Combining Texts

All the ideas for 'Set Theory and related topics (2nd ed)', 'Consciousness, Philosophy and Mathematics' and 'Languages of Art (2nd edn)'

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6 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
8920 Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]
     Full Idea: A relation R on a non-empty set S is an equivalence relation if it is reflexive (for each member a, aRa), symmetric (if aRb, then bRa), and transitive (aRb and bRc, so aRc). It tries to classify objects that are in some way 'alike'.
     From: Seymour Lipschutz (Set Theory and related topics (2nd ed) [1998], 3.9)
     A reaction: So this is an attempt to formalise the common sense notion of seeing that two things have something in common. Presumably a 'way' of being alike is going to be a property or a part
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8728 Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
     Full Idea: Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths.
     From: Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2
     A reaction: Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time!
21. Aesthetics / B. Nature of Art / 1. Defining Art
20440 Art is a referential activity, hence indefinable, but it has a set of symptoms [Goodman]
     Full Idea: No definition of art is possible (since it is a referential activity), …but the symptoms of art are syntactic density, semantic density, syntactic repleteness, exemplificationality, and multiple and complex reference.
     From: Nelson Goodman (Languages of Art (2nd edn) [1968], p.22-255), quoted by Alessandro Giovannelli - Nelson Goodman (aesthetics) 4
     A reaction: I wish these labels were more self-explanatory. Goodman seems to want to assimilate art to his earlier interests in linguistic anti-realism and mereology. I wouldn't have thought he now had many followers.
21. Aesthetics / B. Nature of Art / 5. Art as Language
20439 Artistic symbols are judged by the fruitfulness of their classifications [Goodman, by Giovannelli]
     Full Idea: Artistic symbols are to be judged for the classifications they bring about, for how novel and insightful those classifications are, for how they change our world perceptions and relations.
     From: report of Nelson Goodman (Languages of Art (2nd edn) [1968]) by Alessandro Giovannelli - Nelson Goodman (aesthetics) 4
     A reaction: This seems to be an awfully long way from our normal experience of art. I understand 'symbols' in early Flemish art, but not in Mondriaan, or even Rembrandt.
21. Aesthetics / B. Nature of Art / 7. Ontology of Art
20438 A performance is only an instance of a work if there is not a single error [Goodman]
     Full Idea: The most miserable performance without actual mistakes does count as an instance of a work, …but the most brilliant performance with a single wrong note does not.
     From: Nelson Goodman (Languages of Art (2nd edn) [1968], p.186), quoted by Alessandro Giovannelli - Nelson Goodman (aesthetics)
     A reaction: Mereological essentialism applied to art! You need to be a highly theoretical and technical philosopher (which Goodman was) to maintain such a weird and contrary-usage proposal.
21. Aesthetics / C. Artistic Issues / 2. Copies of Art
20437 A copy only becomes an 'instance' of an artwork if there is a system of notation [Goodman]
     Full Idea: Paintings and sculptures do not work within a notation; hence, there is no copying of an original that would preserve its originality. A copy of a painting is a copy, not an instance of the original.
     From: Nelson Goodman (Languages of Art (2nd edn) [1968], p.212), quoted by Alessandro Giovannelli - Nelson Goodman (aesthetics) 2
     A reaction: Sounds conclusive, but isn't. Is a poetry manuscript a 'notation' or an original? Why is an etching plate a notation, but painting on canvas is an original? Can I create a painting specifically so that it can be copied (by my students)? Intention matters.