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Stronger/Weaker/Field/(s): higher order systems are stronger.
E.g. "There is a proof of ~ A> ~ MA" - stronger: "There is a model of A > MA".
Theory/Nominalism/strong/weak/(s): a strong theory: has more consequences - if mathematical entities (m.e.) should be dispensable, a platonic theory must have no (physical) consequences, which a nominalistic (physical entities only) does not have.
Weaken/"too rich"/"too strong"/Field: E.g. a theory (or schema) asserts the existence of more entities (such as regions) than you ever need. - Then unsecured empirical consequences can occur. - (unverifiable) - Solution: Weakening of the theory.
Fragment/stronger/weaker/Field/(s): weak fragment of substitutional quantification. (sQ): - without substitutional quantifiers: treating scheme characters as variables for sentences. - Then the schemata themselves are part of the language, not only their instances.
Weak/Field/(s): Weaker: Scheme letters are weaker than substitutional allquantification - Modal operator: demands stronger expressions.
Ad II ~ 290
Vagueness/logic/(s): gradations: strong: certain instances of the sentence of the excluded third are wrong. - weaker: some cannot be identified. - "wrong"/strong: "has a true negation". -...Field: to express assertions and denials of determinacy e.g. D-A, D-A, -D-DA, D-D-A, etc. (A is atomic) - so we have reduced the problem considerably of explaining the determinateness.
S4: there are the following possibilities: Positive limit: ~ DA u D ~ D ~ A u ~ D ~ DA. - Negative limit: ~ D ~ A u D ~ DA u ~ D ~ D ~ A - "Definitely indeterminate": D ~ DA u D ~ D ~ A - "hopelessly indeterminate": ~ D ~ DA u ~ D ~ D ~ A - - i.e. not even definite limit - potential indeterminacy of the first order/Field: for an agent this means that if he treats A as potentially indeterminate, then he must have degree of believe in it and its negation, which adds up to less than one.
Definition weak a priori sentence/Field: can be reasonably believed without empirical evidence. -> III 39 second order Logic.
Stronger/Weaker: weaker theories have rather non-standard models (unintend models) - a higher order systems is stronger than a 1st order system.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980