|Model Theory: The model theory investigates whether an axiom system is fulfilled and thus provides one (or more) models. Model theory belongs to the semantics because it uses the concept of truth, while the proof theory belongs to the domain of syntax by asking for the existence of finite character string (of proofs). One problem is the exclusion of unintended models._____________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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Answer/Model Theory/Hintikka: before we have criteria for a complete (exhaustive) answer, we cannot understand how answers provide any information at all.
Model theory: we proceed here model-theoretically.
Definition knowledge/semantics of possible worlds/model theory/Hintikka: the set of possible worlds that are compatible with what the subject knows. E.g.
(1) b knows that p
is true iff. it is true that p in all epistemic b alternatives to w0.
A W-question like E.g.
(2) Who killed Roger Ackroyd?
((s) figure of Agatha Christie).
Is analyzed as a request for information that is present when one can say truthfully
(3) I know who killed Roger Ackroyd.
Definition Desideratum/Hintikka: is the piece of information that provides a complete answer to a question. E.g. (3) is the desideratum of (2).
(3) can be analyzed as
(4) (Ex) I know that (x killed Ackroyd)
Whereby "x" is about people.
Model Theory/Hintikka: Model theoretically, (4) means that there is an individual x, so that in any world compatible with my knowledge x killed Ackroyd. That is, the same as that I have enough information to rule out that x has not done it._____________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.
Jaakko and Merrill B. Hintikka
The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989
J. Hintikka/M. B. Hintikka
Untersuchungen zu Wittgenstein Frankfurt 1996