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 7
Standard semantics/Kripke semantics/Hintikka: what differences are there? The ditch between them is much deeper than it first appears.
Cocchiarella: he 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 1. level/Hintikka: the quantified standard modal logic of 1. level is in a sense more powerful than 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.
Definition equally strong/stronger/weaker/Hintikka: (here): to show an equally difficult decision-making problem.
Decision problem: for standard logic 2. level can be reduced to that for quantified standard modal logic 1. level.
Reduction: this reduction is weaker than translatability.
I 9
Quantified standard modal logic 1. level/Hintikka: this logic is very strong, comparable in strength with 2. level logic. It follows that it is not axiomatizable. (HintikkaVsKripke).
The stronger a logic is, the less manageable it is.
I 28
Branched quantifiers/branching/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).
I 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.
I 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 even John's acquaintance even if John does not know b as b! ((S) because of y).
I 123
Everyday language/ambiguity/Hintikka: the following expression is ambiguous:
(32) I see d
(33) (Ex) I see that (d = x)
That says the same as (31) if the information is visual or
(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.

Hin I
Jaakko Hintikka
Merrill B. Hintikka
The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989

J. Hintikka/M. B. Hintikka
Untersuchungen zu Wittgenstein Frankfurt 1996

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