Monday, May 30, 2016

"Therefore … !" Proof or Spoof?

Sir, (a+bn)/n = x, therefore God exists. Please respond! -- Euler to Diderot, 1773.
An Unlikely Story. In 1773 atheist philosopher Denis Diderot visited the Imperial Court at St. Petersburg to personally thank Catherine for the patronage which was to spare him an impoverished old age. So that his often disconcerting though entertaining atheistic polemics not remain unremonished by his Christian hosts, it was arranged that he be present at a "mathematical" demonstration of the existence of God.

The mathematician Leonhard Euler was to make the initial statement in what was hoped would be another entertaining debate. Euler, addressing himself to Diderot, declared with a tone of perfect conviction, “Monsieur, (a+bn)/n = x, donc Dieu existe; respondez!" Diderot, totally ignorant of mathematics (according to Dieudonné Thiébault as related to DeMorgan), was dumbfounded. Diderot was granted permission to return immediately to France.

Although this anecdote has become something of a legend, it ignores the fact that Diderot, himself, was quite a good mathematician. He would have easily recognized Euler’s assertion to be a non sequitur. The point here, of course, is not whether God exists or not. Rather it is whether reciting a mathematical formula proves God’s existence when it is connected with the word “therefore.” Does any statement, call it A, prove another statement, B, when we all we do is connect them with the word, “therefore”? For example, “Dogs are mammals; therefore, the moon is not made of green cheese?”

We would hardly deny that dogs being mammals has no connection to what the moon is made of. The Euler-Diderot story illustrates, however, what is to this day a common use of the word “therefore” -- or any of its many synonyms --: to foist off a nonsequitur on an unattentive or naïve audience.

The Many Synonyms of Therefore. Therefore connects a statement or body of statements (sometimes called “premises”) to a concluding statement, generally known as a “conclusion.” In contexts in which the word, therefore, would sound too high-falutin’, there are many other variations available: for example,
in conclusion we must recognize that
it follows that
proves that
the weight of the evidence indicates that
But the most important thing for us to realize -- that which makes them most dangerous -- is that using any of these words or phrases to support possible conclusions rules out what may be real live options. Therefore and its family members insinuate that other possible considerations are not supported by the option already singled out by the therefores. (See An Introduction to Models of Reasoning)

Obscuring or Discarding Live Options. This is far more than a “mere” theoretical lesson. When, for example, we face a problem for which we are considering alternative solutions for decision, we must be on guard that the therefores of different partisan interests be more than attempts to intimidate or seduce us into acceptance of their special concerns. Intimidation and seduction need seldom be employed if everyone -- or a majority, at least -- can be convinced that the selected decision is adequately and reasonably supported.

To continue this train of thought see Rationales for Intervention: From Test to Treatment to Policy: A forensic theory of warrants & rebuttals

--- EGR