David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
In this paper, I suggest that infinite numbers are large finite numbers, and that infinite numbers, properly understood, are 1) of the structure omega + (omega* + omega)Ө + omega*, and 2) the part is smaller than the whole. I present an explanation of these claims in terms of epistemic limitations. I then consider the importance, part of which is demonstrating the contradiction that lies at the heart of Cantorian set theory: the natural numbers are too large to be counted by any finite number, but too small to be counted by any infinite number – there is no number of natural numbers.
|Keywords||Cantor paradox infinite|
|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
Jeremy Gwiazda (2012). On Infinite Number and Distance. Constructivist Foundations 7 (2):126-130.
Yaroslav D. Sergeyev (2008). A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities. Informatica 19 (4):567-596.
Yaroslav Sergeyev (2009). Numerical Computations and Mathematical Modelling with Infinite and Infinitesimal Numbers. Journal of Applied Mathematics and Computing 29:177-195.
Richard Schlegel (1965). The Problem of Infinite Matter in Steady-State Cosmology. Philosophy of Science 32 (1):21-31.
Paolo Mancosu (2009). Measuring the Size of Infinite Collections of Natural Numbers: Was Cantor's Theory of Infinite Number Inevitable? Review of Symbolic Logic 2 (4):612-646.
Eric Steinhart (2002). Why Numbers Are Sets. Synthese 133 (3):343 - 361.
Jeremy Gwiazda (2013). Throwing Darts, Time, and the Infinite. Erkenntnis 78 (5):971-975.
Yaroslav Sergeyev (2009). Numerical Point of View on Calculus for Functions Assuming Finite, Infinite, and Infinitesimal Values Over Finite, Infinite, and Infinitesimal Domains. Nonlinear Analysis Series A 71 (12):e1688-e1707.
Yaroslav Sergeyev (2007). Blinking Fractals and Their Quantitative Analysis Using Infinite and Infinitesimal Numbers. Chaos, Solitons and Fractals 33 (1):50-75.
A. W. Moore (1990/2002). The Infinite. Routledge.
Charles Sayward (2002). A Conversation About Numbers and Knowledge. American Philosophical Quarterly 39 (3):275-287.
Zvonimir Šikić (1996). What Are Numbers? International Studies in the Philosophy of Science 10 (2):159 – 171.
Zvonimir Šikić (1996). What Are Numbers? International Studies in the Philosophy of Science 10 (2):159-171.
Brian Rotman (1996). Counting Information: A Note on Physicalized Numbers. [REVIEW] Minds and Machines 6 (2):229-238.
Added to index2011-07-12
Total downloads221 ( #1,957 of 1,096,272 )
Recent downloads (6 months)15 ( #8,745 of 1,096,272 )
How can I increase my downloads?