People reason inductively about what was, is, or will be true. People sample to find outcome frequencies. People have information or feelings about outcome values. Simple algorithms can determine probabilities and risks {Bayesian inference}. Statistical models {Bayesian approach} show how previous events change current or future event probabilities.
Complex systems can build from simpler elements {bootstrapping}|, with nothing from outside system. For each hypothesis, bootstrapping assumes all hypotheses but one are true and uses evidence to support that hypothesis.
Thinking and knowing methods {formal reasoning} can use deduction, induction, argument, and logic.
Commonsense rules, simplifications, guesses, and trial and error {heuristics}| can discover knowledge or solve problems. Heuristics apply in connectionist nets, neural networks, hidden Markov processes, indefinite integration, semantic networks with Finite State Machine operators and related variables, morphological analysis, focal-objects method, equations, rule induction, fuzzy systems, regression trees, case-based reasoning, declarative languages as opposed to functional languages, graphs, combinatorial geometry, data mining, machine learning, and natural-language understanding.
Repetitions, successions, and regular conjunctions can predict next steps {induction, epistemology}|. Induction indicates truth but does not prove. Induction {enumerative induction} can observe many similar cases to find categories that remain constant or have true predicates. Induction {eliminative induction} can observe many different cases to see categories that remain constant, keep predicates true, or remove untrue predicates.
Three laws {laws of thought} underlie thinking: identity, contradiction, and excluded middle. It is impossible to prove laws of thought true.
Something identical to true thing is true {law of identity}, or what is, is.
Nothing is both true and false {law of non-contradiction} {law of contradiction}, or nothing both is and is not.
Something is either true or false {law of the excluded middle}.
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Date Modified: 2022.0225