The foundation of our logical system is that every statement has a true and false component. This was expressed algebraically as: T = t + f.
Paradox and Flaw?
The astute observer applied this rule to this foundational statement to presumably discover a major paradox and flaw in the system.
The resulting statement:
The statement that every statement has a true and false component means that this statement itself has a true and false component. The false component is that every statement does not have a true and false component.
This immediate paradox is insurmountable when looking at the issue through traditional definitions of true and false.
Numerical and Verbal Logic used to purify each other
However all our definitions were based upon the reality of words not the dictates of traditional or numerical logic with all their truth tables - Not that we’re against them - In fact we are attempting to use numerical logic to establish the foundations of verbal logic. Alternately we will regularly apply the T/F postulate of verbal logic to numerical logic used in a verbal context in order to deconstruct it.
Anyway, the transcendence of the paradox of the T/F Postulate applied to itself comes in the simple realization that our system is founded in communication with words - while the deductive logic system is founded in the crisp truths of numbers.
Numerical Logic is Exact and Content Based
While it might seem that numbers and mathematics are based in words, they are not. While it is possible to describe mathematical processes verbally, it is very cumbersome and quite confusing. Mathematicians rarely create their pure, and perfectly consistent structures in words. Indeed it is almost painful to turn mathematics into words. Read the Pythagorean theorem as it is expressed in words as compared with the simple equations that say every thing much more eloquently, concisely, exactly. And that is the point. Deductive logic when applied to the exact concepts of mathematical science becomes equally exacting.
In scientific math all statements are either true or false. This is an Either/Or truth system which is perfectly applicable when dealing with the crisp truths of math and science, which is based on dead things. There is no propaganda in Equation Science. Math and scientific statements are either true or false.
Verbal Logic is Relative and Contextual
However as soon as we move from crispness of Numbers to the ambiguity of Words the verbal logical structure comes into play. In Math 1=2 is always false while 1≠ 2 is always true.
Numerical Logic: ((1=2) = False) And ((1≠2) = True))
Verbal Logic: ((1=2) = Indeterminate) And ((1≠2) = Indeterminate))
However when verbal information is transmitted from one to another there exists a tremendous amount of inherent ambiguity - based around the intent of the transmitter and the ability of the Receiver to understand the transmission. Even the simple, one equals two, when transferred into words is not necessarily false - because one and two could be adjectives used as pronouns. The words they are modifying could be infinite in variety.
While many of the statements would be false, (indeed all statements where one and two are modifying the same noun are probably false) there are some that would be true. For instance one couple equals two things. Thus the context of a verbal statement is very important in determining whether it is true or false. However, ultimately as we’ve already established, the truth or falsehood does not exist inside the words themselves, as it does in Math/Science, but instead it is in the accuracy and intent of the transmission.
Despite inadequacies Numerical Logic applied to Verbal Systems
Unfortunately because of the incredible descriptive power of the language of Math/Science, the same rules and logical structure have been applied to the verbal reality despite some obvious problems. Indeed the cultural icon of the Rocket Scientist with no common sense, like Einstein, reveals this dichotomy between logic and practical thinking. The logic of the engineer applied to day to day life is the subject of comic strips and TV sitcoms. This is another example of our cultural sense that there is a difference between scientific and common logic.
Despite the inadequacies of Math Logic applied to Verbal systems, it still seems to be the system of choice for most critically thinking people. Perhaps due to the prestige of science. Perhaps due to the either/or way of thinking that is prevalent in Western Civilization. Who knows? But it is.
This is why we must Blah, Blah on.
Necessity of Deconstructing the Logic Box
Before any progress can be made we must deconstruct the Logic Box that has been cultivated since Birth. If this cultural condition didn’t exist, there would be no need for this rebuttal and we could move right ahead. Instead we must clean up the room before we can put new furniture inside. Thus our first deconstruction was to say that the numerical logic of equations is not the same as the verbal logic of words.
This is true because of the contextual nature of words, which negates the either/or logic of numbers.
We are not in any way attacking the either/or logic of science, which works quite well in the crisp precise world of algebra and numbers. However because of the inherent ambiguity of verbal communication - based upon all sorts of symbolic shorthand, which is easily misunderstood, this is not the appropriate logical system for words.
Intended vs. Unintended meaning of T/F Postulate
Anyway, back to the original supposed paradox, which is the T/F Postulate applied to itself. Obviously it makes no sense in terms of the absolute truths of numerical, algebraic, science, however in terms of our original definition, it makes mathematical and logical sense.
The T/F Postulate simply states that every verbal statement has its intended meaning which we called true and the meaning which was not intended which we call false.
When applied to itself this simply means that the T/F Postulate has its intended meaning which is defined as true and also an unintended meaning which is defined as false. This is a truism in any logical system. Therefore, in this system the quest for absolute truth is not an issue whatsoever - as it is in science. Instead the issue is to determine the truth and falsehood behind each statement.
False Component has to do with absolute vs. relative truth
Indeed this longwinded exposition has been to describe the false component of the T/F Postulate. The False component is founded in the misinterpretation of the words ‘true’ and ‘false’ in the postulate. Thinking that they were absolute mathematical constructs led to the seeming paradox, when in reality the ‘True’ & ‘False’ in the Postulate are adjectives modifying the received meaning by the transmitter.
Therefore, the transmission of the T/F postulate is a False one, if the Receiver - can’t read my writing or understand my words. It is also false, if the receiver interprets the words differently than was intended.
(If you’re into assigning blame, this could be either the Writer or Reader’s fault. The Writer could be unclear or the Reader could be dumb. Or in this case the words fly against the scientific way of thinking; and so the concepts will tend to be misunderstood - unless there is this extensive discussion to deconstruct the pre-existing boxes - which is what this is all about.)
True Component has to do with accuracy of transmission
Therefore the true meaning of the T/F postulate is based in the accuracy of the transmission rather than the accuracy of the words. As mentioned this is different than math truths. If you don’t understand this, the transmission was false despite what seemed to be a thorough explanation. If you disagree, then the transmission was false because there is nothing to disagree with.
Partial Transmission Verbal, not Mathematical
If you the Reader partially understood, then the transmission was partially true. Wait a minute. How can something be partially true? Is that blue a half truth?
One question at a time.
A math statement can not be partially true, while a verbal statement can be partially understood, in which case, it is partially true under the definition is of our T/F postulate. For instance in our ‘Take out the Trash’ example - the person who understood the literal meaning of the words, but not the idiomatic contextual meaning, was in the condition of partially true.
Partial Truth not the same as Half-truth of Propagandist
This is not a half-truth in the traditional sense. There was no deception intended. Half-truths are the domain of the Propagandist and the subject of this paper. Half-truths are the Tools of the Propagandist, mentioned above, where they intend the Reader to understand the false meaning of the words. In the ‘Take out the Trash’ example there was simply an incomplete understanding - not a deliberate attempt to mislead and confuse.
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