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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14305
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In the truth-functional account a burnt-up match was soluble because it never entered water [Carnap]
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Full Idea:
If a wooden match was completely burned up yesterday, and never placed in water at any time, is it not the case, therefore, that the match is soluble (in the truth-functional view). This follows just from the antecedent being false.
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From:
Rudolph Carnap (Testability and Meaning [1937], I.440), quoted by Stephen Mumford - Dispositions
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A reaction:
This, along with Edgington's nice example of the conditional command (Idea ) seems conclusive against the truth-functional account. The only defence possible is some sort of pragmatic account about implicature.
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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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