But given simply a notation, mathematical or otherwise, and indeed as thoroughly understood a notation as you please in point of the translation or truth conditions of its statements, who can say which of its true statements rank as postulates?
The other species want a name in our language, and in most others; I suppose, because it was not requisite for any, but philosophical purposes, to rank them under a general term or appellation.
And though virtue and honour be allowed their proper weight and authority, that perfect disinterestedness, so often pretended to, is never expected in multitudes and parties; seldom in their leaders; and scarcely even in individuals of any rank or station.
And thus the impostor above mentioned was enabled to proceed, from his ignorant Paphlagonians, to the enlisting of votaries, even among the Grecian philosophers, and men of the most eminent rank and distinction in Rome; nay, could engage the attention of that sage emperor Marcus Aurelius; so far as to make him trust the success of a military expedition to his delusive prophecies.
But suppose, that all the historians who treat of England, should agree, that, on the first of January, 1600, Queen Elizabeth died; that both before and after her death she was seen by her physicians and the whole court, as is usual with persons of her rank; that her successor was acknowledged and proclaimed by the parliament; and that, after being interred a month, she again appeared, resumed the throne, and governed England for three years: I must confess that I should be surprised at the concurrence of so many odd circumstances, but should not have the least inclination to believe so miraculous an event.
He says [Hume]: \"I believe it will not be very necessary to employ many words in explaining this distinction. Every one of himself will readily perceive the difference betwixt feeling and thinking. The common degrees of these are easily distinguished, though it is not impossible but in particular instances they may very nearly approach to each other. Thus in sleep, in a fever, in madness, or in any very violent emotions of soul, our ideas may approach to our impressions; as, on the other hand, it sometimes happens, that our impressions are so faint and low that we cannot distinguish them from our ideas. But notwithstanding this near resemblance in a few instances, they are in general so very different, that no one can make a scruple to rank them under distinct heads, and assign to each a peculiar name to mark the difference\" (\"Treatise of Human Nature,\" Part I, Section I).
We might provisionally, though perhaps not quite correctly, define "memory" as that way of knowing about the past which has no analogue in our knowledge of the future; such a definition would at least serve to mark the problem with which we are concerned, though some expectations may deserve to rank with memory as regards immediacy.
Those who think that utility requires distinctions of rank, do not consider it unjust that riches and social privileges should be unequally dispensed; but those who think this inequality inexpedient, think it unjust also.
The important rank, among human evils and wrongs, of the disappointment of expectation, is shown in the fact that it constitutes the principal criminality of two such highly immoral acts as a breach of friendship and a breach of promise. Few hurts which human beings can sustain are greater, and none wound more, than when that on which they habitually and with full assurance relied, fails them in the hour of need; and few wrongs are greater than this mere withholding of good; none excite more resentment, either in the person suffering, or in a sympathizing spectator.
That first of judicial virtues, impartiality, is an obligation of justice, partly for the reason last mentioned; as being a necessary condition of the fulfilment of the other obligations of justice. But this is not the only source of the exalted rank, among human obligations, of those maxims of equality and impartiality, which, both in popular estimation and in that of the most enlightened, are included among the precepts of justice. In one point of view, they may be considered as corollaries from the principles already laid down.