Posts tagged ‘cantor’

May 14th, 2013

Infinity + 1 = ?

by Max Andrews

When we think of infinity we usually think of the usual two categorical distinctions:  a potential infinite and an actual infinite.  A potential infinite suggests that infinity is only an idea or a concept but doesn’t actually exist in the Platonic sense or in the physical sense. In any set, one may always be added.  An actual infinite is the notion that there exists such a set, Platonic or physical, whichis infinite.  A potential infinity may be symbolized by a lemniscate:  ∞.  An actual infinite can be depicted by the aleph-null or aleph-nought:  ℵ0 (The Hebrew letter aleph with a subscript zero).

First, let’s have a brief refresher on set theory. A set is any collection of things or numbers that belong to a well-defined category.  In a set notation, this would be written as {2, 3, 5, 7, 11} being the first five prime numbers, which is a finite set of things.  Let’s simply signify this set as S.  There is a proper subset (SS) of S.  There are members in S that are not in SS, but no member of SS that is not in S.  

January 17th, 2012

William Lane Craig’s “J. Howard Sobel on the Kalam Cosmological Argument”–A Review

by Max Andrews

A Review of William Lane Craig’s “J. Howard Sobel on the Kalam Cosmological Argument.” Canadian Journal of Philosophy 36 (2006): 565-584.

William Lane Craig formulates retort to J. Howard Sobel’s objection to kalam as he typically formulates it.[1] Premise 1 seems obviously true—at least, more than its negation.  To suggest that things could just pop into being uncaused out of nothing is to quit doing serious metaphysics and is a premise that Sobel acknowledges to be true.  Sobel’s objection is with 2—that the universe began to exist.  This would then run into an infinite regress, which is philosophically and mathematically untenable.  Because an actually infinite number of things cannot exist, the series of past events must be finite in number and, hence, the temporal series of past, physical events is not without beginning.[2]

November 22nd, 2011

The Different Versions of Infinity and Cantorian Sets

by Max Andrews

When we think of infinity we usually think of the usual two categorical distinctions:  a potential infinite and an actual infinite.  A potential infinite suggests that infinity is only an idea or a concept but doesn’t actually exist in the Platonic sense or in the physical sense. In any set, one may always be added.  An actual infinite is the notion that there exists such a set, Platonic or physical, which is infinite.  A potential infinity may be symbolized by a lemniscate:  ∞.  An actual infinite can be depicted by the aleph-null or aleph-nought:  ℵ0 (The Hebrew letter aleph with a subscript zero).

First, let’s have a brief refresher on set theory.