Lexicon of Arguments

 

I (d) 107
Definition ω model/Putnam: a ω model is a model for a set theory in which the natural numbers are ordered "as it should be", that means, the sequence of "the natural numbers" of the model ω-sequence.
I (d) 109f
Countable/over-countable/uncountable/infinity/Loeweheim/Putnam: e.g. an instrument that will detect the presence of a particle within a volume, will at most give countable measurements. But if the instrument is shifted by r centimeters and r can be any real number, then there are over-countable many measurements. N.B.: then operational conditions cannot be identified with the totality of facts that can be observed, but only with the actual observed. If the shifted intervals are then rational, there are only a countable number of facts. Loewenheim: then, a model can be constructed that matches with all facts.
>Löwenheim sentence.
Counterfactual Conditional: a model with a predicate "makes subjunctive necessary" for not occurred cases can be constructed that induces an interpretation of counterfactual speech that makes precisely those counterfactual conditionals true that are according to some completion to our theory true. This means, the appeal to counterfactual observations cannot exclude models.
Wittgenstein: the question of what God could calculate, is a matter within the math and cannot determine the interpretation of mathematics (PU §§ 193,352,426).
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II 112
There are possible set theories with and without the axiom of choice. Skolem: we should assign a truth value only as a part of a previously accepted theory.
>Truth value, >Set theory, >Selection axiom.