Combining Texts

All the ideas for 'Nominalism', 'The Beautiful in Music' and 'fragments/reports'

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8 ideas

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? [Szabó]
     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.
5. Theory of Logic / L. Paradox / 1. Paradox
If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
     Full Idea: The 'undetected' or 'veiled' paradox of Eubulides says: if you know your father, and don't know the veiled person before you, but that person is your father, you both know and don't know the same person.
     From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
     A reaction: Essentially an uninteresting equivocation on two senses of "know", but this paradox comes into its own when we try to give an account of how linguistic reference works. Frege's distinction of sense and reference tried to sort it out (Idea 4976).
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
     Full Idea: The liar paradox of Eubulides says 'if you state that you are lying, and state the truth, then you are lying'.
     From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
     A reaction: (also Cic. Acad. 2.95) Don't say it, then. These kind of paradoxes of self-reference eventually lead to Russell's 'barber' paradox and his Theory of Types.
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
     Full Idea: The 'sorites' paradox of Eubulides says: if you take one grain of sand from a heap (soros), what is left is still a heap; so no matter how many grains of sand you take one by one, the result is always a heap.
     From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
     A reaction: (also Cic. Acad. 2.49) This is a very nice paradox, which goes to the heart of our bewilderment when we try to fully understand reality. It homes in on problems of identity, as best exemplified in the Ship of Theseus (Ideas 1212 + 1213).
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 [Szabó]
     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 [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.
18. Thought / E. Abstraction / 5. Abstracta by Negation
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?
21. Aesthetics / C. Artistic Issues / 4. Emotion in Art
Music is not an expressive art, because it expresses no familiar emotions [Hanslick, by Wollheim]
     Full Idea: Hanslick concluded from the fact that music doesn't express definite feelings like piety, love, joy, or sadness, that it isn't an art of expression.
     From: report of Eduard Hanslick (The Beautiful in Music [1854]) by Richard Wollheim - Art and Its Objects 48
     A reaction: Whether music is 'expressive' (which it may not be) should not be confused with whether it is emotional, which it clearly is, even in its coolest examples. Hanslick viewed music as a code, not a language.