15716
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If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert]
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Full Idea:
If the arbitrarily given axioms do not contradict each other with all their consequences, then they are true and the things defined by the axioms exist. For me this is the criterion of truth and existence.
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From:
David Hilbert (Letter to Frege 29.12.1899 [1899]), quoted by R Kaplan / E Kaplan - The Art of the Infinite 2 'Mind'
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A reaction:
If an axiom says something equivalent to 'fairies exist, but they are totally undetectable', this would seem to avoid contradiction with anything, and hence be true. Hilbert's idea sounds crazy to me. He developed full Formalism later.
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16459
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Is it coherent that reality is vague, identities can be vague, and objects can have fuzzy boundaries? [Evans]
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Full Idea:
Maybe the world is vague, and vagueness is a necessary feature of any true description of it. Also identities may lack a determinate truth value because of their vagueness. Hence it is a fact that some objects have fuzzy boundaries. But is this coherent?
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From:
Gareth Evans (Can there be Vague Objects? [1978])
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A reaction:
[compressed] Lewis quotes this introduction to the famous short paper, to show that Evans wasn't proposing a poor argument, but offering a reductio of the view that vagueness is 'ontic', or a feature of the world.
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16460
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Evans assumes there can be vague identity statements, and that his proof cannot be right [Evans, by Lewis]
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Full Idea:
The correct interpretation is that Evans trusts his reader (unwisely) to take for granted that there are vague identity statements, that a proof of the contrary cannot be right, and that the vagueness-in-describing view affords a diagnosis of the fallacy.
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From:
report of Gareth Evans (Can there be Vague Objects? [1978]) by David Lewis - Vague Identity: Evans misunderstood p.319
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A reaction:
[Lowe 199:11 is a culprit!] Lewis put this interpretation to Evans, who replied 'Yes, yes, yes!'.
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14484
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If a=b is indeterminate, then a=/=b, and so there cannot be indeterminate identity [Evans, by Thomasson]
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Full Idea:
We cannot accept the existence of vague objects, according to Evans's argument that there cannot be indeterminacy of identity. ...From the assumption that it is indeterminate whether a = b, we conclude, determinately, that it's not the case that a = b.
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From:
report of Gareth Evans (Can there be Vague Objects? [1978]) by Amie L. Thomasson - Ordinary Objects 05.6
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A reaction:
I think we should keep intrinsic identity separate from identity between entities. A cloud can be clearly identified, while being a bit fuzzy. It is only when you ask whether we saw the same cloud that Evans's argument seems relevant.
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16224
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There can't be vague identity; a and b must differ, since a, unlike b, is only vaguely the same as b [Evans, by PG]
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Full Idea:
Two things can't be vaguely identical, because then a would have an indeterminacy which b lacks (namely, being perfectly identical to b), so by Leibniz's Law they can't be identical.
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From:
report of Gareth Evans (Can there be Vague Objects? [1978], 4.7) by PG - Db (ideas)
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A reaction:
[my summary of Katherine Hawley's summary (2001:118) of Evans] Hawley considers the argument to be valid. I have grave doubts about whether b's identity with b is the sort of property needed for an application of Liebniz's Law.
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