Logic, Form, and Grammar

Logic, Form, and Grammar

Logic, Form, and Grammar

Logic, Form, and Grammar


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.


Common to the three essays printed here is a preoccupation with the notion of logical form, and, thereby, with that of a formal relation.

In the last two essays, where the concern is primarily with the notion of logical form as it applies to propositions, the formal relation is a relation internal to propositions. Thus we speak of the relation of a thing’s having a property (of an object’s falling under a concept) or of the relation of a relation’s relating its terms, and here the relation is one that is expressed in a proposition through its being of the form Fa or Fab and so on. the confusion of such formal relations with relations proper—relations for which there exists or could exist an expression in the language—is common in philosophy and appears at its most blatant in Locke’s theory of a substratum or property-less subject of properties and Bradley’s polemic against relations, where he asserts that a relation has to be related to its terms in order to relate them. the confusion is at the root of the theory that properties and relations are universals and is responsible for the assimilation of facts to complexes, which is found in the early pages of the Tractatus.

In the first, major, essay, the concern is primarily with the notion of logical form as it applies to arguments, and here the formal relation is a relation between propositions. Thus in the syllogism ‘Every Athenian is Greek; Socrates is an Athenian: therefore Socrates is Greek’, the third proposition is inferable from the first two in that they are respectively of the forms Ga, every F is G, Fa, or, as we may put it, in that the first two stand to the third in the relation every F is G, Fa: Ga. the propositions standing in this relation are all asserted in the syllogism, but it is not hard to show that an argument in which not all three propositions are asserted may have the same logical form as the syllogism. An example would be ‘Every Athenian is Greek: therefore if Socrates is an Athenian then he is Greek’, in which the conclusion is a hypothetical statement, so that only one of the three propositions is asserted. We thus arrive at the concept of a hypothetical variant of an argument—a concept which is indispensable for understanding the role of hypothetical in inference, whether as premisses or conclusion.

A classic example of such is a modus ponens, in which the consequent of a hypothetical is inferred from it together with its antecedent. No argument

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