His is a valid perspective, but it is more a function of definition than a useful basis for defining mathematics in a pragmatic sense. There are always limits in awareness and in understanding as well. People think of mathematics as being an absolute standard to which other fields and disciplines pale in comparison, in not having built-in validity, but that is not really the case. Mathematics have much that is arbitrary in the construction and utilization. In a sense, it is like constructing a language that is entirely novel. Once it is far enough along, it will be workable and an accurate representation of facts and information because enough has been divined with accuracy to provide a pragmatic tool. But, in an absolute sense, there will be gaps and holes in logic, and in thoroughness and depth of content, in what has been expressed and for which words in the new language have meaning. All of mathematics is like that as well. So this gives rise to many interesting debates, reconfigurations, and revisions of mathematical thought, and this author is focusing in on one of the gaps.
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