The notion of logical form and its applications are at the heart of some of the classical problems in philosophical logic and are the focus of Peter Long’s investigations in the three essays that comprise this volume.
In the first, major, essay the concern is with the notion of logical form as it applies to arguments involving hypotethical statements, for example ‘If today is Wednesday then tomorrow is Thursday; today is Wednesday: therefore tomorrow is Thursday.’ Whilst such an argument (an argument by modus ponens) is cited by logical textbooks as a paradigm of one that is ‘formally valid’, it is not hard to show that the conjunction forming a hypothetical statement is not a logical constant, in which case the argument form If p then q; p: therefore q is not a logical form. But, then, how can logic claim to be the science of formal inference? The author resolves this difficulty by drawing a fundamental distinction within the notion of the form under which an argument is valid. With this distinction it becomes possible for the first time to determine the status of any formally valid argument involving hypotheticals, whether as premises or conclusion or both.
The second and third essays take up the notion of logical form as it applies to such simple propositions as ‘This sheet is white’ and ‘London is north of Paris.’ When we speak of the first as giving expression to the relation of relations’s relating to its terms, what is in question is a formal relation and we call it such because the relation is expressed through these propositions having the respective forms Fa and Fab. It is shown that the confusion of formal relations with relations proper explains the assimilation of facts to complexes and is that the root of the theory of universals.
Peter Long has taught at the University of Leeds and University College London, and is a past Fellow of Trinity College, Cambridge.