In mathematical logic, a formal calculation is a calculation which is systematic, but without a rigorous justification. This means that we are manipulating the symbols in an expression using a generic substitution, without proving that the necessary conditions hold. Essentially, we are interested in the form of an expression, and not necessarily its underlying meaning. This reasoning can either serve as positive evidence that some statement is true, when it is difficult or unnecessary to provide a 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.
Famous quotes containing the words formal and/or calculation:
“True variety is in that plenitude of real and unexpected elements, in the branch charged with blue flowers thrusting itself, against all expectations, from the springtime hedge which seems already too full, while the purely formal imitation of variety ... is but void and uniformity, that is, that which is most opposed to variety....”
—Marcel Proust (1871–1922)
““To my thinking” boomed the Professor, begging the question as usual, “the greatest triumph of the human mind was the calculation of Neptune from the observed vagaries of the orbit of Uranus.”
“And yours,” said the P.B.”
—Samuel Beckett (1906–1989)