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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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8978
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Events are made of other things, and are not fundamental to ontology [Bennett]
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Full Idea:
Events are not basic items in the universe; they should not be included in any fundamental ontology...all the truths about them are entailed by and explained and made true by truths that do not involve the event concept.
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From:
Jonathan Bennett (Events and Their Names [1988], p.12), quoted by Peter Simons - Events 3.1
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A reaction:
Given the variable time spans of events, their ability to coincide, their ability to contain no motion, their blatantly conventional component, and their recalcitrance to individuation, I say Bennett is right.
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8790
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The 'doctrine of the given' is correct; some beliefs or statements are self-justifying [Chisholm]
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Full Idea:
In my opinion, the 'doctrine of the given' is correct in saying that there are some beliefs or statements which are 'self-justifying' and that among such beliefs are statements some of which concern appearances or 'ways of being appeared to'.
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From:
Roderick Chisholm (The Myth of the Given [1964], §12)
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A reaction:
To boldly assert that they are 'self-justifying' invites a landslide of criticisms, pointing at a regress. It might be better to say they are self-evident, or intuitively known, or primitive, or true by the natural light of reason.
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10364
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Facts are about the world, not in it, so they can't cause anything [Bennett]
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Full Idea:
Facts are not the sort of item that can cause anything. A fact is a true proposition (they say); it is not something in the world but is rather something about the world.
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From:
Jonathan Bennett (Events and Their Names [1988], p.22), quoted by Jonathan Schaffer - The Metaphysics of Causation 1.1
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A reaction:
Compare 10361. Good argument, but maybe 'fact' is ambiguous. See Idea 10365. Events are said to be more concrete, and so can do the job, but their individuation also seems to depend on a description (as Davidson has pointed out).
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