# Logical Refutation

## Logical Refutation

demonstration of the falseness of a judgment (proposition), an inference (argument), or a group of hypotheses (judgments) and inferences constituting a scientific theory or part of a theory.

One also may speak of logical refutation with respect to formal analogues of the concepts enumerated above—the formulas of some calculus, the sequences of formulas that figure as formal conclusions and proofs, systems of formulas (and subsystems thereof) that function as the axioms of a calculus, systems of consequences of axioms, and formal systems (calculi) as a whole. The logical refutation of a formula is the (formal) proof of its negation; the logical refutation of a formal derivation or proof is an effective specification that the given sequence of formulas does not satisfy the definition of a derivation (or proof); and finally, the logical refutation of a system of axioms or of a calculus as a whole is a contensive proof of the contradictory nature (inconsistency) of the given system, arrived at by means of the metalanguage of the given calculus (in its metatheory). One of the mostly widely used methods of logical refutation consists in reducing the hypothesis (or judgment, inference, or theory as a whole) to a contradiction.

In general, in accordance with the diverse interpretations of the terms “proof and “negation,” which figure in the explanation of the term “logical refutation,” this term may be interpreted in many different, albeit related, ways.

The concept of logical refutation plays an important part in the methodology of science, especially in the methodology of the empirical sciences, because the term “inductive proof,” which is often applied to experimental verifications of facts, may be interpreted literally (not metaphorically) only if negative assertions are proved. The agreement of experimental results with theoretical prediction can, in principle, always be explained in terms of insufficient accuracy of measurement. But a discrepancy between theoretical and experimental data that goes beyond the bounds of the permissible “spread” of results refutes a given version of a theory. It does not follow from this, of course, that the “positive value” of the concept of logical refutation consists in its purely theoretical, methodological aspect. A logical refutation of some of the possible hypotheses, if indisputable, increases the degree of likelihood of the competing hypotheses (this degree is assessed in some instances by the rules of inductive logic) and, when a competing hypothesis is unique, serves as an entirely rigorous proof.