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| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Fixed Points | Logic Texts | Read III 196 Kripke's Fixed Points/Read: 1. Separate truth and falsehood conditions (i.e. falsehood is not equal to non-truth). 2. Two sentence sets S1: true sentences, S2 false sentences. 3. Do evaluation on each level, therefore you have to choose a higher level. In this way, all sentences are "collected". Fixed point/(s): where evaluation (output) is identical to input. Read: Success: then the extension fails - i.e. the meta language does not contain any further truth-attributions than the object language(1). >Meta language, >Object language, >Levels (Order). III 197 Kripke's Fixed Points/Kripke: the extension fails: the meta language has no further truth-attributions. There is a paradox in the fixed point without truth value. Falsehood does not equal non-truth! >Truth value. Truth-predicate/Kripke's Fixed Points/Read: we separate the truth-predicates truth and falsehood - the truth-predicate is formed by the pair (S1, S2), whereby S1 contains the true sentences and S2 contains the wrong sentences. >Truth predicate. 1st level: here, a sentence has, e.g. ""Snow is white" is true" has no truth value because evaluation at this stage is not possible. >Valuation. Solution: weak matrices for evaluating compound sentences, some of which are without truth value (without truth value) - (A v B) without truth value if one of A or B has no truth value (partial interpretation). III 198 Fixed point/Kripke's Fixed Points/Kripke/Read: the fixed point is reached by transfinite induction - recursive or successive with partial evaluations. 1st transfinite level: all finite partial evaluations of S1 and S2 are collected separately. N.B.: at an early point (before adding all possible sentences), the reinterpretation of the truth-predicate no longer succeeds in adding something new. Special case of the result about fixed points of normal functions over ordinal numbers. Phi/f: represents the operation of expanding by allowing new interpretations. The fixed point here is f(S1, S2) = (S1, S2). III 200 Unfounded assertions: the separation of S1 and S2 leaves some statements without a truth value - e.g. "this statement is true". It has no truth value at the minimum fixed point. One level higher we can give it an arbitrary value-but not to the liar paradox. Paradox/Kripke: follows Tarski: it cannot be expressed in one's own language. The entire discussion belongs to the meta language, as well as the predicates: "paradoxical" and "unfounded". They do not belong to the semantically terminated fixed point. Tarski's truth schema does not work here - (... + ...). >Disquotation schema. 1. Saul Kripke Outline of a Theory of Truth (1975) in: R.L.Martin (Ed.) Recent Essays on Truth and the Liar Paradox Clarendon Oxf/NY 1984 |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 |
| Truth Value Gaps | Field | I 245 Truth-value gaps: Kripke (1975)(1): Kripke accepts temporarily indeterminate truth values up until the level has been assigned. >Indeterminacy, >Truth values, >Fixed points/Kripke, >Truth/Kripke. 1.Kripke, S. 1975. Outline of a theory of truth. Journal of Philosophy 72 (19):690-716 |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
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