Algebra and Logic

Contemporary Math Logics have varied in ambition. Some aim to systematize Mathematical processes, but others, the more prevalent types, aim to reduce Mathematics to a branch of Logic. Perhaps the most authoritative critic of the latter effort is Wittgenstein, who was a prominent advocate of Logicist Mathematics before repudiating the project. He characterizes Mathematics and Logic as two different 'language games', and observes that the attempt to reduce the former to the latter does not merely not illuminate Mathematics, but, rather, tends to cloud its operations. A further analysis of the 'Logic' that is the basis of such reduction notices that its central element is the Variable, used to mediate between Universal formulas and their instances. In other words, this 'Logic' is Algebraized language, perhaps the fulfillment of Leibniz' dream of a Universal language. Now, as much as Contemporary Logic is touted as a significant improvement over Aristotelian Syllogistics, it remains within the scope of the latter, namely within the Universal-Particular relation. So, as 'Universal' as this 'Logic' presumes itself to be, its Particularism cannot accommodate Logics of either Autonomy, e. g. Kantianism, or of Idionomy, e. g. Existentialism or Evolvementalism.