Logic | |

I recall asking the math teacher in ninth grade, "How do you know that 1 is 1?" "That's an axiom," he said. "An axiom cannot be proven, and being an axiom, it does not need proof by definition - 1 is 1 because there is an axiomatic agreement with the assertion." "That's not a satisfactory answer," I said after some thought. I wanted to understand what is beyond axioms. He kicked me out of class for the rest of the year, apparently hoping that would be a satisfactory answer. Since Euclid, mathematics has been built on axiomatic ground. When we start with something defined and not the process of definition, then we need grounding principles, root assumptions upon which we can elaborate. When we attempt to define an object's "true nature" independent of our involvement in the process of its definition, when we try to understand objective reality unaffected and unbiased by our interaction with it, then we necessarily have to start with an axiom that in essence asserts, "That's how it is. Period."
The structure of the possibility of there being an axiom is full of inconsistencies
Later, philosophers did question whether we could know the "true nature" of anything objectively, and based upon their observations, they assumed that we could not. They reached the conclusion that a logical structure was needed to replace the intuitive axiomatic statements that described the "true nature" of phenomena, and they attempted to create such a logical structure by defining a final set of axioms wherein each axiom in the set was defined by the others while each axiom on its own was meaningless. The hope was that this set would become the logical fundament of geometry and mathematics, consisting of purely logical statements containing no information whatsoever about phenomena. These attempts failed because no logical structure consisting of empty symbols ( Axioms were utilized as basic assumptions of certain models and theories. They were the hidden bedrock of the search for THE TRUTH, for simplicity in the sense of the term as something single, or the search for the One, which becomes the many. However, explaining Creation with axioms would be endeavoring to achieve an objective explanation of the start of the universe independently of the one doing the explanation. If so employed, axioms would be self-defeating because one could always question what was there before the basic axiom, or how the basic axiom came about. That's probably why there is no axiomatic theory of Creation.
Today science accepts that there might be several right theories or models that could describe Creation, but the basic aspiration to reach totality through finding the common denominator, the ONE TRUTH, points toward the same paradigm, the same framework of linear thinking. That means, if I have many right descriptions, then these are necessarily secondary descriptions and there must be a
SHET's teaching is not axiomatic. An axiomatic theory requires consistency of its structure. Before the 19
The abstractization of mathematics in the 19 "True" means factual, observable. True is a relation of equivalence with something perceived - which is not a very reliable logical tool of consistency.[1] Although success in proving consistency was achieved by transforming the problem of proof into another domain (for instance, by showing the consistency of Euclidean axioms through an algebraic model), this is not considered an absolute proof because it does not prove that the algebra is consistent. Furthermore, observing any number of true facts in agreement with the axioms is no guarantee that there will be no future fact that might contradict those found earlier, and consequently, ruin the consistency of the system. So any axiomatic system relying on the truth-value of its models for consistency is incomplete because most models are infinite, and consequently, carry insufficient truth-value. So here we have two serious problems: 1) If the model is infinite, no matter how many elements conform to the consistency of the system, by virtue of being infinite, it is impossible to check them all. 2) Using a model to prove consistency is relative because it assumes the consistency of some other system. The purpose of axiomatizing a branch of mathematics, or any system, was to achieve the dream of laying down a simple set of propositions from which all the true theorems of that field could be derived. According to this line of reasoning, the set of propositions should be finite, the theorems derived should be consistent with the propositions, and the consistency of such a system should be proved within the system. It was hoped that an absolute proof of consistency would be attained if both the propositions (sentences stating something) and also the logical reasoning (if-then, or, etc., which is the dynamics of inference) could be translated into empty, meaningless signs. "Empty" and "meaningless" meant for them total transparency, or in other words, these signs would only contain their explicit symbolization. If nothing was left implicit, these theoreticians reasoned, then the coveted absolute proof of consistency could be established.
Why was it so important that the abstract expressions should be solely explicit and well defined? How is this demand connected to the proof of consistency? Simply stated, the implicit, hidden relations are hidden because they are indefinite. Indefinite means not defined or indefinable. If logical inference leads to a theorem that is not well defined, then it might be indefinite or undecidable, which means that it could be "
Translating sentences into signs was no problem. To translate the logical reasoning, however, it had to be broken down into well defined relations, such as "identical," "not-identical", etc., which then could be translated into signs on a one-to-one basis. Of course, the purpose of representing the dynamics of logical inference by signs was to exclude the possibility of anything implicit and to only offer explicit expressions. In the language I am using to explain the Holophanic loop, replacing the dynamics with "empty" signs would be trying to turn "Structure" into "Significance". Structure is the dynamics of the process of definition, whereas significance is the defined entity, the Stating that SHET's teaching is not axiomatic means that he proposes a logical system consisting of propositions (significance) and logical inference (structure) wherein these are co-dependent, which means that structure only gains meaning when there is a realization (significance) and there can only be significance if it has structure. The initial framework of SHET's logic is the dynamics of paradoxes. Such a system gains consistency if and only if it is based on the structure of a "Paradox" (inconsistency). This new paradigm is elucidated in my book, Holophany, The Loop of Creation. In Holophany, consistency is demanded from the non-linear dynamics that stabilizes defined entities, whereas conventional logic assesses consistency only between the defined propositions and the inference. Of course, the latter is based on consistency being truth, and truth being well defined (logical) objects so the relation between these objects renders them either true or false.
