We cannot indeed say a thing is probably true upon one very slight presumption for it; because, as there may be probabilities on both sides of a question, there may be some against it; and though there be not, yet a slight presumption does not beget that degree of conviction, which is implied in saying a thing is probably true. But that the slightest possible presumption is of the nature of a probability, appears from hence; that such low presumption often repeated, will amount even to moral certainty. Thus a man’s having observed the ebb and flow of the tide to-day, affords some sort of presumption, though the lowest imaginable, that it may happen again to-morrow: but the observation of this event for so many days, and months, and ages together, as it has been observed by mankind, gives us a full assurance that it will.
This is fairly interesting, since Butler is arguing that "the slightest possible presumption" must be a kind of probability for what is presumed because by accumulation it can reach even full assurance. Butler takes moral certainty to come in degrees, and "full assurance", I take it, is what he calls "the highest moral certainty".
Beattie very clearly draws on Butler's argument in his account of probable reasoning in the Essay on Truth, even using the same example of the ebb and flow of tides. However, Beattie's probability only concerns the future, e.g., our expectation that the tide will keep ebbing and flowing, whereas it is quite clear that Butler is only using it as just one kind of example for a much larger phenomenon.
