Originally posted by Acolyte
I disagree: what about reductio ad absurdum?
"reducing to the point of sbsurdity" is a valuable logical tool, in which you reach a level of what would be absurd, but arguing an absurdity to start with is not a valid way to prove something.
in a similar vein, consider "proof by contradiction" in which you assume the
opposite of what you are trying to prove and show that this is impossible so your original assertion must be true. it goes without saying, of course, that the original assertion must be a statement or the "proof" is not valid.
here is an example of attempting to prove an absurdity in geometry:
assertion: all triangles are isosceles.
"proof": in triangle
abc, draw the perpendicular bisector to side
bc (calling the intersection point with that side
d) to vertex
a. triangles
adb and
adc contain a common side (
ad), congruent sides (
bd and
dc), and the angle between is a right angle since
ad is a perpendicular bisector. therefore, those two "sub-triangles" are congruent by side-angle-side, and so sides
ab and
ac are congruent by corresponding parts.
the flaw?
you can't draw a perpendicular bisector to side bc from vertex a unless you have an isosceles triangle to begin with! otherwise, the bisector to
a is
not perpendicular and is called the
median. the perpendicular bisector will hit side
ab or
ac but not the vertex--unless the triangle is isosceles from the start.
so, sometimes, what seems to be perfectly logical turns into an absurdity.