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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9626
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A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro]
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Full Idea:
A structure is the abstract form of a system, focussing on the interrelationships among the objects, and ignoring any features of them that do not affect how they relate to other objects in the system.
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From:
Stewart Shapiro (Structure and Ontology [1989], 146), quoted by James Robert Brown - Philosophy of Mathematics Ch.4
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A reaction:
I find this account very attractive, even though it appeals to supposedly outmoded psychological abstractionism. It seems pretty close to Aristotle's view of things. Shapiro's account must face up to Frege's worries about these matters.
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