## Philosophy Dictionary of ArgumentsHome | |||

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Impredicativeness: Impredicatives are concepts which are defined only by means of the propositional sets to which they themselves belong. Problems arise in connection with possible circular conclusions. To avoid paradoxes, the demand is sometimes made to avoid impredicative concepts. See also Paradoxes, Russellian Paradoxy, Poincaré._____________ 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 |
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I 214 Definition impredicative/Field: completely impredicative properties: are not at all derived from previously available properties. - In particular, there is no property to be a property. Quasi-impredicative: also allows "property to be a property". --- I 216 Classic example for impredicative definition: E.g. What is it for an ordinal number to be finite? - Fin (ON) P [P is inductive & P (0)> P (ON)] - whereby P is inductive is defined as: b [P(b) > P(b + 1)] - ((s) All successors have the same property (to be a number)). The invalid objection against the impredicative definition (> VsImpredicativity) is that one cannot know that a given number, e.g. 2 is finite because, in order to show this, we must be able to show that 2 has every inductive property of 0. - To show that 2 is finite, we must show first that exactly this 2 is finite (circular). Solution/Field: the solution is simple: if finiteness is an inductive property, then 2 is finite. - No circle. _____________ 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. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
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 InTheories of Truth, Paul Horwich, Aldershot 1994 |

> Counter arguments against **Field**

> Counter arguments in relation to **Impredicativeness**

Ed. Martin Schulz, access date 2020-05-28