“A definition of a concept uniquely determines what objects exemplify the concept under any possible circumstances. There is more than one way to do this. The most straightforward kind of definition is an explicit definition. An explicit definition gives necessary and sufficient conditions for something to exemplify the concept. For example, one might define ‘bachelor’ by saying that something is a bachelor iff it is an unmarried man. But frequently in logic, mathematics, and technical philosophy, we encounter definitions of another sort. For instance, in the propositional calculus we might define ‘formula’ by stipulating:

(i) an atomic formula is a formula;

(ii) if P is a formula the ~P is a formula;

(iii) if P and Q are formulas then (P&Q) is a formula;

(iv) nothing is a formula that cannot be obtained by (i)-(iii).

Here we give rules for constructing formulas from a basic set (the atomic formulas) and one another, and then stipulate that something is a formula only if it can be constructed using those rules. This is an example of a recursive definition. Recursive definitions look circular… [but it is] possible to replace recursive definitions with explicit definitions.”

Pollock, John L. Technical Methods in Philosophy. Boulder: West View, 1990. Print. p. 37