Even though a physical theory, the Scale Relativity Theory (SRT) means more than physics, as its creator noticed himself. In fact it targets the very foundation of the entire positive knowledge, and we are set here to prove this fact. Mathematically one needs the description of a transition between infrafinite, finite and transfinite orders, while physically one needs a transition between microcosmos, daily world (quotidian cosmos) and universe. With SRT the mathematical categories of infrafinite, finite and transfinite, become differentiae of the same general concept of ‘finite’. As it turns out, there is a parallelism of the physical transition between the worlds and the mathematical transition between degrees of ‘finite’: it is followed here historically and logically, in a first part of the present work, with the benefit of extracting the mathematical principles of a physical description of matter.
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