# Kalevi Kolttonen philosophy page

**Metalevels in thinking** (updated September 23rd, 2018)
**Alternative definition of cardinality** (v4.21, October 21th, 2018) This paper challenges Georg Cantor's proof about the cardinality of real numbers being bigger than the cardinality of natural numbers. I had to use LaTeX because working with MathML turned out to be too frustrating. So this article is available as a PDF document. **NOTE**: I have added **Responding to criticism** section to *v3.00*. **NOTE 2**: v4.00 corrects my logical blunder: We *cannot* deduce that equality of the set N and R implies Aleph 0. We can only prove *equality*, but based on the alternative definition, the ranks of infinity disappear altogether. Cardinality, then, is simply one infinity.
**Misinterpretations of Kolmogorov complexity** (v1.01, October 18th, 2018) This paper warns mathematicians and logicians about the dangers of confusing abstraction levels. Kolmogorov complexity is used as a specific example to drive the point home. This article is published here in PDF format.