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18189
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ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
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Full Idea:
We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC.
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From:
Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics
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A reaction:
Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30).
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21982
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I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
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Full Idea:
"I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people."
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From:
Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7
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A reaction:
[Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork.
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16616
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Substances 'substand' (beneath accidents), or 'subsist' (independently) [Eustachius]
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Full Idea:
It is proper to substance both to stretch out or exist beneath accidents, which is to substand, and to exist per se and not in another, which is to subsist.
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From:
Eustachius a Sancto Paulo (Summa [1609], I.1.3b.1.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 06.2
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A reaction:
This reflects Aristotle wavering between 'ousia' being the whole of a thing, or the substrate of a thing. In current discussion, 'substance' still wavers between a thing which 'is' a substance, and substance being the essence.
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16585
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Prime matter is free of all forms, but has the potential for all forms [Eustachius]
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Full Idea:
Everyone says that prime matter, considered in itself, is free of all forms and at the same time is open to all forms - or, that matter is in potentiality to all forms.
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From:
Eustachius a Sancto Paulo (Summa [1609], III.1.1.2.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1
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A reaction:
This is the notorious doctrine developed to support the hylomorphic picture derived from Aristotle. No one could quite figure out what prime matter was, so it faded away.
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