I 62
Generalization/Bigelow/Pargetter: one advantage of our relational theory (of the 3 levels) is that it allows generalizations and variations.
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Relation theory/Bigelow.
I 63
Vector: especially an easy explanation of vectors, with which other theories struggle.
See Relation-Theory/Bigelow, here in the lexicon.
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Vectors.
I 218
Generalization/Bigelow/Pargetter: logical form, if without exception:
(x) (Fx > Gx)
if it has modal status
natN (x)(Fx > Gx)
But sometimes it is good enough to say
Most F's are G's.
Even such statements can have modal character, but beware: probably not of the form
NatN (most F's are G's)
But of the form
Most F's are necessarily G's.
Necessity: then only refers to consequence.
For example, although not all living creatures necessarily have a mother, so surely our cat.
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Range, >
Operators.
Modal Operator/Range/Bigelow/Bigelow/Pargetter: even if it only refers to the consequence, it can be important, e.g. for justifying the explanation domain.
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Modal operators.
Logical form/Bigelow/Pargetter: one could think it should look like this:
(most x)(Fx > natN Gx)
I 219
But that does not cover the whole meaning. This would be equivalent to
(most x)(~Fx v natNGx)
and that is true when most things are not F. And that is not what is meant here!
Wrong solution/Generalization/Bigelow/Pargetter: a counterfactual conditional would not help here:
(most x)(Fx would be > would be natN Gx)
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Counterfactual conditional.
Problem: this could be true for the wrong reasons, for example
Counterfactual conditional/Lewis: is trivially true if the antecedent Fx is not true in any possible world.
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Possible worlds.
Logical form/Generalization/Regularity/Law/Bigelow/Pargetter: of "most F's are necessarily G's" must allow the predicate F limits the range over which the quantifier "most" goes. i.e. it must be something like:
((Fx)(most x) natNGx.
Language/Level/Bigelow/Pargetter: this is not possible with the languages we discussed in chapter 3. (Quantification 2. Level, higher level, logic 2. level).
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Levels/order, >
Description levels, >
Second order logic.
Generalisation/Regularity/Law/Solution/Bigelow/Pargetter: we avoid formalisation and deal with the problem intuitively.
Generalization/Bigelow/Pargetter: often we find such generalization in our daily life: they are not strictly true.
Laws/Bigelow/Pargetter:
1. The characteristic feature is that they involve generalizations.
2. And that they often attribute a kind of necessity to generalization.
I 220
That is, not every correlation should be considered a law.
Necessity: For example, if it is a law that all things fall to the center of the earth,
a) it must not be true that things move like this, but
b) it must be true that they have to move in this way.
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Necessity.
Generalizations/Bigelow/Pargetter:
a) some are only true because each of their instances is true. ((s) without necessity).
Such generalizations without necessity are not laws.
b) for other generalizations, the direction of explanation is reversed: the generalization is not true because their instances are true, but the instances are true because they are instances of generalization.
Those are laws.
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Laws.
The law explains the instances.
Instances explain a (non-necessary) generalization.
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Explanation.
