Quasi-empirical method

Quasi-empirical methods are scientific methods used to gain knowledge in situations where empirical evidence cannot be gathered through experimentation, or experience cannot falsify the ideas involved. Quasi-empirical methods aim to be as closely analogous to empirical methods as possible.

Empirical research relies on, and its empirical methods involve experimentation and disclosure of apparatus for reproducibility, by which scientific findings are validated by other scientists. Empirical methods are studied extensively in the philosophy of science, but they cannot be used directly in fields whose hypotheses cannot be falsified by real experiment (for example, mathematics, philosophy, theology, and ideology). Because of such limits, the scientific method must rely not only on empirical methods but sometimes also on quasi-empirical ones. The prefix quasi- came to denote methods that are "almost" or "socially approximate" an ideal of truly empirical methods.

Quasi-empirical method usually refers to a 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. To disprove a theory logically, it is unnecessary to find all counterexamples to a theory; all that is required is one counterexample. The converse does not prove a theory; Bayesian inference simply makes a theory more likely, by weight of evidence. Since it is not possible to find all counter-examples to a theory, it is also possible to argue that no science is strictly empirical, but this is not the usual meaning of "quasi-empirical".

Examples
Albert Einstein's discovery of the general relativity theory relied upon thought experiments and mathematics. Empirical methods only became relevant when confirmation was sought. Furthermore, some empirical confirmation was found only some time after the general acceptance of the theory.

Thought experiments are almost standard procedure in philosophy, where a conjecture is tested out in the imagination for possible effects on experience; when these are thought to be implausible, unlikely to occur, or not actually occurring, then the conjecture may be either rejected or amended. Logical positivism was a perhaps extreme version of this practice, though this claim is open to debate.

Quasi-empiricism in mathematics is an important topic in post-20th-century philosophy of mathematics, especially as reflected in the actual mathematical practice of working mathematicians.