Philosophy of mathematics

Weyl, Herman, Philosophy of Mathematics and Natural Science (New York Atheneum, 1963), 116. 

In this chapter, I discuss a problem that at first seems confined to Aristotle s categorial scheme. As shall become apparent, however, what I take to be the correct resolution to the problem has several implications for the relationship between hylomorphism and the categories. Moreover, coming to grips with the problem requires substantive views about Aristode s philosophies of mathematics, motion, substance, form and matter. So this particular issue provides a convenient place to begin the treatment of the topics that will be the focus of the rest of the book. 

Aristode, then, is committed to theses (l)-(3). In this chapter, however, I show that, far from revealing a deep contradiction in Aristotle s thought, the body problem admits of a resolution that throws considerable light on several aspects of his metaphysical system. The resolution begins with a thesis concerning Aristotle s philosophy of mathematics and its relation to the conception of science Aristode articulates in the Posterior Analytics. In order to resolve completely the body problem, though, such a thesis must be combined with theses about the relationship between substance, form, motion and quantity. 

The answer to this difficulty requires first an interpretation about the source of mobility and its relation to substantiality and second an extension and ptecisification of die claims involved in Aristodes philosophy of mathematics. 

I am in general agreement with Jonathan Lear, Aristotle s Philosophy of Mathematics) Philosophical Review, XCI, No. 2 (1982) 161-192, about the correct way to understand the qua locution. Lear does not discuss how to interpret Aristotle s claim that one can demonstrate a feature of something not qua F but he does provide die following schema with which I agree for... 

It should be dear the way in which this interpretation intersects with the interpretation of Aristode s philosophy of mathematics that I articulated in chapter 2. 

So what does it mean to say that mathematicians study bodies but not qua mobiles One could answer this question by putting a psychologists spin on Aristode s philosophy of mathematics. According to some interpreters, Aristode thinks that mathematicians mentally... 

THE PHILOSOPHY OF MATHEMATICS An Introductory Essay, Stephan Komer. Surveys the views of Plato, Aristotle, Leibniz 8c Kant concerning propositions and theories of applied and pure mathematics. Introduction. Two appendices. Index. 198pp. 54 x 84. 25048-2 Pa. 5.95... 

The Mathematical Intelligencer Reflections on Bishops Philosophy of Mathematics (p. 63)... 

The philosophy of chemistry What would that be In what respects would it be similar to a philosophy of physics, philosophy of biology, and/or a philosophy of mathematics In what respects different What relationship would it have to each of these Would it yield up the same sorts of insights, or entirely new, unanticipated ones ... 

Weyl thus answered the second question in his investigations of the mathematical analysis of the space problem. His researches with the representation theory of Lie groups started because of his diverse background, from the philosophy of mathematics to the natural sciences. Further, he clarified Heisenberg s non-commuting physical quantities in quantum mechanics, which were initially stated in a mathematical form rather than a physical form. 

Discrete Smooth Interpolation DSI is as much a philosophy of mathematical modelling as it is an interpolation method [113, 114]. A topological structure, in the form of a set of nodes with a pre-assigned neighbourhood structure, is assumed. A local roughness function is then defined for each node. An essential feature of the method is the assumption that each roughness function is a quadratic form in the values to be interpolated. Note that the interpolated function can be vector valued. 

Depressurization and Blowdown Capabilities - A mathematical calculation of the system sizing and amount of time needed to obtain gas depressurization or liquid blowdown according to the company s philosophy of plant protection and industry standards (i.e., API RP 521). 

For the harmony of the world is made manifest in Form and Number, and the heart and soul and all poetry of Natural Philosophy are embodied in the concept of mathematical beauty. 1... 

Physics and Chemistry Commensurate or Incommensurate Sciences " The Invention of Physical Science Intersections of Mathematics, Theology and Natural Philosophy Since the Seventeenth Century. Essays in Honor of Erwin N. Hiebert, ed. Mary Jo Nye et al. (Dordrecht Kluwer, 1992) 105224 "National Styles Research Schools in French and English Chemistry, 18801930," Osiris [2]8 (1993) 3049 and "Philosophies of Chemistry since the Eighteenth Century," in Seymour Mauskopf, ed., Chemical Sciences in the Modern World (Philadelphia University of Pennsylvania Press, in press). I am grateful for permissions to publish materials previously published. 

By common agreement among many historians of science, "chemistry" and "physics" became fairly well demarcated communities or disciplines around 1830, some hundred years before the founding of the Journal of Chemical Physics2 This was about the time that Auguste Comte was embarking on his Cours de philosophie positive, in which he laid out a hierarchy of the positive sciences as he observed them in contemporary Paris. In this hierarchy, the mastery of mathematics and physics was historically and foundationally prior to chemistry. 

In influencing the history and philosophy of science of later decades, Comte s positivist classification created the conviction that the constitution of mathematics and physics was historically prior to chemistry and conceptually more fundamental than chemistry. 4 But the positivist history we often have accepted from Comte is flawed. "Chemistry" as a discipline preceded "physics." In the next two chapters, I will deal with the claim that physics is conceptually a more fundamental science than chemistry and will analyze the characteristic aims and methods of nineteenth-century chemistry, particularly as reinforced through the hegemony of organic chemistry. 

In 1928, Van Vleck took a physics professorship at the University of Wisconsin. He had done his doctoral research at Harvard with Kemble, and he would return to Harvard in 1934, eventually to be named the Hollis Professor of Mathematics and Natural Philosophy. Van Vleck made a distinction between physicists and chemists by saying,... 

I have described a reasonably complete set of mathematical techniques for improving the precision of calibration-curve-based analyses and measuring their precision. Each technique may not be the optimum solution to each problem, but the overall philosophy should be correct. We should develop statistical techniques to measure precision which are self-consistent and... 

Born in about 1214, Bacon became a monk but was educated at Oxford before gaining a doctorate in Paris. His subjects included philosophy, divinity, mathematics, physics, chemistry and even cosmology. He carefully purified potassium nitrate (by recrystallisation from water) and went on to experiment with different proportions of the other two ingredients (sulfur and willow charcoal) until he was satisfied that. 

Yellow in any of man s [or woman s] vehicles always indicates intellectual capacity, but its shades vary and it may be complicated by the admixture of other hues. Generally speaking, it has a deeper and duller tint if the intellect is directed chiefly into lower channels, more especially if the objects are selfish. In the astral or mental body of the average man [or woman] it would show itself as yellow ochre, while pure intellect, devoted to the study of philosophy or mathematics, appears frequently to be golden, and this rises gradually to a beautiful clear and luminous lemon or primrose yellow when a powerful intellect is being employed absolutely unselfishly for the benefit of humanity. 

Jules) Henri Poincard, 1834-1912. French mathematician, physicist, and astronomer. Prolific and gifted writer on mathematical analysis, analytical and celestial mechanics, mathematical physics, and philosophy of science. 

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