{"title":"Undecidability in the completion of truth-function logic","authors":"Frank J. Wroblewski","doi":"10.1109/ISMVL.1991.130734","DOIUrl":null,"url":null,"abstract":"The inchoate rules of truth of logicism are cohered into the epistemic genesis for mathematics. First the formal truth conditions are exhausted with the complementary indeterminate value, not true and not false. The alternant truth assignments of the determinate Sheffer truth-conferring rules are not exhaustive of the propositional states of affairs necessary for conferring the founding truths. By completing the states-of-affairs assignments, the quantizer axioms reduce to degenerate consequents of Sheffer's rules in the manner of tautologies. The completion is prerequisite for deducing the indeterminate Sheffer truth-conferring rule which continues the bivalent truth tables to trivalence. Undecidability reduces to one of three degrees-of-truth whose alternants include the indeterminate.<<ETX>>","PeriodicalId":127974,"journal":{"name":"[1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.1991.130734","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The inchoate rules of truth of logicism are cohered into the epistemic genesis for mathematics. First the formal truth conditions are exhausted with the complementary indeterminate value, not true and not false. The alternant truth assignments of the determinate Sheffer truth-conferring rules are not exhaustive of the propositional states of affairs necessary for conferring the founding truths. By completing the states-of-affairs assignments, the quantizer axioms reduce to degenerate consequents of Sheffer's rules in the manner of tautologies. The completion is prerequisite for deducing the indeterminate Sheffer truth-conferring rule which continues the bivalent truth tables to trivalence. Undecidability reduces to one of three degrees-of-truth whose alternants include the indeterminate.<>
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