|Generalization: a generalization is the extension of a statement (an attribution of properties) that applies to a domain D of objects to an object domain E that is larger than D and contains D. Time points may also belong to the subject domain. A property which fully applies to the objects of an object domain may be partially applicable to the objects of a larger domain. See also validity, general invalidity, general, predication, methods._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
Generalization/Bigelow/Pargetter: one advantage of our relational theory (of the 3 levels) is that it allows generalizations and variations.
Vector: especially an easy explanation of vectors, with which other theories struggle.
See Relation-Theory/Bigelow, here in the lexicon.
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.
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.
Logical form/Bigelow/Pargetter: one could think it should look like this:
(most x)(Fx > natN Gx)
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)
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.
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).
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.
1. The characteristic feature is that they involve generalizations.
2. And that they often attribute a kind of necessity to generalization.
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.
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.
The law explains the instances.
Instances explain a (non-necessary) generalization._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990