Tuesday, December 27, 2011

Definitional Logic

Logic the recognition of association between definitions and/or axioms such as to reveal an associated truth.
Definitional Logic the recognition of association between definitions such as to reveal an associated definitional truth.
Definitional Truth a statement wherein a portion or portions of reality have been identified by definition as that portion of reality.

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.

Logic is a process wherein cross associations are discovered that must be true due simply because of the defined concept consistency involved. When the defined concepts are then firmly associated with physical reality, relevant “truth” is revealed.

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

Above all else, Logic is defined by its 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 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. They are declaration to be accepted for the duration. If they conflict with standard or common definitions, the arguments might be pointless, but not incorrect or invalid, merely a wast 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
"2" == two individual entities.
"=" == the same as

"1+1 = 2" is correct.

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.

And thus the conclusion is true “by definition”:

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

Definitional proofs are always merely about 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, it is defined by its form and function. Thus the 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.

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.

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 properness, 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.

No comments:

Post a Comment