Quantum Mechanics without the quantum

Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to study the wave-particle dualism and the energy-time uncertainty relation. Afterwards we look upon the present state of the quantum mechanical formalism. We demonstrate that the two incompatibilities are employed in the same treatment forming a "hybrid" description of the phenomena and leading to a contradiction.Comment: Corrected typos Changed conten

A BIBLIOGRAPHY: JOHN CORCORAN’S PUBLICATIONS ON ARISTOTLE 1972–2015

This presentation includes a complete bibliography of John Corcoran’s publications devoted at least in part to Aristotle’s logic. Sections I–IV list 20 articles, 43 abstracts, 3 books, and 10 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article that antedates Corcoran’s Aristotle’s studies and the Journal of Symbolic Logic article first reporting his original results; it ends with works published in 2015. A few of the items are annotated with endnotes connecting them with other work. In addition, Section V “Discussions” is a nearly complete secondary bibliography of works describing, interpreting, extending, improving, supporting, and criticizing Corcoran’s work: 8 items published in the 1970s, 22 in the 1980s, 39 in the 1990s, 56 in the 2000s, and 65 in the current decade. The secondary bibliography is annotated with endnotes: some simply quoting from the cited item, but several answering criticisms and identifying errors. As is evident from the Acknowledgements sections, all of Corcoran’s publications benefited from correspondence with other scholars, most notably Timothy Smiley, Michael Scanlan, and Kevin Tracy. All of Corcoran’s Greek translations were done in consultation with two or more classicists. Corcoran never published a sentence without discussing it with his colleagues and students. REQUEST: Please send errors, omissions, and suggestions. I am especially interested in citations made in non-English publications

Laws of Thought and Laws of Logic after Kant

George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians Wilhelm Traugott Krug and Wilhelm Esser, among others. In his 1854 work An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Boole argues that the laws of thought acquire normative force when constrained to mathematical reasoning. Boole’s motivation is, first, to address issues in the foundations of mathematics, including the relationship between arithmetic and algebra, and the study and application of differential equations (Durand-Richard, van Evra, Panteki). Second, Boole intended to derive the laws of logic from the laws of the operation of the human mind, and to show that these laws were valid of algebra and of logic both, when applied to a restricted domain. Boole’s thorough and flexible work in these areas influenced the development of model theory (see Hodges, forthcoming), and has much in common with contemporary inferentialist approaches to logic (found in, e.g., Peregrin and Resnik)

Is Euler’s circle a symbol or an icon?

The most familiar scheme of diagrams used in logic is known as Euler’s circles. It is named after the mathematician Leonhard Euler who popularized it in his Letters to a German Princess (1768). The idea is to use spaces to represent classes of individuals. Charles S. Peirce, who made significant contributions to the theory of diagrams, praised Euler’s circles for their ‘beauty’ which springs from their true iconicity. More than a century later, it is not rare to meet with such diagrams in semiotic literature. They are often offered as instances of icons and are said to represent logic relations as they naturally are. This paper discusses the iconicity of Euler’s circles in three phases: first, Euler’s circles are shown to be icons because their relations imitate the relations of the classes. Then, Euler’s circles themselves, independently of their relations to one another, are shown to be icons of classes. Finally, Euler’s circles are shown to be iconic in the highest degree because they have the relations that they are said to represent. The paper concludes with a note on the so-called naturalness of Euler’s circles

Logic and reality in the philosophy of John Stuart Mill

This study of the leading principles of Mill's empiricist metaphysics and philosophy of logic aims to provide accurate (and often revisionary) exegesis and criticism of his theories, and to show their pertinence to current philosophical debates. Mill's views on the attainment of knowledge by inference, the problems of suasive syllogisms, and the possibility of inductive inference are first discussed, and it is argued that his philosophy of logic is informed by a realist theory of error. Subsequently, attention is paid to his uncompromising rejection of a priori avenues to knowledge about objective reality, and his allegiance to a radical empiricist principle that all knowledge is of phenomena alone. A scrutiny of Mill's theories of the experienced world and of the experiencing self: brings the discussion; to the point at which it emerges clearly that there is a deep tension within his thought between a form of empiricism which approximates to a variety of scientific realism, and another which leans towards sensationalistic reductionism