Russell's Propositional Functions Viewed as Tichý's Constructions
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| Year of publication | 2008 |
| Type | Conference abstract |
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| Description | In the era of his no-class theory, Russell held that there are no functions in the modern sense and he admitted only individuals, propositions and propositional functions; these were classified by means of his ramified theory of types. This proposal was criticized in length and many adopted the opinion of Ramsey and Quine that there are only individuals, functions and expressions which were (allegedly wrongly) assumed by Russell as intensional entities. Yet Russell's variables are genuine objects (represented in language by "signs"), Russell did not subscribe to modern paradigm that variables are letters. Consequently, propositional functions cannot be expressions, since expressions cannot contain such variables-letters. I propose to view Russell's propositional functions as Pavel Tichý's constructions, expressions-independent structured procedures (generalized algorithms; for their huge defence see Tichý 1988). Now all Russell's key ideas acquire a very good sense: vicious circle principle is entirely natural and ramified theory of types becomes its inevitable consequence. However, Tichý's RTT does contain also ordinary functions, thus we have another point for the interpretation of Russell's thoughts. The author suggests also two formulations of the Axiom of reducibility (which is a correct principle), only one of which was somehow formalized by Russell; the other formulation - covering the notion of im/predicativity - was illegal in Russell's system but I suggest a modification of (Tichý's) RTT in order to legalize it. Hence, when propositional functions are viewed as Tichý's constructions, Russell's utmost contribution to the philosophy of logic is of a high plausibility. |
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