 | This article needs attention from an expert in mathematics. The specific problem is: Replace the current - essentially wrong - definition by an appropriate one, based on a mathematical textbook, rather than (at best) a materials science book. (June 2021) |
In mathematical logic, a formal calculation, or formal operation, is a calculation that is systematic but without a rigorous justification. It involves manipulating symbols in an expression using a generic substitution without proving that the necessary conditions hold. Essentially, it involves the form of an expression without considering its underlying meaning. This reasoning can either serve as positive evidence that some statement is true when it is difficult or unnecessary to provide proof or as an inspiration for the creation of new (completely rigorous) definitions.
However, this interpretation of the term formal is not universally accepted, and some consider it to mean quite the opposite: a completely rigorous argument, as in formal mathematical logic.