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In science and the philosophy of science, falsifiability refers to the property of empirical statements that they must admit of logical counterexamples. This stands in contradistinction to formal and mathematical statements that may be tautologies, that is, universally true by dint of definitions, axioms, and proofs. Some philosophers and scientists, most notably Karl Popper, have asserted that no empirical hypothesis, proposition, or theory can be considered scientific if it does not admit the possibility of a contrary case.
For example, the proposition "all swans are white" would be falsified by observing a black swan, which would in turn depend on there being a black swan somewhere in existence. A falsifiable proposition or theory must define in some way what is, or will be, forbidden by that proposition or theory.
