David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
In a remarkable development, I have constructed a new definition for a self-delimiting universal Turing machine (UTM) that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory (AIT), which is the theory of the size in bits of programs for selfdelimiting UTM's. Previously, AIT had an abstract mathematical quality. Now it is possible to write down executable programs that embody the constructions in the proofs of theorems. So AIT goes from dealing with remote idealized mythical objects to being a theory about practical down-to-earth gadgets that one can actually play with and use.
|Keywords||No keywords specified (fix it)|
|Categories||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
Mark Colyvan (2012). An Introduction to the Philosophy of Mathematics. Cambridge University Press.
Kit Fine (2002). The Limits of Abstraction. Oxford University Press.
Stewart Shapiro (2004). Foundations of Mathematics: Metaphysics, Epistemology, Structure. Philosophical Quarterly 54 (214):16 - 37.
John Mayberry (1994). What is Required of a Foundation for Mathematics? Philosophia Mathematica 2 (1):16-35.
Robert J. Titiev (1998). Finiteness, Perception, and Two Contrasting Cases of Mathematical Idealization. Journal of Philosophical Research 23:81-94.
Solomon Feferman, The Development of Programs for the Foundations of Mathematics in the First Third of the 20th Century.
Stewart Shapiro (2000). Set-Theoretic Foundations. The Proceedings of the Twentieth World Congress of Philosophy 2000:183-196.
Stojan Obradović & Slobodan Ninković (2009). The Heuristic Function of Mathematics in Physics and Astronomy. Foundations of Science 14 (4):351-360.
Charalampos Toumasis (1993). Ideas and Processes in Mathematics: A Course on History and Philosophy of Mathematics. Studies in Philosophy and Education 12 (2-4):245-256.
Pierre Cassou-Nogués (2006). Signs, Figures and Time: Cavaillès on “Intuition” in Mathematics. Theoria 21 (1):89-104.
Ermanno Bencivenga (2006). Mathematics and Poetry. Inquiry 49 (2):158 – 169.
Richard Zach (2006). Hilbert's Program Then and Now. In Dale Jacquette (ed.), Philosophy of Logic. North Holland. 5--411.
Added to index2010-12-22
Total downloads5 ( #326,926 of 1,696,590 )
Recent downloads (6 months)1 ( #345,974 of 1,696,590 )
How can I increase my downloads?