Natural language and set theoretical and formal logic reductions – A philosophical account
A sheer love for propositions – An obsession with analytic philosophy, logics and mathematics
Analytic philosophy was born out of the general problem of solving metaphysics through a careful diagnostic of natural language. After the early days of formal logics and set theory with Boole and Cator, Frege and Russell arrived at the conclusion that natural language spontaneously produces irreducible paradoxes such as the liar and the sorites paradoxes. Through the length of these paradoxes, they concluded that traditional metaphysics was a gigantic mistake, formulable as it was under mistaken conception of language. The idea was ingenuous and simple to grasp. If I use very bad components and tools, I can only produce flawed engines, whose appearance is similar to a working engine until we check it. This ‘diagnostic’ approach to philosophy is as old as the Greeks, who were the first to outline different ways to ‘unveil life-threating mistakes through reasoning’. This was firstly tried in the realm of ethics, especially during the Alexandrine philosophies.[1] Wildly differently, this was tried again by the founding fathers of analytic philosophy.
Frege elaborated an entire philosophical system out of a new conception of logics applied to semantics through the instruments of the ‘new’ developments in formal logic, a Leibnizian ideal language through which all problems could be formulated and, then, solved by ‘brute force’ calculations.[2] In this broad category I am including set theory – in fact, it is arguable that formal logics and set theory cannot even be thought independently in the human mind.[3] In the following writing, I will consider set theory as the broad category including naïve set theory and Zermelo-Frankel theory plus the axiom of choice (ZFC).[4] It could be a matter of contentious, but set theory is, itself, a parallel endeavor that overlaps with the development of formal logic as we know. Moreover, set theory and formal logics are intended to mirror one another, where the sets are intended to be the object-domain of the propositions formulable in a formal language.[5] Set theory and formal logics tied together for solving all the natural language’s problems posed to human understanding, or so the founding fathers of analytic philosophy believed.
