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9469
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Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]
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Full Idea:
I argue (against Quine) that the existential quantifier substitutionally interpreted has a genuine claim to express a concept of existence, which may give the best account of linguistic abstract entities such as propositions, attributes, and classes.
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From:
Charles Parsons (A Plea for Substitutional Quantification [1971], p.156)
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A reaction:
Intuitively I have my doubts about this, since the whole thing sounds like a verbal and conventional game, rather than anything with a proper ontology. Ruth Marcus and Quine disagree over this one.
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17447
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Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
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Full Idea:
In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
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From:
report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
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A reaction:
This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
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13417
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If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
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Full Idea:
If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics.
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From:
Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2)
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A reaction:
This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course.
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3398
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Epiphenomenalism makes the mind totally pointless [Alexander,S]
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Full Idea:
Epiphenomenalism supposes something to exist in nature which has nothing to do and no purpose to serve.
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From:
Samuel Alexander (works [1927]), quoted by Jaegwon Kim - Philosophy of Mind p.129
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A reaction:
An objection, but not, I think, a strong one. The fact, for example, that sweat is shiny is the result of good evolutionary reasons, but I cannot think of any purpose which it serves. All events which are purposeful are likely to have side-effects.
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14494
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Epiphenomenalism is like a pointless nobleman, kept for show, but soon to be abolished [Alexander,S]
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Full Idea:
Epiphenomenalism supposes something to exist in nature which has nothing to do, no purpose to serve, a species of noblesse which depends on the work of its inferiors, but is kept for show and might as well, and undoubtedly would in time be abolished.
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From:
Samuel Alexander (Space, Time and Deity (2 vols) [1927], 2:8), quoted by Jaegwon Kim - Nonreductivist troubles with ment.causation IV
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A reaction:
Wonderful! Kim quotes this, and labels the implicit slogan (to be real is to have causal powers) 'Alexander's Dictum'. All the examples given of epiphenomena are only causally inert within a defined system, but they act causally outside the system.
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