Philosophy Lexicon of Arguments

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Strength of theories, philosophy: theories and systems can be compared in terms of their strength. With increasing expressiveness of a system, e.g. the possibility that statements refer to themselves, however, grows the risk of paradoxes. Strength and expressiveness do not always go hand in hand. Thus, e.g. the modal logical system S5, which is stronger than the system S4, is unable to establish a unique temporal order. Aspects of strength and weakness are inter alia the set of derivable sentences, or the size of the subject area of a theory or system. See also theories, systems, modal logic, axioms, axiom systems, expansion, mitigation, areas.

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.

Author Item Summary Meta data
I 36
Stronger/Weaker/Field/(s): higher order systems are stronger.
I 121
E.g. "There is a proof of ~ A> ~ MA" - stronger: "There is a model of A > MA".
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.
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.
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.
II 123
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.
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.
II 361
Def Weak a priori sentence/Field: can be reasonably believed without empirical evidence. -> III 39 second order Logic.
III 39
Stronger/Weaker: weaker theories have rather non-standard models (unintend models) - a higher order systems is stronger than a 1st order system.

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.

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

H. Field
Science without numbers Princeton New Jersey 1980

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Ed. Martin Schulz, access date 2018-06-25