About: Philosophical Formalism   Sponge Permalink

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The inherent formality of mathematics, and the related desire to mathematicize all logical methods, such as permutation, hierarchy, and delineation, along with the seeming logical obsession with the provability of rhetorical arguments, marked by the invention of the reductio ad absurdium, led to a schism between logical systems ('entities', 'quantities') and rhetorical arguments ('causes', 'conditionals').

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  • Philosophical Formalism
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  • The inherent formality of mathematics, and the related desire to mathematicize all logical methods, such as permutation, hierarchy, and delineation, along with the seeming logical obsession with the provability of rhetorical arguments, marked by the invention of the reductio ad absurdium, led to a schism between logical systems ('entities', 'quantities') and rhetorical arguments ('causes', 'conditionals').
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  • The inherent formality of mathematics, and the related desire to mathematicize all logical methods, such as permutation, hierarchy, and delineation, along with the seeming logical obsession with the provability of rhetorical arguments, marked by the invention of the reductio ad absurdium, led to a schism between logical systems ('entities', 'quantities') and rhetorical arguments ('causes', 'conditionals'). The divide increased as each of the two areas experienced a certain marked degree of specialization, each form of student or researcher being obsessed with his or her own traditional arguments and familiar terrain. Aristotelian logic, itself more rational than scientific, became absconded in the problem of reducibility which became evident at the time of Godel, Tarski, and Russell (the three paradoxes of incompleteness and incoherency, which amount to one idea: the incomprehensiveness of mathematics). Developing from Aristotle and Wittgenstein's logical positivism, the Modal Realists such as David Lewis became caught on a double-horned dilemma, that experience provided proof, while only abstraction could provide a theory. Now arguments could be divided between the empirical and the theoretical, just as logical formalism could be divided into theories and facts. However, neither theories nor facts automatically constitute arguments. Indeed, not every theory of fact might qualify as rhetorical validity. The uniqueness of Aristotle's deductive reasoning was proven again and again, as hundreds of less successful forms of argument were discovered. However, the modal realists were caught on the subject of the old relation between entities and conditionals. The new rhetoric, it seemed, needed to relate with either the world of universal language, or the world of atomical facts. But Modal Realism was neither a theory of language, nor a method for deriving psychic evidence of the ordinary.
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