Thursday, March 31, 2016

The fallacy of the invisible cat

 Isaac Newton
In Chapter 1 of his book Astrology, science or belief? published in 1992, Manuel Toharia writes:
However wise they can be about certain subject matters, there is always some element that contradicts the myth of the perfect genius. For example, it is well-known that Newton was an angry man, terribly unfriendly and probably a repressed homosexual. Lest there be any misunderstanding, we must add immediately that what we find wrong with this alleged homosexuality of the English genius is its repression, which certainly made him a bitter person, no doubt with a minimal dose of self-esteem.
Probably a repressed homosexual? And how can we know this, if it is true that Newton repressed it? Or did Toharia (or whoever was his original source) have inside information, or perhaps he came to this conclusion because he knows that Newton suffered at least two psychic crises in his life, and believes that their cause must have been his repressed homosexuality? Observe the use of the qualifiers certainly and no doubt. If so, his argument would be a textbook example of the fallacy of the invisible cat:

If there were an invisible cat on that table, we would see nothing.
We see nothing.
Therefore there is an invisible cat on that table.

 The Cheshire cat,famous invisible cat
It is clear that the conclusion of this syllogism does not have to be true, even though both premises may be. What is the fallacy? Simplifying the syllogism at the utmost, we get:

B is true if A is true.
B is true.
Therefore A is true.

The error is now clearer. Even when the first assumption is correct, B could also be true without A being true. Hence the conclusion does not follow from the premises. On the other hand, the following syllogism would be correct:

B is true only if A is true.
B is true.
Therefore A is true.

The problem is now apparent. The fallacy is the result of the confusion between what in mathematics is called a necessary condition and a sufficient condition. The phrase B is true if A is true tells us that the truth of A is a sufficient condition for the truth of B. Sufficient, but not necessary. The syllogism can only be applied if the truth of A is a necessary condition for the truth of B. Therefore the second syllogism is valid, because in that case the truth of A is a necessary condition of the truth of B, although it is not a sufficient condition.
In Newton’s case, was this probably repressed homosexuality a necessary condition for his nervous crises? Not at all, there are other possible explanations. For instance, it is well-known that he had an unhappy childhood, as his mother remarried and left him in the care of his grandmother. Also, in 1979 it was shown that his hair contained a concentration of mercury fifteen times higher than normal, probably as a result of his alchemical experiments. Since mercury is neurotoxic, this discovery (which was made 13 years before the publication of Toharia’s book) provides a much more plausible explanation of his psychic crises than his allegedly repressed homosexuality.

Manuel Alfonseca