Dialectical Reason and Limitation of Mathematics
By Admin on Apr 13, 2010 | In Hegelian Philosophy
Sripad Bhakti Madhava Puri Maharaja, Ph.D.
This is all just common sense at this point. Eventually we want to be able to scientifically develop and show how all this is necessarily so. We can make the same three-fold logical division for seeing, knowing, thinking, etc. In all these, two elements are subjective and one is objective, viz. the experiencer (agent) and experience are subjective, and only the thing experienced is considered objective. For a certain set of objects, viz. sense objects this is problematical. How does an object in the world produce an effect in a subjective observer? We may call this the problem of thought and being, where thought represents the subjective and being the objective component in this interactive event.
This is a philosophical problem that can be solved only by rational thinking, and more particularly by dialectical reason. An equation implies mathematical thinking, or thinking in terms of identities. The whole concept of mathematics is based on identities (equalities or equations). But in the field of subjectivity and objectivity, we have an exchange going on. Here, what is objective becomes subjective, and what is subjective becomes objective. They do not preserve their distinct identities. This is called dialectics, and although an attempt has been made to mathematize dialectics, it has not been successful. Gödel has also shown the inherent limitations of mathematics to consistently describe a complete system. Dialectical reason does not suffer that limitation. You will have to read a book like Hegel's "Science of Logic" to get a grasp of this.
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