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13412
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Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
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Full Idea:
Not all numbers could possibly have been learned à la Frege-Russell, because we could not have performed that many distinct acts of abstraction. Somewhere along the line a rule had to come in to enable us to obtain more numbers, in the natural order.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165)
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A reaction:
Follows on from Idea 13411. I'm not sure how Russell would deal with this, though I am sure his account cannot be swept aside this easily. Nevertheless this seems powerful and convincing, approaching the problem through the epistemology.
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13413
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We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
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Full Idea:
Both ordinalists and cardinalists, to account for our number words, have to account for the fact that we know so many of them, and that we can 'recognize' numbers which we've neither seen nor heard.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166)
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A reaction:
This seems an important contraint on any attempt to explain numbers. Benacerraf is an incipient structuralist, and here presses the importance of rules in our grasp of number. Faced with 42,578,645, we perform an act of deconstruction to grasp it.
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13411
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If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
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Full Idea:
If we accept the Frege-Russell analysis of number (the natural numbers are the cardinals) as basic and correct, one thing which seems to follow is that one could know, say, three, seventeen, and eight, but no other numbers.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164)
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A reaction:
It seems possible that someone might only know those numbers, as the patterns of members of three neighbouring families (the only place where they apply number). That said, this is good support for the priority of ordinals. See Idea 13412.
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20327
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Modern attention has moved from the intrinsic properties of art to its relational properties [Lamarque/Olson]
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Full Idea:
In modern discussions, rather than look for intrinsic properties of objects, including aesthetic or formal properties, attention has turned to extrinsic or relational properties, notably of a social, historical, or 'institutional' nature.
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From:
Lamargue,P/Olson,SH (Introductions to 'Aesthetics and the Phil of Art' [2004], Pt 1)
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A reaction:
Lots of modern branches of philosophy have made this move, which seems to me like a defeat. We want to know why things have the relations they do. Just mapping the relations is superficial Humeanism.
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20326
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Early 20th cent attempts at defining art focused on significant form, intuition, expression, unity [Lamarque/Olson]
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Full Idea:
In the early twentieth century there were numerous attempts at defining the essence art. Significant form, intuition, the expression of emotion, organic unity, and other notions, were offered to this end.
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From:
Lamargue,P/Olson,SH (Introductions to 'Aesthetics and the Phil of Art' [2004], Pt 1)
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A reaction:
As far as I can see the whole of aesthetics was demolished in one blow by Marcel Duchamp's urinal. Artists announce: we will tell you what art is; you should just sit and listen. Compare the invention of an anarchic sport.
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20330
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The dualistic view says works of art are either abstract objects (types), or physical objects [Lamarque/Olson]
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Full Idea:
The dualistic view of the arts holds that works of art come in two fundamentally different kinds: those that are abstract entities, i.e. types, and those that are physical objects (tokens).
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From:
Lamargue,P/Olson,SH (Introductions to 'Aesthetics and the Phil of Art' [2004], Pt 2)
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A reaction:
Paintings are the main reason for retaining physical objects. Strawson 1974 argues that paintings are only physical because we cannot yet perfectly reproduce them. I agree. Works of art are types, not tokens.
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