Syntax-directed discovery in mathematics
Erkenntnis 43 (2):241 - 259 (1995)
| Abstract | It is shown how mathematical discoveries such as De Moivre's theorem can result from patterns among the symbols of existing formulae and that significant mathematical analogies are often syntactic rather than semantic, for the good reason that mathematical proofs are always syntactic, in the sense of employing only formal operations on symbols. This radically extends the Lakatos approach to mathematical discovery by allowing proof-directed concepts to generate new theorems from scratch instead of just as evolutionary modifications to some existing theorem. The emphasis upon syntax and proof permits discoveries to go beyond the limits of any prevailing semantics. It also helps explain the shortcomings of inductive AI systems of mathematics learning such as Lenat's AM, in which proof has played no part in the formation of concepts and conjectures. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,705 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesJean 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.
Alfred Driessen (2005). Philosophical Consequences of the Gödel Theorem. In Eeva Martikainen (ed.), Human Approaches to the Universe. Luther-Agricola-Society.
Marian Mrozek & Jacek Urbaniec (1997). Evolution of Mathematical Proof. Foundations of Science 2 (1):77-85.
Robert Tubbs (2009). What is a Number?: Mathematical Concepts and Their Origins. Johns Hopkins University Press.
David Harriman (2010). The Logical Leap: Induction in Physics. New American Library.
Felix Mühlhölzer (2006). "A Mathematical Proof Must Be Surveyable" What Wittgenstein Meant by This and What It Implies. Grazer Philosophische Studien 71 (1):57-86.
Carlo Cellucci (2008). The Nature of Mathematical Explanation. Studies in History and Philosophy of Science Part A 39 (2):202-210.
Imre Lakatos (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads3 ( #202,008 of 549,128 )Recent downloads (6 months)0How can I increase my downloads? |
My notes
Discussion
