Volume 55, 2018
Philosophy of Logic
Hartley Slater
Pages 47-51
Realist Logic
It is shown that the Nominalism of much of Modern Logic is what has given rise to many of its problems, especially The Liar Paradox. Shifting to a Realist Logic, in which ‘that’-clauses have a central place, overcomes these problems. The move involved, from the study of mentioned sentences to the employment of ‘that’-clauses, reveals the indexicality of referring phrases, and it is that which enables an escape from The Liar. But also it is shown that no parallel paradox is obtainable with the propositions that ‘that’-clauses designate. Several theoretical issues, however, then need to be faced about what ‘that’-clauses designate, primarily what has been called the problem of ‘The Unity of the Proposition’. The term ‘proposition’, it turns out, is not always appropriate for what ‘that’-clauses designate, so a richer language is introduced to handle all cases. But the problem of the unity of what is designated arises in all cases, and is solved by noting a parallel with Russell’s treatment of individuals and descriptive phrases.