Theme: Decidability

DEAR MISEDUCATED WORLD:

Logic is at least ternary, not binary. (Meaning three states, not two)

…………… FALSE…….TRUE……..UNDECIDABLE

FALSE…..FALSE…….FALSE……UNDECIDABLE

TRUE……FALES…….TRUE……..UNDECIDABLE

UNDEC…FALSE…….UNDEC…..UNDECIDABLE

MATHEMATICS

In mathematics, which for millennia was unfortunately the gold standard of logic, we use the word true when we mean either “balanced” (retaining constant relations), or we mean “proven” (possible to demonstrate), because in mathematics we create proofs of possibility rather than statements of truth. We may claim that we speak truthfully that we have constructed a proof. But mathematics consists of operations, deductions, inferences and guesswork, by which we identify means of demonstrating the possibility and necessity of a series of constant relations (ratios).

COMPUTER SCIENCE

In the gold standard of reasoning: computer science – when we refer to values, we call this same sequence true, false, and null (unknown). So in computer science, we either possess sufficient information to state something is provable (true or false), or unprovable (false), or undecidable (lacking the information).

FORMAL LOGIC

( I’ll avoid formal logic because in my view, like all game theory, beyond use in very simple human perceivable scales, it’s been a waste of a century. I mean. I can dismantle the liars paradox in five minutes or less. it was a wasted century.

PHYSICAL SCIENCE

In sciences we use the terms False, Possibly True (an hypothesis, theory, or law), and Undecidable. Between the choice of true and false, it is false that we know with certainty. Truth always remains uncertain in all but the most simple of questions.

EPISTEMOLOGY

In epistemology we say something is knowingly false, possibly true, and undecidable, or unknown. In epistemology, just as in science, we must determine if an argument survives attempts to falsify it. If it is true, then we can decide if it is possible. I it is possible then we can decide if it is preferable. If it is preferable without causing harm to others, then we have determined that it is good.

MORALITY, PHILOSOPHY, AND THEOLOGY

In morality, philosophy, theology, we say (lie) that if we can find an excuse for something (a justification) it is true, or moral, or good. When that only means that according to the established norms, scriptures, and laws. in other words, one is free of blame if he can justify his actions as permissible, moral or good. In morality philosophy and theology, we attempt to survive justification.

LAW

When we encounter LAW we use the jury, and debate between two parties, and moderated by a judge, to test both whether we are justified under law, and whether our testimony and our arguments are believable. In law we attempt to survive the battle between three forces: the law as written, the standards of rational behavior of the jury, the logical testing of your statements by the judge, and the subjective testing of your truthfulness by the jury. And in case you don’t know this, most cases are decided by the test of truthfulness, which is why american courts are so useful for commerce. The first sin of american law is failure of informational reciprocity. Failure and error are forgivable. Violation of reciprocity is not.

HIERARCHY OF CERTAINTY

… FALSE, that which does not survive tests of falsification.

… … TRUE, that which survives all tests of falsification

… … … PROVEN, that which survives tests of possibility.

… … … … UNDECIDABLE that which cannot be decided.

THE TRUTH TABLE OF CERTAINTY

F:False, T:True, P:Provable, U:Undecidable

…..F…..T…..P…..U

F…F…..F…..F…..U

T…F….*T*…P…..U

P…F…..P…..P…..U

U..F…..U….U…..U