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+\chapter{1966 Mathematical Studies: 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 "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}.
+