The 19 This dynamics, the structure, the process of definition is a complex loop of relations that eventually define each other. These are the parameters by which any defined entity gains existence. It could be thought - wrongly - that the complex loop of relations that eventually define each other is like saying that there is no basic word, which is a self-evident truth, on which all other words are built because any word can be defined by other words, whereas these other words can be defined by still other words, and so on until we cover the whole gamut of definitions of all words. So the word we intended to define in the first place is defining those words that define the word we intended to define. This kind of description is not the loop that I am discussing. The portrayal of one word being defined by other words that are defined by other words delineates significance, not the process of definition. Although words define each other, they are all defined, whereas the process of definition deals with defining the indefinite. In the Holophanic loop every process is generated by other processes, every process is defined by other processes. The totality of this inter-defining activity produces discrete processes that aim at defining the indefinite. Stated differently, this is the process of measurement that utilizes discrete means to measure with, whereas the measured is continuous. To best illustrate what I mean, think about a living organism: It is alive, dynamic, and it can survive within a certain range of environs. It consists of numerous feedback systems, such as the thyroid metabolism between the thyroid and the pituitary gland, oxygen availability, and red blood cell production, etc. The function of all these systems is to regulate something. To regulate means to provide/allow not too much, not too little, but enough. What "enough" means for each system depends on other systems with which that system is interconnected. For instance, during hypoxia (too little oxygen), the body creates more erythrocytes (red blood cells) that carry hemoglobin that carry oxygen to vital organs. This process occurs to utilize the available oxygen so that life can be sustained. Too many red blood cells will impede the blood flow and too much oxygen will turn into free radicals (too much of which are damaging). So, how does the body regulate its oxygen intake? When the heart recognizes too much oxygen, the myocytes, heart cells, simply release chemicals to contract the blood vessels. When the brain recognizes too much carbon dioxide (the result of too much oxygen), it slows down the automatic breathing urge. Each feedback system is connected to all the others, and all of them together regulate each other. The keyword here is, regulate. Each system consists of other systems, which consist of other systems, in a dynamic loop - each system regulating itself and being regulated by the others. Furthermore, the normal range of values for a given system might change due to aging or other circumstances that change the whole organism. For example, the need for oxygen is different during aerobic stress (panic, physical exertion, etc.) than during blissful sleep. So the live organism is not so much a conglomeration of valid values, but more the act of regulation (complex non-linear loop dynamics) that maintains the necessary dynamic balance that can perpetuate the act of regulation. Even DNA can be viewed as a dynamic sub-system. The DNA is not identical in all cells, parts of it can be corrupted, free radicals can steal an electron from a DNA sequence and disrupt it and thus change its function, or it can change in minor or major ways due to interaction. That's probably why the clone of a red cat could be a black cat. So what is being regulated? This is the wrong question, of course. The living organism is structure. It is the process that gains expression as living cells. There is no basic material that becomes a cell. For example, if you put carbon and water and oxygen in a cauldron, you still won't have a live cell. Asking what is being regulated is like asking what are the basic axioms, the indubitable fundamental truths, the four pillars of the universe. The loop logic is not about that. It is not about correct initial conditions that bring about desired results. It is not a language wherein each constituent part is well defined by the others, but a dynamic structure that eventually stabilizes. In the case of the living organism, structure stabilizes into the right space of action of a given biological sub-system. This sub-system interacts with other sub-systems of the organism, and this non-linear interaction re-stabilizes all the sub-systems, which dynamics is the regularization of the whole organism. There is nothing uninfluenced or non-interactive within the live organism. The live organism is its function, which is, regulation of its sub-systems so it can continue to interact with itself and the rest of the world - or in other words, survive.
The loop logic does not deal with defined entities as something given within a system, but defines all its elements, including the process of definition with which it defines. As SHET put it,
The new paradigm taught by SHET is that
Creation myths starting with (single) oneness, a matter particle in space from which point time starts rolling, receives the
[1] In English, the word "Truth" is a cognate of the Old Norse word " |