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diff --git a/essays/mathematical_studies.otx b/essays/mathematical_studies.otx new file mode 100644 index 0000000..e386199 --- /dev/null +++ b/essays/mathematical_studies.otx @@ -0,0 +1,17 @@ +\chapter 1966 Mathematical Studies + +% \fancyhead{} \fancyfoot{} \fancyfoot[LE,RO]{\thepage} +% \fancyhead[LE]{\textsc{Mathematical Studies (1966)}} \fancyhead[RO]{\textit{Introduction}} +\sec Introduction + + +Pure mathematics is the one activity which is intrinsically formalistic. It is the one activity which brings out the practical value of formal manipulations. Abstract games fit in perfectly with the tradition and rationale of pure mathematics; whereas they would not be appropriate in any other discipline. Pure mathematics is the one activity which can appropriately develop through innovations of a formalistic character. + +Precisely because pure mathematics does not have to be immediately practical, there is no intrinsic reason why it should adhere to the normal concept of logical truth. No harm is done if the mathematician chooses to play a game which is indeterminate by normal logical standards. All that matters is that the mathematician clearly specify the rules of his game, and that he not make claims for his results which are inconsistent with his rules. + +Actually, my pure philosophical writings discredit the concept of logical truth by showing that there are flaws inherent in all non-trivial language. Thus, no mathematics has the logical validity which was once claimed for mathematics. From the ultimate philosophical standpoint, all mathematics is as \dq{indeterminate} as the mathematics in this monograph. All the more reason, then, not to limit mathematics to the normal concept of logical truth. + +Once it is realized that mathematics is intrinsically formalistic, and need not adhere to the normal concept of logical truth, why hold back from exploring the possibilities which are available? There is every reason to search out the possibilities and present them. Such is the purpose of this monograph. + +The ultimate test of the non-triviality of pure mathematics is whether it has practical applications. I believe that the approaches presented on a very abstract level in this monograph will turn out to have such applications. In order to be applied, the principles which are presented here have to be developed intensively on a level which is compatible with applications. The results will be found in my two subsequent essays, \essaytitle{Subjective Propositional Vibration} and \essaytitle{The Logic of Admissible Contradictions}. + |