Essays on the Logical

Logic does not operate within the Universe or Nature itself, but within the universe of discourse (the world–language–thought triangulation) in which logical and linguistic variables can be transformed into constants through logical operations compatible with mathematical procedures grounded in general algebra and set theory. Formal logic is calculus or computation with concepts, propositions, predicates, logical functions in symbolic notation. Each logical form is defined by a specific degree of logical generality as its quantitative property, which is manipulated within logical calculus through operators, quantifiers, and rules of deduction. It is necessary to granulate each linguistic variable until syntactic correspondence is achieved between the word, the concept, and the object to which the statement refers. Logical activity is always three‑dimensional, whether it concerns real or virtual objects and their classes, modal or classical propositions, or the totality or parts of thought content. What matters is that the construction of the logical syntax of a proposition and its semantic interpretation lead to the truth value of our statements. From Aristotle's syllogistic, through symbolic and mathematical logic, to logical programming and artificial intelligence - logic is always calculus and manipulation of symbolic notation.