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)
We extend the construction of a global square sequence in extender models from Zeman  to a construction of coherent non-threadable sequences and give a characterization of stationary reflection at inaccessibles similar to Jensen’s characterization in L.
The paper is concerned with the semantics of knowledge attributions(K-claims, for short) and proposes a position holding that K-claims are contextsensitive that differs from extant views on the market. First I lay down the data a semantic theory for K-claims needs to explain. Next I present and assess three views purporting to give the semantics for K-claims: contextualism, subject-sensitive invariantism and relativism. All three views are found wanting with respect to their accounting for the data. I then propose a hybrid (...) view according to which the relevant epistemic standards for evaluating K-claims are neither those at the context of the subject (subject-sensitive invariantism), nor those at the context of the assessor (relativism), but it is itself an open matter. However, given that we need a principled way of deciding which epistemic standards are the relevant ones, I provide a principle according to which the relevant standards are those that are the highest between those at the context of the subject and those at the context of the assessor/attributor. In the end I consider some objections to the view and offer some answers. (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)
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)
Summary An introductory article, giving first a short historical exposition of philosophical thinking in Russia and Czechoslovakia. Second, basic trends in the Philosophy of Science in Russia and Poland are dealt with, followed by a briefer consideration of similar trends in other East European countries. A special article on Czechoslovakia will be published later. Some original philosophical contributions, especially of Polish philosophers, are mentioned. Supplemented with selected bibliography.
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)
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)
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..
Over a decade ago, John Sowa (1984) 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)
The paper deals with one of the key notions in Epicurean epistemology, preconception. Together with perceptions, preconceptions are the second criterion of truth. The aim of the paper is to explore their epistemological status on the basis of their origin and formation. I argue that the process of formation of preconception is purely empirical, since they are produced through repeated perceptions of individual instances of a particular type of thing. Given the way they are formed, I claim that preconceptions are (...) the means by which we recognize types of object and as such are fundamental to Epicurus’ account of how we gain knowledge of things. Exactly this gives them a distinctive criterial role, since preconceptions––unlike perceptions––enable us to engage in the process of interpretation of perceptual content. (shrink)
Recent discussions on the political role of some 20th Century philosophers and their ideas, from Heidegger to Sartre and Lukacs, offer some new venues for our analysis of the similar role played by some of the classical figures in the history of modem philosophy. We have attempted to review some relevant aspects of Fichte’s philosophy, in particular as to their possible influence on the war supporting ideology created by German intellectuals at the outbreak of the World War I - so-called (...) ideas of Fall 1914.Des discussions récentes sur le rôle politique de certains philosophes du XXe siècle et de leurs idées, de Heidegger à Sartre et Lukacs, offrent de nouvelles avenues pour I’analyse du role similaire qu’auraient joué quelques figures classiques de I’histoire modeme de la philosophie. Nous nous sommes penché sur quelques aspects pertinents de la philosophie fichtéenne, en particulier sur ceux qui serapportent à son influence possible sur l’idéologie belliciste défendue par les intellectuels allemands au début de la Première Guerre mondiale, connue en tant qu’idées d’Automne 1914. (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)