003], 2.2)
     A reaction: [the quoted phrase is from Gideon Rosen] It certainly seems unlikely that the concept of the perfect hexagon depends on a perfect hexagon having existed. Human minds have intervened between the concrete and the abstract.
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Geometrical circles cannot identify a circular paint patch, presumably because they lack something
     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.
18. Thought / E. Abstraction / 5. Abstracta by Negation
Abstractions are imperceptible, non-causal, and non-spatiotemporal (the third explaining the others)
     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?