10184
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Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess]
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Full Idea:
On the structuralist interpretation, theorems of analysis concerning the real numbers R are about all complete ordered fields. So R, which appears to be the name of a specific structure, is taken to be a variable ranging over structures.
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From:
John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1)
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A reaction:
Since I am beginning to think that nearly all linguistic expressions should be understood as variables, I find this very appealing, even if Burgess hates it. Terms slide and drift, and are vague, between variable and determinate reference.
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10187
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Abstract algebra concerns relations between models, not common features of all the models [Burgess]
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Full Idea:
Abstract algebra, such as group theory, is not concerned with the features common to all models of the axioms, but rather with the relationships among different models of those axioms (especially homomorphic relation functions).
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From:
John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1)
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A reaction:
It doesn't seem to follow that structuralism can't be about the relations (or patterns) found when abstracting away and overviewing all the models. One can study family relations, or one can study kinship in general.
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18925
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If talking donkeys are possible, something exists which could be a talking donkey [Williamson, by Cameron]
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Full Idea:
Williamson's view on modality is that everything that could exist does exist: since there could exist a talking donkey there actually exists some thing that could be a talking donkey.
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From:
report of Timothy Williamson (Modal Logic as Metaphysics [2013], n20) by Ross P. Cameron - Truthmaking for Presentists n20
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A reaction:
Well that thing certainly isn't me, or Tim Williamson. I'm guessing that the thing is an actual donkey, probably a rather bright one. Actually, I think this is one of those views that invites the incredulous stare. (Barcan formulae).
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7903
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The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
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Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
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From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
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A reaction:
What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
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