|
9469
|
Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]
|
|
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.
|
|
From:
Charles Parsons (A Plea for Substitutional Quantification [1971], p.156)
|
|
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.
|
|
6007
|
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).
|
|
6008
|
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).
|
|
17447
|
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
|
|
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.
|
|
From:
report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
|
|
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'.
|
|
13417
|
If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
|
|
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.
|
|
From:
Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2)
|
|
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.
|