Laplace’s masterwork can be found for free here. It reads unbelievably well. He was a fantastic writer – entertaining, crisp, pithy, smart.
Laplace is, of course, the guy who – when asked by Napoleon why he did not mention God (in a book on astronomy with the very cool name “The System of the World“) – retorted “I have no need of that hypothesis.” And in some academic circles – particularly English – Laplace is mocked for saying “it is therefore obvious…” when he wished to skip proving something; the mocker does this by…. saying “it is therefore obvious” before skipping over the place where his proof of his assertion should be. Apparently Laplace does this a lot in The System of the World. For example, “it is therefore obvious that Fermat’s last theorem is true.” That’s a snarky dig at the French.
Nevertheless, Laplace was a complete and utter genius, and Bayes theorem should be named for him. Or co-named.
A philosophical essay on probability – which, historically speaking, put probability theory on the map, and kick-started its ascent to the pinnacle of the scientific method – is online in English (Laplace was French and wrote in it – as the French will do) in several places. I got mine at Google Books (which I’ve just noted has a different web address for each page; don’t worry – it changes as you scroll).
From Chapter 2, pages 3-4:
“All events, even those which on account of their insignificance do not seem to follow the great laws of nature, are a result of it just as necessarily as the revolutions of the sun. In ignorance of the ties which unite such events to the entire system of the universe, they have been amde to depend upon final causes or upon hazard, according as they occur and are repeated with regularity or appear without regard to order; but these imaginary causes have graudally receded with the widening bounds of knowledge and disappear entirely before sound philosophy, which sees in them only the expression of our ignorance of the true causes. Present events are connected with preceding ones by a tie based upon the evident principle that a thing cannot occur without a cause which produces it. This axiom, known by the name of the principle of sufficient reason, extends even to actions which are considered indifferent…
We ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow….
[and here comes his famous bit about God]: Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it – an intelligence sufficiently vast to submit these data to analysis – it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.”
This is all a set up, of course, to saying “but since we’re not God, we need probability.”