Russell's Propositional Functions Viewed as Tichý's Constructions

RACLAVSKÝ, Jiří. Russell's Propositional Functions Viewed as Tichý's Constructions. In Perspectives on Russell. 2008.

Základní údaje

• Originální název: Russell's Propositional Functions Viewed as Tichý's Constructions
• Název česky: Russellovy propoziční funkce chápané jako Tichého konstrukce
• Autoři: RACLAVSKÝ, Jiří (203 Česká republika, garant, domácí).
• Vydání: Perspectives on Russell, 2008.

Další údaje

• Originální jazyk: angličtina
• Typ výsledku: Konferenční abstrakt
• Obor: 60300 6.3 Philosophy, Ethics and Religion
• Stát vydavatele: Chorvatsko
• Utajení: není předmětem státního či obchodního tajemství
• Kód RIV: RIV/00216224:14210/08:00029130
• Organizační jednotka: Filozofická fakulta
• Klíčová slova anglicky: Russell; propostional functions; constructions; Tichý; ramified theory of types; axiom of reducibility; impredicativity; vicious circle principle
• Štítky: axiom of reducibility, constructions, impredicativity, propostional functions, ramified theory of types, Russell, Tichý, vicious circle principle
• Příznaky: Mezinárodní význam

Anotace

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.

Anotace česky

V době zastávání no-class theory, Russell nepřipouštěl žádné funkce v moderním smyslu, přijímal pouze idnividua, propozice a propoziční funkce; tyto byly klasifikovány jeho rozvětvenou teorií typů. Daný návrh byl velmi kritizován, Russellovy "intenzionální funkce" byly odmítnuty a vlastně ztožněny s jazykovými výrazy. Ovšem propoziční funkce nemohou být výrazy, neboť obsahují proměnné a ty jsou znaky pouze označovány. Navrhuji chápat Russellovy propoziční funkce jako Tichého konstrukce, neboť ty jsou také na jazyce nezávislými abstraktními strukturovanými entitami, které mohou obsahovat objektuální proměnné. Následně dostávají Russellovy ideje velmi dobrý smysl: princip bludného kruhu je naprosto přirozený a rozvětvená teorie typů je nevyhnutelným důsledkem. Tichého rozvětvená teorie typů ovšem obsahuje i funkc ev moderním smyslu; tím získáváme další možnost interpretaci Russella. Následně jsou studovány impredikativní definice a axióm reducibility. 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.

Návaznosti

• GP401/07/P280, projekt VaV: Název: Singulární termíny - filosofie a logika

Investor: Grantová agentura ČR, Singulární termíny - filozofie a logika