Quasi-empirical method

Quasi-empirical methods are applied in science and in mathematics. The term 'empirical methods' refers to experiment, disclosure of apparatus for reproduction of experiments, and other ways in which science is validated by scientists. These are studied extensively in the philosophy of science but are not directly applicable to fields not invalidated by real experiment (mathematics, theology, ideology). In these fields, the prefix 'quasi' came to denote methods that are 'almost' or 'socially approximate' an ideal of truly empirical methods.

One can argue that no science is capable of finding all counter-examples to a theory, therefore, no science is strictly empirical, it's all quasi-empirical. But usually, the term 'quasi-empirical' refers to the means of choosing problems to focus on (or ignore), selecting prior work on which to build an argument or proof, notations for informal claims, peer review and acceptance, and incentives to discover, ignore, or correct errors. These are common to both science and mathematics - and do not include experimental method.

Post-20th-century philosophy of mathematics is mostly concerned with quasi-empirical methods especially as reflected in actual mathematical practice of working mathematicians. Hard scientists are also concerned with the reliability of these methods to some degree, but only in fields (e.g. string theory) where direct experimental invalidation (i.e. finding counter-examples) is difficult or impossible. In such circumstances a scientist falls back on the same quasi-empirical methods as mathematicians.