Like Leibniz, C. S. Peirce drew much of the inspiration for his philosophical work from a close study of logical and mathematical reasoning. Now what insights did this study reveal to Peirce? His own answer is formulated as follows: “My first real discovery about mathematical procedure was that there are two kinds of necessary reasoning, which I call the Corollarial and the Theorematic.…” The import of this discovery was lost on philosophers for a long time. The purpose of the present (...) paper is to show what Peirce's insight amounts to, to point out some of its applications, relate it to certain recent developments in the philosophy of logic, and thereby vindicate Peirce's distinction. This undoubtedly will also help to show its present day relevance. (shrink)

Peirce discusses the nature and structure of propositions in several manuscripts written in the 1890’s and during the first decade of this century. In this paper I shall outline the main features of Peirce’s theory of the proposition, especially his account of what may be called indeterminate indices in propositions.

Since the publication of Husserl's Logische Untersuchungen at the outset of this century, the notion of phenomenology has had a long and important history on the European continent. Of the many claims made on its behalf perhaps the most interesting is that phenomenology is able to ground philosophical assertions in a manner which is neither purely formal nor purely empirical, i.e., that phenomenology as a method is capable of transcending this very distinction. For example, phenomenologists argue that their reduction of (...) essences provides a way of knowing which is neither analytic nor synthetic but both. Having reached such an eidetic intuition phenomenologists claim to have attained a non-trivial universality and necessity. (shrink)

Like Leibniz, C. S. Peirce drew much of the inspiration for his philosophical work from a close study of logical and mathematical reasoning. Now what insights did this study reveal to Peirce? His own answer is formulated as follows: “My first real discovery about mathematical procedure was that there are two kinds of necessary reasoning, which I call the Corollarial and the Theorematic.…” The import of this discovery was lost on philosophers for a long time. The purpose of the present (...) paper is to show what Peirce's insight amounts to, to point out some of its applications, relate it to certain recent developments in the philosophy of logic, and thereby vindicate Peirce's distinction. This undoubtedly will also help to show its present day relevance. (shrink)