If science means, as it originally did, searching for certain knowledge by means of evidence in order to separate true from false, then it is a basic human endeavour. Indeed, the Science of Conjecture goes back to the dawn of civilisation, where its first domain was the evaluation of legal evidence.
The typical legal hypothesis is Guilt, where True and False become Guilty and Innocent. Our four cases of conclusive evidence are named after the hypothesis of Guilt. Two features of the legal sphere make it particularly interesting for the analysis of the relationship between hypotheses and evidence. The first is that, unlike fiction, and more so than in other domains, conclusive legal evidence is rare: in most cases, judges and juries are not in the position to reach full certainty as to whether a defendant is guilty or innocent. The second is that, while we can keep arguing about global warming, psychic phenomena or even the colour of swans, in a legal trial the evidential tug of war must come to an end: the jury must take a decision and reach a verdict. In the absence of conclusive evidence, the verdict must be based on a standard of proof.
The standard of proof defines the minimum level of probability of guilt that is considered sufficient for a conviction, in the light of the available evidence. In deference to the Blackstone Principle: “It is better that ten guilty persons escape than that one innocent suffer”, the standard of proof increases with the gravity of the allegation and the corresponding severity of the punishment. Therefore, most civil cases only require a Preponderance of evidence, i.e. PP>50%: conviction occurs if the defendant is more likely to be guilty than innocent. But more serious cases demand Clear and convincing evidence, which – although no legal system specifies it – may mean something like PP>70%. The next level is the standard in most criminal cases: Beyond reasonable doubt, which – again, nowhere specified in numerical terms – may be expressed as PP>90%, or 95% or even 99%. The last level, which has no legal status, is Beyond the shadow of a doubt, which could be interpreted as PP>99.9%.
It is the burden of the prosecution (at least in civilised countries) to produce enough evidence to move the jury’s posterior probability beyond the required standard of proof, starting from a Presumption of Innocence, which, in our terms, means BR close, but not equal to 0 (BR=0 would imply, as we know, PP=0 irrespective of any evidence). The prosecution tugs first, producing confirmative evidence which, unless the case is totally without merit, moves PP away from its near zero starting point. Then the defence responds, trying to invalidate the prosecution’s evidence and providing its own disconfirmative evidence. And so on. The tug of war lasts until the trial comes to an end. At that point, the jury must decide: the defendant is either convicted, if the prosecution has managed to tug the rope beyond the standard of proof, or acquitted, if it hasn’t.
In theory, the prosecution is convinced that the defendant is guilty, the defence is convinced that he is innocent and the jury, starting from a presumption of innocence, decides to convict or acquit, based on the evidence produced at the trial. Reality is often much more complicated. But let’s stay with the theory and imagine a criminal case in which we can observe PP=80%: the jury is quite convinced that the defendant is guilty, but not enough as to be beyond reasonable doubt. As it stands, therefore, they will acquit. What can the prosecution do to obtain a conviction? As we have seen in the example of Tony and Margot, the prosecution should resist the temptation to look for conclusive evidence of guilt. True, if the evidence can be found, it will ensure a doubtless conviction. But if, as it is more likely, it can’t, and the new evidence turns out to be disconfirmative, PP may decline to well below the standard of proof, thus reinforcing the case for acquittal. The best route to conviction is instead to define and look for conclusive evidence of innocence. The prosecutor, who is convinced that the defendant is guilty, should ask himself Popper’s question: What reasonable evidence would be enough for me to change my mind? If the evidence can be found, it will ensure a doubtless acquittal. But if it can’t – as it is much more likely – it will bolster PP, possibly pushing it beyond reasonable doubt and thus ensuring a conviction.
It is the same route that James Randi follows to strengthen the hypothesis “Spiritualism is bonkers”: define evidence that would prove the hypothesis wrong and try to find it through a controlled experiment. The fact that he has being doing it since 1964 and still hasn’t found any counterevidence is not a conclusive proof of the hypothesis. This means that the hypothesis remains open to refutation but, at the same time, that it has been proven beyond reasonable doubt.
Likewise for a Blackstonian investor who believes he has found a pearl – a stock with a high probability of a large appreciation: his best route is not to prove that the stock is a pearl, but to try to prove that it isn’t. He will hardly ever manage to be beyond reasonable doubt, but clear and convincing evidence will suffice.
Lack of conclusive evidence means that, without a trial, we can discuss any hypothesis until the cows come home. But if science is separating true from false, we should behave like a considerate jury and reach a verdict.