Open AccessRussell And Frege On The Logic of Functions
Author(s) -
Bernard Linsky
Publication year - 2008
Publication title -
the baltic international yearbook of cognition, logic and communication
Language(s) - English
Resource type - Journals
ISSN - 1944-3676
DOI - 10.4148/biyclc.v4i0.133
Subject(s) - mathematics , principle of compositionality , calculus (dental) , epistemology , algebra over a field , philosophy , pure mathematics , medicine , dentistry
I compare Russell’s theory of mathematical functions, the “descriptive functions” from Principia Mathematica ∗30, with Frege’s well known account of functions as “unsaturated” entities. Russell analyses functional terms with propositional functions and the theory of denite descriptions. This is the primary technical role of the theory of descriptions in P M . In Principles of Mathematics and some unpublished writings from before 1905, Russell offered explicit criticisms of Frege’s account of functions. Consequenly, the theory of descriptions in “On Denoting” can be seen as a crucial part of Russell’s larger logicist reduction of mathematics,aswellasanexcursionintothetheoryof reference.