Remarks on Farrell's Implication

Abstract

The paper provides an analysis of the three-valued implication developed by Robert Farrell in his work “Material Implication, Confirmation, and Counterfactuals” (1979). Our analysis shows that, firstly, Farrell's implication has all the properties sufficient to put it into the category of connexive implications. Secondly, that Farrell's implication, similar in some of its properties to conjunction, can be used for the formal modelling of some peculiarities of understanding of conditional statements which are inherent to the early stages of development of humans' cognitive abilities. The main technical result of the paper is the construction and meta-theoretical study of the three-valued logic $\mathbf{F^{*}_{3}}$ containing Farrell's implication.