I was looking a little bit into this claim that Poincaré used subjective priors to help acquit Dreyfus. In a word, FAIL.
Poincaré′s use of subjective priors was not a betrayal of his own principles because he needed to win, as someone above put it. He was granting his opponent’s own hypothesis in order to criticise him. Strange that this point was not clear to whoever was researching it, given that the granting of the hypothesis was prefaced with a strong protest.
The court intervention in question was a report on Bertillon’s calculations, by Poincaré with Appel and Darboux, « Examen critique des divers systèmes ou études graphologiques auxquels a donné lieu le bordereau » (discussed and quoted [here] ). It speaks for itself.
« Or cette probabilité a priori, dans des question comme celle qui nous occupe, est uniquement formée d’éléments moraux qui échappent absolument au calcul, et si, comme nous ne pouvons rien calculer sans la connaître, tout calcul devient impossible. Aussi Auguste Comte a-t-il dit avec juste raison que l’application du calcul des probabilités aux sciences morales était le scandale des mathématiques. Vouloir éliminer les éléments moraux et y substituer des chiffres, cela est aussi dangereux que vain. En un mot, le calcul des probabilités n’est pas, comme on paraît le croire, une science merveilleuse qui dispense le savant d’avoir du bon sens. C’est pourquoi il faudrait s’abstenir absolument d’appliquer le calcul aux choses morales ; si nous le faisons ici, c’est que nous y sommes contraints … S’il s’agissait d’un travail scientifique, nous nous arrêterions là ; nous jugerions inutile d’examiner les détails d’un système dont le principe même ne peut soutenir l’examen ; mais la Cour nous a confié une mission que nous devons accomplir jusqu’au bout … Nous admetterons toujours, dans les calclus qui suiveront, l’hypothèse la plus favorable au système de Bertillon. »
My translation: « Now this a priori probability, in questions such as the one before us, consists entirely of moral elements which absolutely escape calculation, and since we cannot calculate anything without knowing it, all calculations become impossible. Quite rightly did Auguste Comte also say that the application of probability calculations to the moral sciences was the scandal of mathematics. To want to eliminate moral elements and substitute numbers is just as dangerous as vain. In a word, probability calculations are not, as seems to be thought, a marvolous science which dispenses with the need for the scientist to have good sense. This is why one must absolutely abstain from applying these calculations to moral objects; if we do so here, it’s because we are forced to … If it were a scientific work in question, we would stop there; we would find it useless to examine the details of a system whose principle itself does not stand up to examination; but the Court has entrusted us with a mission which we must accomplish to the uttermost … We will always grant, in the following calculations, the most favourable hypothesis to Bertillon’s system. »
Then it is shown that Bertillon nevertheless made other serious errors, even granting this hypothesis.
I find Poincaré not guilty of the charge bayesianism, and what’s more,
if Bertillon and Poincaré were relevant at all, they would be a counterexample: the bayesian makes a right mess of things and the frequentist saves the world. I can sympathise with Person A above who gets the sudden urge to throw their laptop out the window.
I was looking a little bit into this claim that Poincaré used subjective priors to help acquit Dreyfus. In a word, FAIL.
Poincaré′s use of subjective priors was not a betrayal of his own principles because he needed to win, as someone above put it. He was granting his opponent’s own hypothesis in order to criticise him. Strange that this point was not clear to whoever was researching it, given that the granting of the hypothesis was prefaced with a strong protest.
The court intervention in question was a report on Bertillon’s calculations, by Poincaré with Appel and Darboux, « Examen critique des divers systèmes ou études graphologiques auxquels a donné lieu le bordereau » (discussed and quoted [here] ). It speaks for itself.
« Or cette probabilité a priori, dans des question comme celle qui nous occupe, est uniquement formée d’éléments moraux qui échappent absolument au calcul, et si, comme nous ne pouvons rien calculer sans la connaître, tout calcul devient impossible. Aussi Auguste Comte a-t-il dit avec juste raison que l’application du calcul des probabilités aux sciences morales était le scandale des mathématiques. Vouloir éliminer les éléments moraux et y substituer des chiffres, cela est aussi dangereux que vain. En un mot, le calcul des probabilités n’est pas, comme on paraît le croire, une science merveilleuse qui dispense le savant d’avoir du bon sens. C’est pourquoi il faudrait s’abstenir absolument d’appliquer le calcul aux choses morales ; si nous le faisons ici, c’est que nous y sommes contraints … S’il s’agissait d’un travail scientifique, nous nous arrêterions là ; nous jugerions inutile d’examiner les détails d’un système dont le principe même ne peut soutenir l’examen ; mais la Cour nous a confié une mission que nous devons accomplir jusqu’au bout … Nous admetterons toujours, dans les calclus qui suiveront, l’hypothèse la plus favorable au système de Bertillon. »
My translation: « Now this a priori probability, in questions such as the one before us, consists entirely of moral elements which absolutely escape calculation, and since we cannot calculate anything without knowing it, all calculations become impossible. Quite rightly did Auguste Comte also say that the application of probability calculations to the moral sciences was the scandal of mathematics. To want to eliminate moral elements and substitute numbers is just as dangerous as vain. In a word, probability calculations are not, as seems to be thought, a marvolous science which dispenses with the need for the scientist to have good sense. This is why one must absolutely abstain from applying these calculations to moral objects; if we do so here, it’s because we are forced to … If it were a scientific work in question, we would stop there; we would find it useless to examine the details of a system whose principle itself does not stand up to examination; but the Court has entrusted us with a mission which we must accomplish to the uttermost … We will always grant, in the following calculations, the most favourable hypothesis to Bertillon’s system. »
Then it is shown that Bertillon nevertheless made other serious errors, even granting this hypothesis.
I find Poincaré not guilty of the charge bayesianism, and what’s more, if Bertillon and Poincaré were relevant at all, they would be a counterexample: the bayesian makes a right mess of things and the frequentist saves the world. I can sympathise with Person A above who gets the sudden urge to throw their laptop out the window.