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.

Basic information

• Original name: Russell's Propositional Functions Viewed as Tichý's Constructions
• Name in Czech: Russellovy propoziční funkce chápané jako Tichého konstrukce
• Authors: RACLAVSKÝ, Jiří (203 Czech Republic, guarantor, belonging to the institution).
• Edition: Perspectives on Russell, 2008.

Other information

• Original language: English
• Type of outcome: Conference abstract
• Field of Study: 60300 6.3 Philosophy, Ethics and Religion
• Country of publisher: Croatia
• Confidentiality degree: is not subject to a state or trade secret
• RIV identification code: RIV/00216224:14210/08:00029130
• Organization unit: Faculty of Arts
• Keywords in English: Russell; propostional functions; constructions; Tichý; ramified theory of types; axiom of reducibility; impredicativity; vicious circle principle
• Tags: axiom of reducibility, constructions, impredicativity, propostional functions, ramified theory of types, Russell, Tichý, vicious circle principle
• Tags: International impact

Abstract

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.

Abstract (in Czech)

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.

Links

• GP401/07/P280, research and development project: Name: Singulární termíny - filosofie a logika

Investor: Czech Science Foundation, Singular Terms - Philosophy and Logic