Where does deduction collide?

An inference in which the conclusion follows of necessity from the premises: if the premises are true the conclusion cannot be false, so a valid deduction preserves truth rather than adding to it. Gentzen's 1935 Untersuchungen über das logische Schließen constructed the systems of natural deduction and the sequent calculus, giving formal rules that introduce and eliminate each logical connective and make the notion of a correct proof precise. The referent is a truth-preserving relation between sentences in a formal system, judged valid or invalid by its form alone, not an amount subtracted from income, an error-prone human guess, or a prediction squeezed from a theory.[1]

Unit

A truth-preserving step from premises to conclusion, valid by form

Recovery means

Not applicable

Measured by

Assessed by whether the conclusion follows from the premises under the rules of a deductive system, by constructing or checking a proof

Deductive reasoning as people actually perform it: how ordinary reasoners draw conclusions from given premises, and the systematic ways their conclusions depart from what logic sanctions. Wason's 1968 Reasoning about a Rule introduced the selection task, on which most people fail to test a conditional in the way validity requires, and Johnson-Laird's 1999 review argued that people reason by building and scanning mental models of the possibilities the premises allow rather than by applying formal rules. The referent is an observed psychological process, measured by accuracy and response time in experiments, not a norm of valid inference, a sum subtracted from income, or a method of scientific testing.[2][3]

Unit

A conclusion a person draws from premises, right or wrong

Recovery means

Not applicable

Measured by

Studied experimentally through the accuracy, error patterns, and response times of participants reasoning from set premises, as in the selection task

The hypothetico-deductive method: the practice of deriving observable, testable predictions from a hypothesis by deduction and then confronting those predictions with evidence, so that the hypothesis stands or falls by whether its consequences hold. Popper's The Logic of Scientific Discovery argued that a theory is never proved by its instances but is tested by deducing predictions that could refute it, making deductive derivation the engine by which empirical science is checked. The referent is a normative account of how scientific theories are tested, concerned with confirmation and falsification, not a formal proof relation, a psychological process, or a line on a tax return.[4]

Unit

A testable prediction deduced from a hypothesis for empirical check

Recovery means

Not applicable

Measured by

Appraised by whether the predictions deduced from a hypothesis survive deliberate attempts to refute them through observation and experiment