Since Freges terms were meant to refer always to sets, that is, entities composed of individuals. Classical philosophy up to Leibniz and Kant had a different view on this questionBegriffes syntaxhighercorresponding to the idea which Leibniz used in the construction of his characteristic numbers. Thus, this paper is an addendum to Corcorans theory via predicate logic.

1 INTRODUCTION Above the other titles he might justly have claimed, Charles S. Peirce prized the title 'logician'. He expressed in several places his ...

A logical system is studied whose well-formed representations consist of diagrams rather than formulas. The system, due to Shin [2, 3], is shown to be complete by an argument concerning maximally consistent sets of diagrams. The argument is complicated by the lack of a straight forward counterpart of atomic formulas for diagrams, and by the lack of a counterpart of negation for most diagrams.

A formal system is studied having both sentences and diagrams as well-formed representations. Proofs in the system allow inference back and forth between sentences and diagrams, as well as between diagrams and diagrams, and between sentences and sentences. This sort of heterogeneous system is of interest because external representations other than linguistic ones occur commonly in actual reasoning in conjunction with language. Syntax, semantics, and rules of inference for the system are given and it is shown to be sound and (...) complete. (shrink)

New light is shed on Leibniz’s commitment to the metaphysical priority of the intensional interpretation of logic by considering the arithmetical and graphical representations of syllogistic inference that Leibniz studied. Crucial to understanding this connection is the idea that concepts can be intensionally represented in terms of properties of geometric extension, though significantly not the simple geometric property of part-whole inclusion. I go on to provide an explanation for how Leibniz could maintain the metaphysical priority of the intensional interpretation while (...) holding that logically the intensional and the extensional stand in strictly inverse relation to each other. (shrink)

We specify two problems in syllogistic: the lack of functoriality of predicates and the change of grammatical role of the middle term, from subject to predicate, in some syllogisms. The standard semantics, the class interpretation, by-passes these difficulties but, we argue, in a manner that is at odds with logical intuition. We propose a semantics that is category theoretic to handle these difficulties. With this semantics we specify when syllogisms are valid and we set limits to the class interpretation. To (...) perform this task we show how to construct the categorical notion of an entity in a system of kinds. We devote two brief sections to an argument that our approach is very much in the spirit of Aristotle. (shrink)

In Volume 33:1 of the Notre Dame Journal of Formal Logic, a system for diagramming syllogistic inferences using straight line segments is presented by Englebretsen. In light of recent research on the representational power of diagrammatic representation systems by the authors, we point out some problems with the proposal, and indeed, with any proposal for representing logically possible situations diagrammatically. We shall first outline the proposed linear diagrammatic system of Englebretsen, and then show by means of counterexamples that it is (...) inadequate as a representation scheme for general logical inferences (the task for which the system is intended). We also show that modifications to the system fail to remedy the problems. The considerations we present are not limited to the particular proposal of Englebretsen; we thus draw a more general moral about the use of spatial relations in representation systems. (shrink)

We specify two problems in syllogistic: the lack of functoriality of predicates (although a thief is a person, a good thief may not be a good person) and the change of grammatical role of the middle term, from subject to predicate, in some syllogisms. The standard semantics, the class interpretation, by-passes these difficulties but, we argue, in a manner that is at odds with logical intuition. We propose a semantics that is category theoretic to handle these difficulties. With this semantics (...) we specify when syllogisms are valid and we set limits to the class interpretation. To perform this task we show how to construct the categorical notion of an entity in a system of kinds. We devote two brief sections to an argument that our approach is very much in the spirit of Aristotle. (shrink)