Philosophy Lexicon of Arguments

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I 36
Stronger/Weaker/Field/(s): higher order systems are stronger.
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I 121
E.g. "There is a proof of ~ A> ~ MA" - stronger: "There is a model of A > MA".
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I 132
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.
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I 172
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.
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II 115
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.
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II 123
Weak/Field/(s): Weaker: Scheme letters are weaker than substitutional allquantification - Modal operator: demands stronger expressions.
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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.
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II 295
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.
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II 361
Definition weak a priori sentence/Field: can be reasonably believed without empirical evidence. -> III 39 second order Logic.
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III 39
Stronger/Weaker: weaker theories have rather non-standard models (unintend models) - a higher order systems is stronger than a 1st order system.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980


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Ed. Martin Schulz, access date 2017-05-28