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.
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