A Case Study in Syntactic Markedness. The Binding nature of by Henk C. van Riemsdijk

By Henk C. van Riemsdijk

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85-92, 1919). So it is not unfair to ascribe much of the agreement between mathematicians to the fact that they find no need to use in most proofs dubious notions such as “ all properties of real numbers” ; these occur nevertheless in mathematical textbooks and are an integral part of mathematics. It follows that unless the result of philosophic investigation is to reveal that the contradictions in question are illusory, produced by fallacious reasoning, ambiguity of terms, or some other trivial cause, clarification of the notions used by mathematicians will be inadequate unless supplemented by revision; it will be necessary actually to alter the meanings attached by mathematicians to many terms and imperative to find new meanings so clear and consistent that the contra­ dictions no longer occur.

Which means ‘ equals by definition ' and is used for defining the meaning of new symbols in terms of those already known. ) = { { p i q ) - { q ^ P ) } Df ■ Here, as in general, the definienium is placed to the left and the definiens to the right of the sign of equality, while the occurrence of the symbol Df. signifies that the expression preceding it is a definition and not a theorem of the propositional calculus. The preceding definition indicates the necessity for using brackets in order to render unambiguous the meaning of complicated expressions.

Pn say, by virtue of their logical form alone. The classical syllogistic rules will illustrate this ; for they state the circumstances in which a proposition can be deduced from two others. We call relations which hold between propositions by reason of their logical form internal relations. Among the most obvious kinds of internal relations between propositions are those between compound propositions such as this paper is white and this line has several words and simpler propositions like this paper is white which are part of them.

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