Philosophy Dictionary of ArgumentsHome
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| Grue, philosophy: Artificial predicate in a thought experiment by Nelson Goodman (N. Goodman, Fact, Fiction and Forecast, Indianapolis, 1965) to illustrate his "New riddle of induction". An object x is grue iff x has been observed before time t and is green or has been observed after t and is blue, the time t being in the future. The problem of uncertainty as to whether something is green or grue arises because the set of green objects is a subset of the set of grue objects. See also induction, projectability, predicates._____________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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Gerhard Schurz on Grue - Dictionary of Arguments
I 219 Grue/gred/reen/Goodman/Schurz: logical form: (B: observed. G*: gred). G*: <> ((Bxt0 > Gx) u (~Bxt0 > Rx)). Sa: emerald. Sample: {a:1 ≤ i ≤ n} Then the assertions Sai u Bat0 u Gai and Sai u Bat0 u G*ai are definitionally equivalent. If we apply the inductive generalization inference for both "green" and "gred," our sample yields the two all-hypotheses H:= "All emeralds are green" and H*: = "All emeralds are gred". Problem: However, H and H* imply contradictory predictions (green versus red) for all emeralds not observed before t0. Schurz: There is the following connection to subjective inductive permutability assumptions: for regular probability functions the permutability assumption cannot be valid for a predicate (Gx) and its pathological counterpart (G*) at the same time. Question: What criteria should we use to decide which predicates we consider to be exchangeable or inductively projectable? Many criteria have been proposed and proved to be unsuitable. Carnap: (1947(1),146, 1976(2), 211): Thesis: only qualitative predicates are inducible (projectable) "grue" is a Def "positional" predicate/Carnap, i.e. a predicate that in its definition refers to time t0. Ex grue. Def qualitative predicate/Carnap: has no definitional reference to individual constants. GoodmanVsCarnap: (Goodman 1955/75(3), 105): Problem of language dependence (sic: dependence): By mutual redefinition one can pass from our language (with "green" and "red") to a language equivalent in expressive power, in which "gred" and "reen" (G*x, R*x) function as basic terms (basic predicates): Language L (Gx,Rx primitive) Definitions in L G*x: <> ((Bxt0 > Gx) u (~Bxt0 > Rx)) R*x: <> ((Bxt0 > Rx) u (~Bxt0 > Gx)) Language L* (G*x, R*x primitive) Definitions in L* Gx: <> ((Bxt0 > G*x) u (~Bxt0 > R*x)) Rx: <> ((Bxt0 > R*x) u (~Bxt0 > G*x)). Solution/Schurz: One can distinguish between qualitative and positional predicates language-independently with respect to ostensive learnability! (s) Properties dependent on a future time cannot be shown). I 220 GoodmanVsInduction/Schurz: but this still does not answer why induction should be based on qualitative and not on positional predicates. Induction consists in extending patterns previously observed as constant into the future. In order to formulate induction rules in a meaningful way, we need to know what remained constant! And that depends on qualitative features. Positional features are pseudo-features. Pointe: That individuals are "constant" "grot" means that they change their color from green to red at t0. In this case we have done "anti-induction" and not induction. This is the reason why we have (with Carnap) for induction rules basic predicates for qualitative and not positional features. 1. Carnap, R. "On the Application of Inductive Logic", Philosophy and Phenomenological Research 8, 133-147. 2. Carnap, R. (1976). Einführung in die Philosophie der Naturwissenschaft, 3. Aufl. München: Nymphenburger. (Engl. Orig. 1966). 3. Goodman, N. (1955/75) Tatsache, Fiktion, Voraussage, Frankfurt/M.: Suhrkamp. Engl, Orig. Fact, Fiction and Forecast (1955)._____________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. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
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Ed. Martin Schulz, access date 2024-04-20