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Mathematical Truth

Truth in mathematics is absolute. Given a set of axioms, determine statement that are true and statements that are false. A major exception arises in ClassicalLogic occurs when proof by induction is applied and decidability has not been shown. And even this realm of absolute truth is subject to the LawOfExceptions.

Scientific Truth

Scientific truth is based on measurement. It makes statements that are objective because they can be tested by experiment.

Popular Scientific Truth

What people believe is scientific Truth rarely corresponds to real Science.

Personal Truth

Subjective truths are merely beliefs objectively. subjectively, however, these Truth are consistent with our life's experience and constitute the most powerful truths.


GroupThink is the lowest common denominator of shared Personal Truth.

Spiritual Truth

Spiritual Truth is highest level of shared Personal Truth. It includes group hysteria and religion. It may involve animals as well as humans as it manifests common perception or feeling in the world of ideas rather than the concrete.

  I feel more with God in the presences of animals than with humans. - anonymous

The Nature of Truth (originally from )

Truth with a capital “T” has become a religious issue independent of science. The following discussion is intended to distinguish the various meanings of Truth from its objective usage in this paper and its relationship to truth-values in information physics. It is not intended as a sermon but it is hoped that this will help to demystify Truth as it applies to knowledge.

The history of Truth in western thought has a sworded past. It is what I call the “Truth Wars” in which all scientists are, in principle, crusaders. For early Man, truth was simple, it was what the gods wanted it to be and everybody thought they knew what that was.

The first real heretic was Socrates who taught that we don’t know what we think we know. He chose death over agreement that Man has any real knowledge of the nature of God. People hate to be told they don’t know what they think they know. It is no wonder he was put to death.

His student Plato applied the critical thinking of Socrates to define classical logic, as we know it. Truth, according to Plato, by God given axiom, has a value of True or False, and there exists in Nature no third alternative.

Plato’s student Aristotle applied this “Law of the excluded middle” to all aspects of how the physical world behaves. And his philosophy ruled through the dark ages.

Aristotle had proclaimed that surely a heavier body would fall faster than a light body. But along came another heretic. Galileo reasoned that if you attach a light body to a heavy body with a thread there was a contradiction. The system of the two bodies would be heavier than either alone and fall faster, but the drag of the lighter body should make them fall slower, so, he reasoned, all bodies must fall at the same speed. But no one would believe him, after all Aristotle’s reasoning was impeccable and unquestioned. So Galileo fudged some experiments to prove his point spawning Science, as we know it. Truth, again, became whatever God wants it to be, but it is measurable by experiment.

Newton resurrected Plato’s logic demonstrating that with mathematics assisted by experimental results we could explain everything in the universe exactly. Plato was absolved, and absolute Platonic Truth reigned through the age of reason.

Experiments in the late nineteenth century began to cast doubts on the accuracy of Newton’s model. Then early last century Einstein noticed a slight problem. It had been determined by experiment that light had a finite speed. Einstein reasoned that if you could exceed the speed of light you would turn cause and effect topsy-turvy. For Einstein this was absolutely absurd and clearly the universe could not work this way. It must be impossible to get someplace before you arrive. It was apparent that Newton’s truths had limited context. But Einstein himself resurrected logic by creating a mathimagical extrapolation between Newton’s physics and the world of relativity. He postulated that Plato’s Truth lived on in the mathematical realm where there is no preferred observer.

Just as Hilbert was proclaiming the impending triumph of rationalism in science the next attack on the nature of truth came as a rebellion from within mathematics itself. Godel showed that no complete logical system is self-consistent. Paradox in complete systems is unavoidable. Turing, father of computation theory, who invented the Universal Computing Machine that could solve any problem ran into a related problem, not all problems are solvable.

The computer I am typing on along with the Internet it is connected to, by equivalence to a Turing machine, is a complete logical system. This alone is sufficient reason to presume that the universe itself must be a complete logical system. There for, by Godel’s theorem, the universe is not self consistent.

Can it really be true that the universe itself does not abhor absurdity? Godel and then Turing contradicted Plato’s law of the excluded middle by showing that not all questions are answerable, yet most philosophers in the early twenty-first century either remain in a state of denial, or have simply abandoned the quest for true objectivity. By Godel’s theorem it is clear, that all truth is relative to logical context.

By Godel’s theorem the consistent system of the un-preferred observer that Einstein imagined does not exist in mathematics, or the universe. By extension Aristotle-ian axioms of mathematics, including Plato’s logic and even number theory are all ultimately arbitrary.

Godel’s theorem demands that Science revisits all proofs by induction and prove decidability first, and that Science address the relative nature of truth.

Any scientist shivers at the though of relative truth, it seems counter to everything Science stands for. Yet defining a consistent logical context for truths is not a bad thing, it just requires that we reformulate all of physics in terms of a logical window, or window of observation. This restores objectivity to Science. It is really no big deal that not all problems are solvable. The important thing to science is that any real problems can be solved if you limit the logical context of the problem. Knowledge and objectivity is gained by answering the problem in as many consistent contexts as you can.

In 1955, Shannon ignoring the law of the excluded middle redefined truth as a conditional probability. In Shannon’s model we receive bits (truth values) of information about the state of some logical system and each bit reduces our uncertainty about the state of the system by one half. This view of truth leads naturally to an information systems model of the universe.

If we are to say we truly understand something, we must explore the various relevant contexts where it may be true, false, probably true, probably false, undecidable, incomputable, incomprehensible, irrelevant or however Truth chooses to manifest itself. The bottom line is that Man cannot dictate the nature of objective truth, as scientists we must discover how truth is manifest.

In eastern thought there is no parallel to Platonic reasoning. Ancient Indian writings convey a model of causality that seems to mirror quantum causality. Perhaps the quantum is not nearly so strange as Platonic thinking might lead us to believe.

In the information systems model, bits simply represent alternatives. One is generally considered true and zero false. This assignment however is an arbitrary one. Bits distinguish between alternatives, hot or cold, up or down or true or false. The Truth of a bit of information does not have a value of zero or one; it is the correct value of the bit based on the alternatives it represents. In information physics the Truth of a bit is not its value per se, it is how the bit is manifest.

Role of Mathematics

Science is a slave to experiment not mathematics. But even though the basic axioms of arithmetic are not God given, they are immensely useful. It would be folly underestimate the power of mathematics.

When I first read Einstein's proof of special relativity I was certain it must be a mathematical trick. He took Newton's equation for energy in a physical system and equated it with Maxwell's equation for the energy of light waves, after some basic simplifications, presto==== -- JimScarver ====


But guess what, the bomb exploded. I thought then, and still do, that he must have had some intuition about the relationship of matter and energy in order to do what he did without thinking it absurd. The fact remains that any high school algebra student could easily have derived the relationship if they simply believed in the mathematics.

Since Newton invented calculus to solve the equations of motion we have seen many new and different mathematical systems developed to help explain new phenomenon in nature. It should be clear by now that nature is not going to oblige us by following our mathematics of choice.

In the information systems model we must be prepared to consider all possible mathematical systems and model the mathematics exhibited my nature what ever it happens to be. We will find analogues to established mathematical disciplines no doubt, but they can only be derived once the unrestricted underlying logical structure has been identified.

For information physicists it may be prudent to spend less time playing with numbers, as defined by Man, and more time looking at the nature of logical systems which correspond to nature as defined by God.

ClassicalLogic, StatisticalThinking, InformationPhysics, WhoIsGod, SeaOfLies, PopularScience, PositiveTruth, NegativeTruth.

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