## Avoiding Epistemic Circularity

Finance, business, and indeed many fields share commonality with mathematics in that there is a need to separate fact from fiction. However, there is much formal terminology that is subtly but significantly different in meaning. What follows is a small sample of the formal terms often used by academics and well-educated practitioners:

**Axiom** - an *axiom *or *postulate *is a proposition that is* not proved or demonstrated* but taken for granted. Therefore, axioms often serve as a starting point for deducing and inferring other truths.

**Theorem** - In mathematics, a theorem is a statement that* has been proven* on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms.

**Conjecture** - In mathematics, a conjecture is a proposition that* is unproven but appears correct* and has not been disproved.

**Lemma** - In mathematics, a lemma is a proven proposition which is used as a stepping stone to a larger result rather than as a statement in-and-of itself. There is no formal distinction between a lemma and a theorem, only one of usage and convention.

**Corollary** - A corollary is a statement of fact that follows readily from a previous statement, usually a theorem. The use of the term corollary, rather than proposition or theorem, is intrinsically subjective.

**Axiomatization** - the act or process of reducing something to a system of axioms. This happens a lot in quantitative finance but not everyone approves of this.

**Hypothesis** - A hypothesis is a proposed explanation, that can be tested, for an observable phenomenon. More specifically, in the mathematical sense statistical hypothesis testing is used to evaluate the hypothesis. Thus, the test is a method of making decisions about the certainty of the stated hypotheses using experimental data. In statistical hypothesis testing a result is called statistically significant if it is unlikely to have occurred by chance.

**Epistemic Circularity** - An epistemically circular argument defends the reliability of a source of belief by relying on premises that are themselves based on the source. You wont sound convincing if you put forward epistemically circular arguments! NB: this is used in philosophy more so than mathematics (hence the photo of Rene Descartes) but non-the-less a useful term to know.

*16 Jun 2010*
*Damien Wintour*