Amirouche Moktefi

It is little known that Schopenhauer (1788–1860) made thorough use of Euler diagrams in his works. One specific diagram depicts a high number of concepts in relation to Good and Evil. It is, hence, uncharacteristic as logicians of that time seldom used diagrams for more than three terms (the number demanded by syllogisms). The objective of this paper is to make sense of this diagram by explaining its function and inquiring whether it could be viewed as an early serious attempt to construct complex diagrams.

In a letter to Bertrand Russell, dated 17 May 1905, Hugh MacColl tells how he abandoned the study of logic after 1884 for about thirteen years and how it was the reading of Lewis Carroll’s Symbolic Logic (1896) that ”rekindled the old fire which [he] thought extinct.” From then onwards, he published several papers containing some of his major logical innovations. The aim of this paper is to discuss MacColl’s acquaintance with and appreciation of Carroll’s work, and how that reading convinced him to come back into the realm of logic. There is no evidence that the two men ever met or exchanged any personal correspondence. However, MacColl reviewed in The Athenaeum several of Carroll’s books, mainly on geometry and logic. Often, Carroll replied to MacColl’s criticisms in the following editions of his works. A discussion of these sources provides interesting insights to MacColl’s (and Carroll’s) mathematical and logical investigations.

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis.

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis.