Developing Non-Calculus Service Courses That Showcase the Applicability of Mathematics

Author(s):  
Lucas Castle
Author(s):  
Mark Steiner

To an unappreciated degree, the history of Western philosophy is the history of attempts to understand why mathematics is applicable to Nature, despite apparently good reasons to believe that it should not be. A cursory look at the great books of philosophy bears this out. Plato's Republic invokes the theory of “participation” to explain why, for instance, geometry is applicable to ballistics and the practice of war, despite the Theory of Forms, which places mathematical entities in a different (higher) realm of being than that of empirical Nature. This argument is part of Plato's general claim that theoretical learning, in the end, is more useful than “practical” pursuits. John Stuart Mill's account of the applicability of mathematics to nature is unique: it is the only one of the major Western philosophies which denies the major premise upon which all other accounts are based. Mill simply asserts that mathematics itself is empirical, so there is no problem to begin with.


Author(s):  
Gilda Rosa Bolaños Evia ◽  
Julio César López Juárez ◽  
Pedro Ulises Salazar Sánchez

Synthese ◽  
2016 ◽  
Vol 194 (9) ◽  
pp. 3361-3377 ◽  
Author(s):  
Nora Berenstain

1982 ◽  
Vol 15 (1) ◽  
pp. 3-25 ◽  
Author(s):  
David C. Lindberg

Roger Bacon has often been victimized by his friends, who have exaggerated and distorted his place in the history of mathematics. He has too often been viewed as the first, or one of the first, to grasp the possibilities and promote the cause of modern mathematical physics. Even those who have noticed that Bacon was more given to the praise than to the practice of mathematics have seen in his programmatic statements an anticipation of seventeenth-century achievements. But if we judge Bacon by twentieth-century criteria and pronounce him an anticipator of modern science, we will fail totally to understand his true contributions; for Bacon was not looking to the future, but responding to the past; he was grappling with ancient traditions and attempting to apply the truth thus gained to the needs of thirteenth-century Christendom. If we wish to understand Bacon, therefore, we must take a backward, rather than a forward, look; we must view him in relation to his predecessors and contemporaries rather than his successors; we must consider not his influence, but his sources and the use to which he put them.


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