14 ideas
| 15327 | Kripke's semantic theory has actually inspired promising axiomatic theories [Kripke, by Horsten] |
| Full Idea: Kripke has a semantic theory of truth which has inspired promising axiomatic theories of truth. | |
| From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Leon Horsten - The Tarskian Turn 01.2 | |
| A reaction: Feferman produced an axiomatic version of Kripke's semantic theory. |
| 15343 | Kripke offers a semantic theory of truth (involving models) [Kripke, by Horsten] |
| Full Idea: One of the most popular semantic theories of truth is Kripke's theory. It describes a class of models which themselves involve a truth predicate (unlike Tarski's semantic theory). | |
| From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Leon Horsten - The Tarskian Turn 02.3 | |
| A reaction: The modern versions explored by Horsten are syntactic versions of this, derived from Feferman's axiomatisation of the Kripke theory. |
| 14966 | The Tarskian move to a metalanguage may not be essential for truth theories [Kripke, by Gupta] |
| Full Idea: Kripke established that, contrary to the prevalent Tarskian dogma, attributions of truth do not always force a move to a metalanguage. | |
| From: report of Saul A. Kripke (Outline of a Theory of Truth [1975], 5.1) by Anil Gupta - Truth | |
| A reaction: [Gupta also cites Martin and Woodruff 1975] |
| 14967 | Certain three-valued languages can contain their own truth predicates [Kripke, by Gupta] |
| Full Idea: Kripke showed via a fixed-point argument that certain three-valued languages can contain their own truth predicates. | |
| From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Anil Gupta - Truth | |
| A reaction: [Gupta also cites Martin and Woodruff 1975] It is an odd paradox that truth can only be included if one adds a truth-value of 'neither true nor false'. The proposed three-valued system is 'strong Kleene logic'. |
| 16328 | Kripke classified fixed points, and illuminated their use for clarifications [Kripke, by Halbach] |
| Full Idea: Kripke's main contribution was …his classification of the different consistent fixed points and the discussion of their use for discriminating between ungrounded sentences, paradoxical sentences, and so on. | |
| From: report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Volker Halbach - Axiomatic Theories of Truth 15.1 |
| 10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
| Full Idea: A logic is a collection of closely related artificial languages, and its older meaning is the study of the rules of sound argument. The languages can be used as a framework for studying rules of argument. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.1) | |
| A reaction: [Hodges then says he will stick to the languages] The suspicion is that one might confine the subject to the artificial languages simply because it is easier, and avoids the tricky philosophical questions. That approximates to computer programming. |
| 10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
| Full Idea: To have a truth-value, a first-order formula needs an 'interpretation' (I) of its constants, and a 'valuation' (ν) of its variables. Something in the world is attached to the constants; objects are attached to variables. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) |
| 10284 | There are three different standard presentations of semantics [Hodges,W] |
| Full Idea: Semantic rules can be presented in 'Tarski style', where the interpretation-plus-valuation is reduced to the same question for simpler formulas, or the 'Henkin-Hintikka style' in terms of games, or the 'Barwise-Etchemendy style' for computers. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) | |
| A reaction: I haven't yet got the hang of the latter two, but I note them to map the territory. |
| 10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
| Full Idea: I |= φ means that the formula φ is true in the interpretation I. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.5) | |
| A reaction: [There should be no space between the vertical and the two horizontals!] This contrasts with |-, which means 'is proved in'. That is a syntactic or proof-theoretic symbol, whereas |= is a semantic symbol (involving truth). |
| 10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
| Full Idea: Downward Löwenheim-Skolem (the weakest form): If L is a first-order language with at most countably many formulas, and T is a consistent theory in L. Then T has a model with at most countably many elements. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
| Full Idea: Upward Löwenheim-Skolem: every first-order theory with infinite models has arbitrarily large models. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
| Full Idea: Compactness Theorem: suppose T is a first-order theory, ψ is a first-order sentence, and T entails ψ. Then there is a finite subset U of T such that U entails ψ. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) | |
| A reaction: If entailment is possible, it can be done finitely. |
| 10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
| Full Idea: A 'set' is a mathematically well-behaved class. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.6) |
| 7482 | Resurrection developed in Judaism as a response to martyrdoms, in about 160 BCE [Anon (Dan), by Watson] |
| Full Idea: The idea of resurrection in Judaism seems to have first developed around 160 BCE, during the time of religious martyrdom, and as a response to it (the martyrs were surely not dying forever?). It is first mentioned in the book of Daniel. | |
| From: report of Anon (Dan) (27: Book of Daniel [c.165 BCE], Ch.7) by Peter Watson - Ideas | |
| A reaction: Idea 7473 suggests that Zoroaster beat them to it by 800 years. |