This folio contains red pencil editing marks probably in the hand of James Mill. Marginal summary also probably in his hand.

2 Nov r 1806

Evidence

Circumstantial

Ch Mend[?] Phys

1

§ 16 Price

A mathematician of considerable celebrity+ has brought forward an argument, by which if it were just, the disprobative force of the species of circumstantial evidence in question would be reduced to little or nothing. Facts highly and indisputably improbable, are what we are accustomed every day to give credence to, and with any practical inconvenience, upon any the slightest evidence. The definition of improbability is to be taken from a source from which it always has been taken—the language—the correct mathematical language of the doctrine of chances. Take any fact whatever let the chances against its happening be to the chances in favour it its happening, as 1000 to one: you can not deny but that this fact is in a very considerable degree improbable. Instead of 1000 to 1, say 10,000 to one, it is now ten times as improbable as before: instead of 10,000 say 50,000, it is now fifty times, it is improbable in the ratio of 50,000 to one. But facts as improbable as this are believed, and turn out to be true every day: and believed and would at any time be believed by any rational man, upon any the slightest evidence: upon the evidence of a paragraph in a newspaper. A lottery is drawn with 50,000 tickets in it: and the first drawn ticket is intitled to a prize. You read that such or such a number has in this way been become intitled to the prize. You make no difficulty in believing it: and yet the chances were 50,000 to 1 against its being the first drawn: so improbable are the facts which the [...?] of men are believing every day without scruple and without error. But suppose instead of 50,000 the tickets were 500,000 or 5,000,000: how prodigious the improbability! But even in this last case would the fact be incredible? incapable of being rendered credible by any number of witnesses? On the contrary you can hardly speak of it as being less credible under these last and highest numbers than it was under the first. In the same way I can make my fact improbable in as high a degree as I please: improbable, if I please in an infinite degree: and still it shall remain not incredible: and in a word perhaps not less credible than at first credible: upon the strength of any ordinary mass of evidence, upon evidence of much less strength than many a mass that is exhibited, and obtain credence, and without prejudice to truth, in truth of justice.

+ D r Price [...?]

1

D r Price's argument y t facts as improbable in proportion to y e numerical chance ag t the happening not true, since facts in the highest degree improbable not as ag t a particular lottery ticket as drawn a prize are believed upon y e slightest evidence