|Type theory: The type theory is a restriction of formal systems to a kind of reference which prevents symbols of a level (of a type) from referring to symbols of the same level (the same type). This is intended to avoid paradoxes arising from a self-reference of the signs or expressions used. Original proposals for type theories are given by 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, 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. |
Branched Type Theory/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 "- Branched Type Theory: not only different types, but also different "orders" should be represented by different symbols._____________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.
Objects of thought Oxford 1971
Arthur N. Prior
Papers on Time and Tense 2nd Edition Oxford 2003