Philosophy Dictionary of ArgumentsHome
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| Type theory: Restriction of formal systems to a type of reference that prevents symbols of one level (of one type) from referring to symbols of the same level (of the same type). This is intended to avoid paradoxes arising from the self-referentiality of the symbols or expressions used. Original proposals for type theories come from B. Russell (B. Russell, Mathematical logic as based on the theory of types, in American Journal of Mathematics 30 (1908), pp. 222-262). See also Self-reference, Circularity, Paradoxes, Russell's paradox, Stages, Branched type theory. _____________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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Arthur N. Prior on Type Theory - Dictionary of Arguments
I 39f Ramified Type Theory/ramified theory of types/Prior: comes in when terms form a sentence of a single name. - Here we must distinguish whether quantified expressions of the same type occur. E.g. "__ has all the qualities of a great commander". Logical form: "For all φ, if (for all x, if x is a great commander, then φx) then F__ ". ∏φ∏xCψxφx". Easier e.g. "__ has one or the other property". Logical form: "For a φ, φ __". "∑φφ". Order/Type: here you can say, even though the predicate of the same type, it also is of different order. - Because this "φ" an internal quantification of "φ" s. Ramified Type Theory: here not only different types, but also different "orders" should be represented by different symbols. >Ramified Type Theory._____________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. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
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> Counter arguments against Prior
> Counter arguments in relation to Type Theory
Ed. Martin Schulz, access date 2024-04-29