Classic Axioms as Exact Ruling on Motion -- The First-Step via Newton's Thoughts on Motion and Frege's Pictures of Logic

Abstract

In this article, we revisit Newton’s Laws on Motion and Frege’s System of Logic, two of the four classic axiom systems in Geometry (Euclid), Mechanic Physics (Newton), Logic (Frege) and Set theory (Zermelo) to understand Classic Axioms as Exact Sentences of Axiomatic Ruling (C.A.E.S.A.R) on the laws of motion of both physical characters within scenes to visual observation and psycho-logical concepts between lines in mental cognition in the same time, kicking off the very first step in this line of research and studies. On the whole, our work intends to bring exploitations in various fields of science and philosophy onto and upon a new base ground that provides fresh prospect and stirs excitement in almost every corner of intellectual movement. The article starts with an overview of the intriguing connection among the historical developments in the four classic axiom systems at the conjunction period of the 19th and 20th century. Combining the insights on Philosophy of Language & Logic and Philosophy of Phenomenology developed through the first two works of this Philosophical Investigation Series, we delineate the delicate form and intricate substance that all four classic axiom systems share in common. Given the new perspective, we point out that the historically-discovered problems of each classic axiom system is not due to the fallacy committed by original authors but the lack in understanding of each system in terms of the Meaning of the definition of each Common Notion in use and the Logic of postulation on every Axiomatic Motion at work instead. That gap is systemic across studies in all four fields, which had led to the ‘anticipated’ finding in chains that each classic system had contained problematic issue to varying degrees. To validate our claim, we develop a simple thought experiment, using Newton’s Laws of Motion, to show a puzzling phenomenon that only can be resolved by admitting the existential being of a true subjective thing, which, like an IRT drawn on paper with a hypotenuse that is Square Root of Two times as long as the equal side of the same IRT, holds its empirical properties in agreement with the counterpart in analytical attributes and in the meantime has attributes that cannot be verified or denied under any condition empirically. We then furnish our discussion by explaining the basic regularities on ‘Being’ of such a Thing based on Frege’s Logic system. Those efforts together bring forth fresh prospect on the intrinsic meaning and natural orientation of studies, both scientific and philosophical, in the areas of mechanic physics and modal logic, two disciplines that hold and bear equal primordial standing with Language and Logic, Geometry and Set theory for the intellectual development of modern human beings.