TITLE:
Some Critical Notes on the Cantor Diagonal Argument
AUTHORS:
Philip Molyneux
KEYWORDS:
Cantor Diagonal Argument, Infinity, Natural Numbers, One-to-One Correspondence, Real Numbers
JOURNAL NAME:
Open Journal of Philosophy,
Vol.12 No.3,
June
14,
2022
ABSTRACT: This paper critically
examines the Cantor Diagonal Argument (CDA) that is used in set theory to draw
a distinction between the cardinality of the natural numbers and that of the
real numbers. The CDA is discussed here using a consensus from the forms found
in a range of recently published sources. Four points critical of the CDA
are raised that cast doubts on its validity and general applicability. Also,
contrary to the conclusion conventionally drawn from the CDA, it is found
possible to set up a one-to-one correspondence between the natural numbers and
the real numbers. Finally, some comments are made on the concept of “infinity”, pointing out that to
consider this as an entity is a category error, since it simply represents an
absence, that is, the absence of a termination to a process.