The Logic within the Logic Reinterpretation of Boolean algebra from Transcurssive Logic
| Main Author: | Salatino, Dante Roberto |
|---|---|
| Format: | Article |
| Bahasa: | eng |
| Terbitan: |
, 2019
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/2667559 |
Daftar Isi:
- In the introduction of Boole’s "Mathematical Analysis of Logic" of 1847, he approaches one of the operative foundations of Transcurssive Logic. He tells us that "those who are familiar with the theory of symbolic algebra, know that the validity of their analysis does not depend on the interpretation of the symbols, but only on the laws of their combination." This statement makes very clear the preponderance that Boole gives to relationships. In response to this interest in the relational, we proposed to try to understand, how it was that Boole gave an algebraic form to logic. To carry out this task, we decided to use the principles that govern Transcurssive Logic (TL). The analysis of the categorical propositions was initiated: universal affirmative, universal negative, particular affirmative and particular negative. In analyzing the latter, we discovered that a whole universe could be described only from it. That is, not only told us that, for example, "some a is not b", but also could tell us: that there is "a which are not b", that there is "b that is not a", that there is "a which is b", and that in the rest of the universe there is "something" that "is not a nor is b". Then, from the TL it was inquired about the relationships that link these contents to try to determine how this algebraic structure could be generated. After some steps, four elements that resulted from this inquiry were given an entity; by relating them, they formed an algebraic structure called the permutation group or Galois group. The structure that constitutes the "universal language" in which the TL is written. In the analysis of the basic principles on which Boole's algebra is based, we have discovered that some aspects of reality that are revealed when we approach it from the subjective hidden between its values of truth and functions. That is, there is an 'implicit logic' underlying the Boolean binary proposal, a logic that we have called 'transcurssive' because it leaves evidence of a particular evolution over time, of what affects an observer. Among the findings, are: a) the existence of a complex system based, not on its constituent elements and a specific purpose, but on the interrelations that link its components. b) a systemic complexity that enables an adaptive dynamic response in front of the demands (inputs). c) the possibility of analyzing through the discovered structure, the relational situation of several binary systems, simultaneously (heterarchical distribution of hierarchical systems). d) the functional non-dependence of the structure concerning the observer ( measurement process), as it is the case with any situation that is objectively addressed, and e) the advantage of being able to consider situations where more than two states are at stake, even if they are exclusive. From the transcurssive perspective, an interesting panorama opens up of possible applications of this way of observing reality.