The major focus of this section is Imre
Lakatos's description of the deductivist style in
Proofs and Refutations. An extreme example of this
style is given in the form of a computer generated proof of
in the box.
Euclidean Methodology has developed a certain obligatory style
of presentation. I shall refer to this as `deductivist style'.
This style starts with a painstakingly stated list of axioms,
lemmas and/or definitions. The axioms and definitions
frequently look artificial and mystifyingly complicated. One is
never told how these complications arose. The list of axioms and
definitions is followed by the carefully worded theorems. These
are loaded with heavy-going conditions; it seems
impossible that anyone should ever have guessed them. The
theorem is followed by the proof. ([11] p. 142)
This is the essence of what we have called formal understanding. We
know that the results are true because we have gone through the
crucible of the mathematical process and what remains is the essence
of truth. But the insight and thought processes that led to the
result are hidden.
In deductivist style, all propositions are true and all inferences
valid. Mathematics is presented as an ever-increasing set of eternal,
immutable truths. ([11] p. 142)
Deductivist style hides the struggle, hides the adventure. The
whole story vanishes, the successive tentative formulations of the
theorem in the course of the proof-procedure are doomed to oblivion
while the end result is exalted into sacred infallibility. ([11]
p. 142)
Annotation Form Interface