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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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6007
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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]
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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.
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From:
report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
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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).
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6008
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Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
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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.
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From:
report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
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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).
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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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14221
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Serious essentialism says everything has essences, they're not things, and they ground necessities [Shalkowski]
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Full Idea:
Serious essentialism is the position that a) everything has an essence, b) essences are not themselves things, and c) essences are the ground for metaphysical necessity and possibility.
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From:
Scott Shalkowski (Essence and Being [2008], 'Intro')
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A reaction:
If a house is being built, it might acquire an identity first, and only get an essence later. Essences can be physical, but if you extract them you destroy thing thing of which they were the essence. Does all of this apply to abstract 'things'.
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14222
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Essences are what it is to be that (kind of) thing - in fact, they are the thing's identity [Shalkowski]
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Full Idea:
The route into essentialism is, first, a recognition that the essence of a thing is "what it is to be" that (kind of) thing; the essence of a thing is just its identity.
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From:
Scott Shalkowski (Essence and Being [2008], 'Essent')
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A reaction:
The first half sounds right, and very Aristotelian. The second half is dramatically different, controversial, and far less plausible. Slipping in 'kind of' is also highly dubious. This remark shows, I think, some confusion about essences.
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9220
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Lewis must specify that all possibilities are in his worlds, making the whole thing circular [Shalkowski, by Sider]
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Full Idea:
If purple cows are simply absent from Lewis's multiverse, then certain correct propositions turn out to be impossible. Lewis must require a world for every possibility. But then it is circular, as the multiverse needs modal notions to characterize it.
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From:
report of Scott Shalkowski (Ontological Ground of Alethic Modality [1994], 3.9) by Theodore Sider - Reductive Theories of Modality 3.9
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A reaction:
[Inversely, a world containing a round square would make that possible] This sounds very nice, though Sider rejects it (p.197). I've never seen how you could define possibility using the concept of 'possible' worlds.
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14224
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Equilateral and equiangular aren't the same, as we have to prove their connection [Shalkowski]
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Full Idea:
That 'all and only equilateral triangles are equiangular' required proof, and not for mere curiosity, is grounds for thinking that being an equilateral triangle is not the same property as being an equiangular triangle.
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From:
Scott Shalkowski (Essence and Being [2008], 'Serious')
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A reaction:
If you start with equiangularity, does equilateralness then require proof? This famous example is of two concepts which seem to be coextensional, but seem to have a different intension. Does a dependence relation drive a wedge between them?
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