David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Among the aims of the author in this wide-ranging article is to draw attention to the numerous formal sciences which so far have received little scrutiny, if at all, on the part of philosophers of mathematics and of science in general. By the formal sciences the author understands such mathematical disciplines as operations research, control theory, signal processing, cluster analysis, game theory, and so on. First, the author presents a long list of such formal sciences with a detailed discussion of their subject matter and with extensive references to the pertinent literature. Turning to the nature of the formal sciences, the author states that “the formal sciences, though they arose in most cases out of engineering requirements, are sciences and can be pursued without reference to applications”. It is argued, through a wealth of examples, that in a great number of cases the formal sciences permit the attainment of provable certainty about actual parts of the world. As Franklin puts it, “knowledge in the formal sciences, with its proofs about network ﬂows, proofs of computer program correctness, and the like, gives every appearance of having achieved the philosophers’ stone; a method of transmuting opinion about the base and contingent beings of this world into the necessary knowledge of pure reason.” Franklin clearly distinguishes between certainty and necessity: “ g¤g¤g what the mathematician in offering is not, in the ﬁrst instance, absolute certainty in principle, but necessity. This is how his assertion differs from one made by a physicist. A proof offers a necessary connection between premises and conclusion. One may extract practical certainty from this g¤g¤g but this is a separate step.” Though Franklin explicitly states that there is a gap between necessity and certainty as one passes from mathematical reasoning to applications, the main thrust of the article consists in arguing that the gap is considerably smaller than generally claimed..
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Kevin de Laplante, Certainty and Domain-Independence in the Sciences of Complexity: A Critique of James Franklin's Account of Formal Science.
James Franklin (1994). The Formal Sciences Discover the Philosophers' Stone. Studies in History and Philosophy of Science 25 (4):513-533.
Kevin de Laplante, Response to Franklin's Comments on 'Certainty and Domain-Independence in the Sciences of Complexity'.
James Franklin (1999). Structure and Domain-Independence in the Formal Sciences. Studies in History and Philosophy of Science 30:721-723.
Harold Kincaid (2000). Formal Rationality and its Pernicious Effects on the Social Sciences. Philosophy of the Social Sciences 30 (1):67-88.
Franklin M. Fisher (1960). On the Analysis of History and the Interdependence of the Social Sciences. Philosophy of Science 27 (2):147-158.
Jarosław Mrozek (2000). Powstanie i perspektywy dowodu matematycznego. Filozofia Nauki 1.
Yehuda Rav (2007). A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians' Proof Practices. Philosophia Mathematica 15 (3):291-320.
Jean Paul Van Bendegem (2005). Proofs and Arguments: The Special Case of Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 84 (1):157-169.
Richard Bornat (2005). Proof and Disproof in Formal Logic: An Introduction for Programmers. New Yorkoxford University Press.
Enrique V. Kortright (1994). Philosophy, Mathematics, Science and Computation. Topoi 13 (1):51-60.
Y. Rav (1999). Why Do We Prove Theorems? Philosophia Mathematica 7 (1):5-41.
R. A. V. Yehuda (1999). Why Do We Prove Theorems? Philosophia Mathematica 7 (1).
Sorry, there are not enough data points to plot this chart.
Added to index2010-12-22
Total downloads1 ( #398,768 of 1,096,425 )
Recent downloads (6 months)0
How can I increase my downloads?