Semiotics as a Metalanguage for Science
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As is well known, Peirce defined semiotics as a doctrine of signs. Doctrines of all kinds constitute a system of notions for understanding something in terms of those notions. In mathematics and science, this set of notion often comes under the rubric of a metalanguage. A perfect example is Bertrand Russell’s and Alfred North Whitehead’s Principia Mathematica which aimed to take human meaning out of logic and mathematics so as to avoid paradoxes (such as the Liar Paradox). But the attempt failed, as Kurt Gödel showed in 1938 that any system of propositions cannot be complete, since it contains inevitably in it a proposition that is undecidable—that is, it cannot be proved to be true or false. The reason for this, in my view, is that such abstract metalanguages lack the dimension of human meaning and interpretation. This presentation will argue that the only viable metaalanguage for mathematics and science is, in fact, one that tackles the problem of meaning and interpretation directly. That metalanguage is semiotics. As Locke argued for philosophy, semiotics somehow allows us to understand ideas in terms of how they are constituted. If we unravel the nature of interpretants in mathematical and scientific laws then we will have penetrated the relation between the human brain and its scientific products.