A question of logic

by Andrew Teller

The readers of ENS News who have followed this column might have noticed that its author is sometimes at pains to point out flaws in the reasoning of the anti-nuclear argument. If the said readers are somewhat sceptical, they might have also realised that highlighting the falsity of a piece of reasoning does not prove the falsity of the conclusion derived. They would be right. Anybody can reach a valid conclusion despite failures in one’s analysis of the question at hand. The assumption that the opponents of nuclear energy might be right at the end of the day despite the mistakes they regularly pile up in their reasoning cannot be lightly dismissed. Why is it then that I have been so far satisfied with exposing the shortcomings of the arguments put forward by the critics of nuclear energy? The answer to this question is not as obvious as one could be tempted to believe.

To understand why, we must first revert to the basic rules of logic and more precisely to the proper use of the logical operator named implication. This operator, which has been known about since the times of Aristotle at least, encapsulates the fundamental dissymmetry between correct and false reasoning. What it says in a nutshell is that true (or valid) and false (or invalid) premises behave differently as to the conclusions that can be derived from them: deriving a true conclusion from a true premise yields a true proposition while deriving a false conclusion from a true premise yields a false proposition. On the other hand, false premises can lead equally well to true or false conclusions. This is a pity. Life would be so much easier if false premises always led to false conclusions. If this were the case, maths teachers would have much less work with exams: they would just look at the answers of their students without bothering to go into the nitty-gritty of the calculations since a valid conclusion would stem only from a valid derivation. But this not being the case, they must also inspect the premises in order to confirm that the correct answer given by the student was indeed legitimately obtained, i.e. not reached by pure chance.

We have so confirmed that spotting a flaw in an argument does not mean that its conclusion is invalid. But we have also shown that it does not mean that it is valid either. Identifying a shortcoming does not therefore kill the argument but is a clear indication that the intended point remains to be made. This is much less than what the supporters of nuclear energy would like, but certainly more than its opponents hoped for. Now let us not delude ourselves: despite our concern for accuracy, we supporters of nuclear energy also make mistakes. When we make use of an invalid premise, the conclusion derived from it does not fall through but remains to be proven. This state of affairs mirrors the one described above: this is much less than what we would like, but certainly more than our opponents hope for.

At this point, the latter could try to seek support from Hans Jonas, the German philosopher whose thinking is at the root of the precautionary principle. They could try to claim that the potential consequences of the use of nuclear energy are so dire that it is preferable to consider their arguments valid even when they are not warranted by a watertight derivation. I am not aware that H. Jonas ever considered contravening the rules of logic; his main proposal was that adverse consequences be systematically given precedence over favourable ones. It can be easily imagined however that an enthusiastic interpretation of his recommendation could invite some to extend the process to bending the rules of logic itself. But this would not do. Flouting the rules of logic is equivalent to giving up the use of reason altogether in the decision process. The argumentation of the anti-nuclear could and would then boil down to claiming that “nuclear energy is bad because it is bad”. This is not however what they are doing. I infer from this fact that they implicitly accept the principle that any piece of reasoning must obey the rules of logic, in which case there is no escape from the fact their points remain to be made in all cases where there is a mistake in the way they try to make it.

The conclusion of this short analysis is that the inconclusive state of the debate between supporters and opponents of nuclear energy is to be put down to the strange behaviour of the logical implication: it leaves the protagonists all too often in a state of doubt and leads to certainty only in very few instances.