Naturalizing the Applicability of Mathematics

PARADIGMI ◽  
2015 ◽  
pp. 25-44
Author(s):  
Carlo Cellucci
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.


Phainomenon ◽  
2012 ◽  
Vol 25 (1) ◽  
pp. 83-107
Author(s):  
Jairo José da Silva

Abstract I present and discuss in this paper Husserl’s investigation of the genesis of the modem conception of empirical reality as carried out in his last work The Crisis of European Sciences and Transcendental Phenomenology. The goal of Husserl’s genetic investigation was to uncover the rnany layers of constitution that frorn the life-world (the Lebenswelt) the modem scientific conception of Nature was originated and to point out the need to ground the scientific project of rnodemity in the life-world so as to overcome the “alienation” that, for him, characterized the “crisis” of European science. I, however, approach his analyses from a different perspective. The problem that interests me here is the applicability of mathematics in the empirical science. My airn is to assess Husserl’s treatment of this question in order to see whether it can be sustained from a strictly scientific perspective. My conclusion is that it cannot. What Husserl takes for the “crisis” of science is inherent to the best scientific methodology. Nonetheless, Husserl’s analyses offer irnportant insights that I incorporate in what I believe to be a more satisfactory treatment of the problern concerning the role of mathematics in the ernpirical science.


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