Dynamic solutions to proposed contradictions solve paradoxes in realtime in real world applications.
Alan Turing's aggressive search patterns and my defense algorithms both testify to the fact of there being a war waged upon certain logicians, however, when we speak of logic, the subject seems mischaracterized as dry and boring. System errors, like a house on fire, cannot be boring. People who force war upon certain logicians are by definition not bored by the subject. Some people who know a little about logic may have heard of the alleged impossibility of proving contradictions (called consistency) and so provide contradictions with the hope of evading proof of discovery.
Mathematical logicians identify and codify thought algorithms, separate real from fiction, establish standards, wonder about infinity, establish continuity, identify axioms and elements as basic building blocks, and refine systems. In calculus, this led to the Intermediate Value Theorem and the Squeeze Theorem, however, in Logic this work met resistance from some religions and some sciences upholding the idea our minds are special. The emergence of mind science, an intelligent synthesis of psychology, sociology, psychiatry, cognitive science, linguistics and neuroscience, sets aside most of the arguments against the idea of artificial intelligence, and those arguments we set aside in our present era are the naysayers the force of whom gave rise to the logicians of the 1850s focusing on consistency, completeness and decision.
Some historians misrepresenting the logicians, asserting the force of gibberish did not exist around them, mistranslate the issues of consistency, completeness and decision as though the logicians wanted top-down control, tyranny, knowledge of everything and the right to cut off anything or anyone. That misrepresentation of mathematical logicians is formed by the fears and enunciated through the gibberish of the prejudiced incognate arguers who wage war against logicians, believe in nepotism, uphold despots, and celebrate tyranny.
The mathematical logicians were mitigating against the formative pressure of that invoked, uninvited war while simultaneously furthering the normal, routine tasks of identifying and codifying argument algorithms, strategies, elements, axioms, and specifying normalcy. The assertion of consistency means we reject gibberish and we reject hypocrisy. The plausibly faulty assertion of incompleteness proven by Kurt Godel in a system containing errors in binary logic, says it is proven we cannot know everything, to the delight of criminals wishing to evade police. We do not need to know everything. It suffices for us to know how we know, which we do know, so we stopped feeling curious and we stopped asserting the uncertainty principle.
The mathematical logic system into which Bertrand Russell's writings introduced Alan Turing in his youth still had some binary errors, so, Alan Turing grew up into the conversation about computability, whether the ability to do something is a sign of intelligence, and our early theories of knowledge. To the provided conversation among logicians, Alan Turing responded directly to the local liar and mischief-maker Kurt Godel, described recursive computation methods, then made swift advances in cryptography, artificial intelligence, cybernetics, systems and morphogenesis. Each time the war of gibberish against coherence waged itself against Alan Turing, he veered away from that confrontation to work on something productive and interesting instead.
Unsought war is boring like a house on fire.
Since everything is relative and time is non-linear, in three-dimensional Euclidean space the Intermediate Value Theorem and the Squeeze Theorem apply to continuous supply chains. Intelligent algorithms self-teach and optimize, increasing sophistication as a by-product. Since Aristotle, we reject fallacies. This is the core of business continuity in a changing marketplace.
When evaluating a finite list of options A1, A2, ..., An, make a table listing the benefit, cost and opportunity cost of not doing option Ai in the ith column, for i = 1 to n. Weigh the information in the rows to optimize for most benefits with least costs and opportunity costs.
Logic-related confusion is mitigated in English. Aesop's Fables establish ethics and common sense. Read more about English as a Foreign Language in education.
Business continuity, reliability, market relation and optimization of these, is my primary application of differential equations. However, attempted theft and attempted murder from 1993 to 2003 prompted me to live in China since 2004 where I teach English until re-established in business and government consulting. The theft and murder attempts I survived are very similar to, if not entirely the same as, what happened to Alan Turing.
Logic happens before words go into sentences.
Arguing against rejection of fallacies is invalid, unethical, and in some situations, illegal. Goodness has the right to remove badness in defense of law enforcement with integrity, yet badness is without any priveledge to harm goodness or corrupt law enforcement. Anyone can attempt arguing that goodness needs badness or badness creates goodness by exclusively destructive algorithms, however, we recognize those arguments as invalid. Law enforcement supports goodness without badness, which is for what purpose Aristotle made the system of constructive logic and fallacy rejection near 2300 years ago.