Over a decade ago, John Sowa did the AI community the great service of introducing it to the Existential Graphs of Charles Sanders Peirce. EG is a formalism which lends itself well to the kinds of thing that Conceptual Graphs are aimed at. But it is far more; it is a central element in the mathematical, logical, and philosophical thought of Peirce; this thought is fruitful in ways that are seldom evident when we first encounter it. In one of his (...) major works on Existential Graphs, Peirce remarks that. (shrink)

Events in the history of thought have often moved as elements of drama—now tense, now tragic, now triumphant. And, it would appear, sometimes ludicrous. This latter is the thrust of a parody which Molière visited upon the savants of his day; he pictures a candidate for a medical degree being solemnly asked why opium puts people to sleep. Just as solemnly and sagaciously, the candidate replies..

Origin of Species was published; he approached the end of his life just before Albert Einstein presented us with General Relativity. His lifetime saw the emergence of psychology as a discipline separate from philosophy, a birth attended by philosopher-psychologists such as his good friend William James. The work of Peirce, like that of the other American Pragmatists, reflects the ferment of the times. His thought bears the imprint of science, not the science of that Nineteenth Century which as Loren Eiseley (...) has remarked, "regarded the 'laws' of nature as imbued with a kind of structural finality, an integral determinism, which it was the scientists’ duty to describe," (Eisele, 1971) but rather, of science as open, as intrinsically revisable, as radically empirical. Working from the model of science in this latter sense, Peirce held that philosophy, and indeed logic.. (shrink)

The roughly two and a half millennia over which we can trace the development of mathematics as a discipline have seen ups and downs in its study; the "ups" have involved varying emphases and interests depending on the problems and the temper of the time. The 19th Century may be characterized as a period of development of rigor and attention to the axiomatic method in mathematics. This focus on the deductive process in mathematics was accompanied by the application of mathematics (...) in the study of the deductive process itself. It is safe, I think, to say that the best-known and most influential of the lines of.. (shrink)

Jay Zeman one must keep a bright lookout for unintended and unexpected changes thereby brought about in the relations of different significant parts of the diagram to one another. Such operations upon diagrams, whether external or imaginary, take the place of the experiments upon real things that one performs in chemical and physical research. Chemists have ere now, I need not say, described experimentation as the putting of questions to Nature. Just so, experiments upon diagrams are questions put to the (...) Nature of the relations concerned (4.530). 1 The diagrammatic nature of mathematical reasoning suggests that as my power to create diagrams increases, so too will my capacity for fruitful mathematical reasoning. Peirce's own work involved an unending series of experiments with different diagrammatic notations, all interesting, some difficult, some extremely fruitful. And the diagrammatic notations available are not only a function of some kind of “internal mental activity.” As Dewey has noted, “Breathing is an affair of the air as truly as of the lungs; digesting an affair of food as truly as of tissues of stomach” (Dewey, 15); so analogously is mathematical reasoning an affair of the diagrams available as truly as of the “mind” (which is then not limited to something inside the head, but includes the relevant diagrams, “external” as well as “internal”); so does mathematical reasoning have its “alembics and cucurbits” just as surely as does chemistry. In doing mathematical reasoning, we make of the diagrams “instruments of thought,” and advances in the technology of diagrams can directly affect our patterns of reasoning. I can imagine Peirce spending hours (and dollars) in a modern artists' supply store. (shrink)

Gestalt Work--the therapeutic and growth activities that are the practice of Gestalt Therapy--is as varied and difficult to characterize, it would seem, as are the situations that give rise to it. I wish to begin an examination of this activity; our perspective may be called philosophical, but it is a philosophy whose entire raison d'être is its impact on lived experience. As such, it makes free use of the results of experience, including in an important way the methodology and insights (...) of science; indeed, the concepts themselves of Gestalt Psychology lend considerable depth and power to this philosophical approach. (shrink)

conditional with his discussions of the hypothetical proposition. Peirce spoke often of the consequentia de inesse ,1 the concept of which is intimately linked with the material, or "Philonian" conditional; indeed, we shall see him calling himself a Philonian. And it is not uncommon to hear Peirce—at least prior to the last decade of his life—declared a Philonian, whose fundamental analysis of the conditional was essentially the same as that of Philo (and of more modern types like Russell and like (...) Quine). (shrink)

This paper sketches out Peirce's "theory of indeterminacy" as part of a larger "triadic" theory within the context of the semiotic. It then examines the theory of the object in his later work, emphasizing the difference between immediate and dynamical object. The role of collateral experience is discussed. Connections are drawn between Peircean indeterminacy and Kant. The relationship of the indeterminate to contradiction and excluded middle is discussed. 'Determination', 'vagueness', and 'generality' are discussed in detail in the context established in (...) this paper. (shrink)

This paper sketches out Peirce's "theory of indeterminacy" as part of a larger "triadic" theory within the context of the semiotic. It then examines the theory of the object in his later work, emphasizing the difference between immediate and dynamical object. The role of collateral experience is discussed. Connections are drawn between Peircean indeterminacy and Kant. The relationship of the indeterminate to contradiction and excluded middle is discussed. 'Determination', 'vagueness', and 'generality' are discussed in detail in the context established in (...) this paper. (shrink)

We come to the full possession of our power of drawing inferences, the last of all our faculties; for it is not so much a natural gift as a long and difficult art. The history of its practice would make a grand subject for a book. The medieval schoolmen, following the Romans, made logic the earliest of a boy's studies after grammar, as being very easy. So it was as they understood it. Its fundamental principle, according to them, was, that (...) all knowledge rests either on authority or reason; but that whatever is deduced by reason depends ultimately on a premiss derived from authority. Accordingly, as soon as a boy was perfect in the syllogistic procedure, his intellectual kit of tools was held to be complete. (shrink)