10476
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The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
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Full Idea:
Late nineteenth century mathematicians said that, although plus, minus and 0 could not be precisely defined, they could be partially 'implicitly defined' as a group. This nonsense was rejected by Frege and others, as expressed in Russell 1903.
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From:
Wilfrid Hodges (Model Theory [2005], 2)
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A reaction:
[compressed] This is helpful in understanding what is going on in Frege's 'Grundlagen'. I won't challenge Hodges's claim that such definitions are nonsense, but there is a case for understanding groups of concepts together.
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10477
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|= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
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Full Idea:
If every structure which is a model of a set of sentences T is also a model of one of its sentences φ, then this is known as the model-theoretic consequence relation, and is written T |= φ. Not to be confused with |= meaning 'satisfies'.
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From:
Wilfrid Hodges (Model Theory [2005], 3)
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A reaction:
See also Idea 10474, which gives the other meaning of |=, as 'satisfies'. The symbol is ALSO used in propositional logical, to mean 'tautologically implies'! Sort your act out, logicians.
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10481
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Models in model theory are structures, not sets of descriptions [Hodges,W]
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Full Idea:
The models in model-theory are structures, but there is also a common use of 'model' to mean a formal theory which describes and explains a phenomenon, or plans to build it.
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From:
Wilfrid Hodges (Model Theory [2005], 5)
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A reaction:
Hodges is not at all clear here, but the idea seems to be that model-theory offers a set of objects and rules, where the common usage offers a set of descriptions. Model-theory needs homomorphisms to connect models to things,
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20082
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Bodily movements are not actions, which are really the tryings within bodily movement [Hornsby, by Stout,R]
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Full Idea:
Hornsby claims the basic description of action is in terms of trying, that all actions (even means of doing other actions) are actions of trying, and that tryings (and therefore actions) are interior to bodily movements (which are thus not essential).
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From:
report of Jennifer Hornsby (Actions [1980]) by Rowland Stout - Action 9 'Trying'
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A reaction:
[compression of his summary] There is no regress with explaining the 'action' of trying, because it is proposed that trying is the most basic thing in all actions. If you are paralysed, your trying does not result in action. Too mentalistic?
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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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