Analytical philosophy defines mathematics as an extension of logic. This research will restructure the progress in mathematical philosophy made by analytical thinkers like Wittgenstein, Russell, and Frege. We are setting up a new theory of mathematics and arithmetic’s familiar to Wittgenstein’s philosophy of language. The analytical theory proposed here proves that mathematics can be defined with non-logical terms, like numbers, theorems, and operators. We’ll explain the role of the arithmetical operators and geometrical theorems to be foundational in mathematics. Our position (...) states that mathematical operators and theorems are tautologies. Here numbers are arbitrary signs of magnitudes whose meaning is arbitrated by the mathematical operator. We will prove that set theory in mathematics doesn’t form a branch of logic and operators arbitrarily form sets into units. Herein are the foundations of numbers. (shrink)

Law is the main regulator of public relations, and the question of the proper use and understanding of legal language is essential for law enforcement. This topic is of interest to both lawyers and philosophers, who often join efforts to study it. This article attempts precisely to take such an interdisciplinary approach when examining legal rules as specific linguistic conventions. First of all, for the sake of a better and more thorough understanding of legal language, legal norms are viewed both (...) from the point of view of semantics and from the point of view of pragmatics. Therefore, for this purpose, a distinction is made between legal norms and legal provisions as their linguistic equivalent. Legal norms are then explored through Wittgenstein's Later Philosophy, which describes their semantic content. The pragmatic aspect of the question is explained through John Austin's theory, thus treating legal rules as a kind of specific speech act of a conventional nature. (shrink)