2 - Logic

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Psion
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2 - Logic

Post by Psion » Thu Sep 14, 2017 2:37 pm

Logic (from the Ancient Greek: λογική, logikḗ), originally meaning "the word" or "what is spoken" (but coming to mean "thought" or "reason"), is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a specific relation of logical support between the assumptions of the argument and its conclusion. (In ordinary discourse, the conclusion of such an argument may be signified by words like therefore, hence, ergo and so on.)

There is no universal agreement as to the exact scope and subject matter of logic (see § Rival conceptions, below), but it has traditionally included the classification of arguments, the systematic exposition of the 'logical form' common to all valid arguments, the study of inference, including fallacies, and the study of semantics, including paradoxes. Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-1800s), and recently logic has been studied in computer science, linguistics, psychology, and other fields.

Source: Wikipedia

J. S. Saint
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Definitional Logic

Post by J. S. Saint » Fri Oct 06, 2017 10:59 am

    Logic ≡ the consistency of language and thought and studies there of.
    Definitional Logic ≡ the consistency in use of defined concepts and words such as to remove presumptuous axioms.
    Definitional Truth ≡ a statement wherein a portion of reality has been identified through precise match of definition.

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    Definitional logic is based strictly upon defined concepts and entities, void of presumed axiomatical truths. In the process of thinking and communicating, it is critical to maintain consistency in word-concept association and avoid presumption when possible.

    Logic is a process wherein relationships between ideas are discovered that must be true simply due to the consistency of defined concept involved. When the defined concepts are then firmly associated with physical reality, relevant “true-to-reality” concept are revealed.

    An error in the use of logic or in a belief in a truth is discovered when there is a conflict, contradiction, inconsistency, or disharmony in the assigned concepts - when something has been inadvertently associated with its contradiction.

    Above all else, Logic is defined by its insistence upon absolute consistency or total lack of contradiction.

    When the only axioms involved in an argument are definitions, all proper conclusions are true “by definition”. Usually such is a simple and obvious association, but sometimes the arguments, even though merely based on definitions, can become complex and surprisingly revealing.

    A simple example would be the proposal that an infinite line has no end to it. If the word “infinite” has been defined to mean “no end associated”, then it can be stated with certainty that “by definition”, an infinite line has no end.. end of discussion. Whether that conclusion is too tautological to be significant or relevant to anyone is another matter.

    Realize that an axiom is a statement of proposed truth. A definition is not. A definition is merely clarifying the concurrent language for the moment. Definitions are not true or untrue although they might be different than a common standard. Definitions are declarations to be accepted for the duration of the discussion. If they conflict with standard or common definitions, the arguments might be pointless, but not incorrect or invalid, merely a waste of time.

    Another simple example is the recent issue of whether “1+1 = 2”.

    Since the symbol “1+1” represents the same conceptual definition as the symbol “2” and the symbol “=” is defined to mean “the same quantity as” (in this context), the statement of “1+1 = 2” is really saying that:

    The definition of concept A is the same as the definition of concept A.

    "1+1" == two individual entities combined
    "2" == two individual entities combined.
    "=" == the same as

    Therefore from "A is A";
    "Two individual entities combined - is the same as - two individual entities combined."
    "1+1 = 2" is correct.

    And thus the conclusion is true “by definition”:

    “1+1 = 2” is true by definition (not by experiment or presumed axioms).

    It is no longer an issue of ether semantic manipulation nor of presumed and debatable axioms. Legal documents are often done in similar manners, much like the license agreements that people so often sign for software without reading.

    Another outstanding example was that of Thomas Aquinas in his five proofs for God. In four of the five, he stated an axiom as an obvious truth, most of which turned out to not actually be true. He was not using definitional logic and thus failed in his effort to actually prove anything, whether it was true or not, although at the time, he was very convincing.

    Definitional proofs are always merely about the consistent use of how the words have been defined to represent their associated concepts.


    In contrast a more common type of argument might be that “cars are manmade”. Typically, one would presume that any car would be made by man. But a car is not defined as an entity made by man, a car is defined by its form and function. Thus any conclusion, whether true or not, is not the product of definitional logic, but rather axiomatical logic, requiring that all parties agree on the axioms involved.

    In any one definitional logic argument, there can be no disagreement as to the definitions involved (assuming that they have been stated) although there can easily be dispute as to whether the definitions are meaningful or useful in common language.

    The significant difference is merely that a declared definition for the duration of the author's argument can't be disputed. If a thousand year old argument begins with, "since we define a circle as..., then... ", the argument cannot be defeated by the claim that "but that isn't what the word 'circle' means" or "but we have discovered that circles aren't really round in the physical universe." The conclusion made by the author might depend on his assumptions that his defined circles apply to a physical world in a manner that turned out to be incorrect, but that is another matter relating to extended axiomatic truth assumptions after the definitional argument.

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    Using Definitional Logic is a means of absolutely knowing that ones conclusions are beyond doubt. The conclusions are not subject to misperceptions, relative measures, or presumptions, although verification of consistency is still required.

    Stemming from a more complex example of definitional logic is the revelation of exactly what causes all of the laws of physics to be what they are; why mass attracts, why particles form, why some particles are positive, neutral, or negative, why opposites attract, and why they don’t merely collapse into each other.

    The results of the logic, once verified for proper consistency, are incontrovertible as they are true “by definition”. Of course ensuring that such conclusions exactly relate to the physical world, not merely a conceptual architecture, is critical before issuing any conclusion concerning truth value.

    J. S. Saint
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    Proper Logical Presentation

    Post by J. S. Saint » Fri Oct 06, 2017 11:16 am

      Definitions (binding concepts to words within presentation)
      Declaratives (scenario givens; for the sake of this discussion..)
      Axioms (already agreed to be true and demarked as axiomatical)
      Conclusive Premises (simple conclusions due to lack of alternatives)
      Observational Premises (we have directly seen this...)
      Conditional Premises (IF this is true, then..)
      Arguments (because that is true, this.. must also be true)
      Conclusions (because all of that has been true, this.. can be concluded)
      Extrapolations (having concluded that, this.. can also be concluded)

      Other than tpyos or other stupidities, such a presentation will be correct 100% of the time. The truth value among the participants will be 100% because NO presumptions are made (other than the notion that anyone cares) and all possible alternatives have been properly denounced. But note that each element in the list should be demarked as to which type it is.

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