A logico-linguistic inquiry into the foundations of physics: Part I

Abstract

Physical dimensions are {\it not numbers}, but used as {\it numbers} to perform dimensional analysis by the physicist. The law of excluded middle falls short of explaining the contradictory meanings of the same symbols. The statements like ``$r\to 0$'', ``$q\to 0$'', used by the physicist, are inconsistent on dimensional grounds because ``$r$'', ``$q$'' represent {\it quantities} with physical dimensions of $[L], [Q]$ respectively and ``$0$'' represents just a number devoid of physical dimension. Consequently, the involvement of the statement ``$\lim_{q\to 0}$, where $q$ is the test charge'' in the definition of electric field leads to either circular reasoning or a contradiction regarding the experimental verification of the smallest charge in the Millikan-Fletcher oil drop experiment. Considering such issues as problematic, by choice, I make an inquiry regarding the basic language in terms of which physics is written, with an aim of exploring how truthfully the verbal statements can be converted to the corresponding physico-mathematical expressions (involving physical dimensions). Necessarily I demonstrate the meaning of the terms ``self inquiry'', ``middle way'', ``dependent origination'', ``emptiness/relational existence'', which signify the basic tenets of Buddhism. In light of this, I explain my view of ``definition''; the relation among quantity, physical dimension and number; the logico-linguistic fallacy of ``zero quantity''; difference between unit and unity. I present a critical analysis of the definitions of electric field due to Maxwell and Jackson. A postulate regarding the existence of charges becomes necessary which, however, resolves the contradiction regarding the oil drop experiment. This work is an appeal for the dissociation of the categorical disciplines of logic and physics and on the large, a fruitful merger of Eastern philosophy and Western science.