Philosophy Dictionary of ArgumentsHome
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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. | |||
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J. Hintikka on Stronger/weaker - Dictionary of Arguments
II 7 Standard Semantics/Kripke Semantics/Hintikka: what differences are there? The ditch between standard semantics and Kripke semantics is much deeper than it first appears. Cocchiarella: Cocchiarella has shown, however, that even in the simplest quantifying case of the monadic predicate logic, the standard logic is radically different from its Kripke cousin. Decidability: monadic predicate logic is, as Kripke has shown, decidable. Kripke semantics: Kripke semantics is undecidable. Decisibility: Decisibility implies axiomatizability. Stronger/weaker/Hintikka: as soon as we go beyond monadic predicate logic, we have a logic of considerable strength, complexity, and unruliness. Quantified standard modal logic of the 1. level/Hintikka: the quantified standard modal logic of the 1. level is in a sense more powerful than the 2. level logic (with standard semantics). The latter is, of course, already very strong, so that some of the most difficult unresolved logical and quantum-theoretical problems can be expressed in terms of logical truth (or fulfillment) in logical formulas of the second level. Def equally strong/stronger/weaker/Hintikka: (here): the terms "stronger" and "weaker" are used to show an equally difficult decision-making problem. Decision problem: the standard logic of the 2. level can be reduced to that for quantified standard modal logic of the 1. level. Reduction: this reduction is weaker than translatability. II 9 Quantified standard modal logic of the 1. level/Hintikka: this logic is very strong, comparable in strength with the 2. level logic. It follows that it is not axiomatizable (HintikkaVsKripke). The stronger a logic is, the less manageable it is. II 28 Branching Quantifiers/stronger/weaker/Hintikka: E.g. branching here: 1. Branch: there is an x and b knows... 2. Branch: b knows there is an x ... Quantification with branched quantifiers is extremely strong, almost as strong as 2. level logic. Therefore, it cannot be completely axiomatized (quantified epistemic logic with unlimited independence). II 29 Variant: variants are simpler cases where the independence refers to ignorance, combined with a move with a single, non-negated operator {b} K. Here, an explicit treatment is possible. II 118 Seeing/stronger/weaker/logical form/Hintikka: a) stronger: recognizing, recognizing as, seeing as. b) weaker: to look at, to keep a glance on, etc. Weaker/logical form/seeing/knowing/Hintikka: e.g. (Perspective, "Ex") (15) (Ex) ((x = b) & (Ey) John sees that (x = y)). (16) (Ex)(x = b & (Ey) John remembers that x = y)) (17) (Ex)(x = b & (Ey) KJohn (x = y)) Acquaintance/N.B.: in (17) b can be John's acquaintance even if John does not know b as b! ((S) because of y). II 123 Everyday Language/ambiguity/Hintikka: the following expression is ambiguous: (32) I see d Stronger: (33) (Ex) I see that (d = x) That says the same as (31) if the information is visual or weaker: (34) (Ex) (d = x & (Ey) I see that (x = y)) This is the most natural translation of (32). Weaker: for the truth of (34) it is enough that my eyes simply rest on the object d. I do not need to recognize it as d._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Hintikka I Jaakko Hintikka Merrill B. Hintikka Investigating Wittgenstein German Edition: Untersuchungen zu Wittgenstein Frankfurt 1996 Hintikka II Jaakko Hintikka Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 |
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> Counter arguments against Hintikka
> Counter arguments in relation to Strength of Theories
Ed. Martin Schulz, access date 2024-04-17