Advertisement

Most of the principles, and reasonings, contained in this volume, were published in a work in three volumes, called A Treatise of Human Nature: A work which the author had projected before he left college, and which he wrote and published not long after. But not finding it successful, he was sensible of his error in going to the press too early, and he cast the whole anew in the following pieces, where some negligences in his former reasoning and more in the expression, are, he hopes, corrected. Yet several writers, who have honoured the author's philosophy with answers, have taken care to direct all their batteries against that juvenile work, which the author never acknowledged, and have affected to triumph in any advantages, which, they imagined, they had obtained over it: A practice very contrary to all rules of candour and fair-dealing, and a strong instance of those polemical artifices, which a bigoted zeal thinks itself authorized to employ. Henceforth, the author desires, that the following pieces may alone be regarded as containing his philosophical sentiments and principles.

Part 1

1 All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, relations of ideas and matters of fact. Of the first kind are the sciences of geometry, algebra, and arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain. That the square of the hypotenuse is equal to the square of the two sides, is a proposition which expresses a relation between these figures. That three times five is equal to the half of thirty, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence.

2 Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise tomorrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood.

1 Though there be no such thing as chance in the world; our ignorance of the real cause of any event has the same influence on the understanding, and begets a like species of belief or opinion.

2 There is certainly a probability, which arises from a superiority of chances on any side; and according as this superiority increases, and surpasses the opposite chances, the probability receives a proportionable increase, and begets still a higher degree of belief or assent to that side, in which we discover the superiority. If a die were marked with one figure or number of spots on four sides, and with another figure or number of spots on the two remaining sides, it would be more probable, that the former would turn up than the latter; though, if it had a thousand sides marked in the same manner, and only one side different, the probability would be much higher, and our belief or expectation of the event more steady and secure. This process of the thought or reasoning may seem trivial and obvious; but to those who consider it more narrowly, it may, perhaps, afford matter for curious speculation.

3 It seems evident, that, when the mind looks forward to discover the event, which may result from the throw of such a die, it considers the turning up of each particular side as alike probable; and this is the very nature of chance, to render all the particular events, comprehended in it, entirely equal.

Part 1

1 There is not a greater number of philosophical reasonings, displayed upon any subject, than those, which prove the existence of a Deity, and refute the fallacies of atheists; and yet the most religious philosophers still dispute whether any man can be so blinded as to be a speculative atheist. How shall we reconcile these contradictions? The knights-errant, who wandered about to clear the world of dragons and giants, never entertained the least doubt with regard to the existence of these monsters.

2 The Sceptic is another enemy of religion, who naturally provokes the indignation of all divines and graver philosophers; though it is certain, that no man ever met with any such absurd creature, or conversed with a man, who had no opinion or principle concerning any subject, either of action or speculation. This begets a very natural question; What is meant by a sceptic? And how far it is possible to push these philosophical principles of doubt and uncertainty?

3 There is a species of scepticism, antecedent to all study and philosophy, which is much inculcated by Descartes and others, as a sovereign preservative against error and precipitate judgment. It recommends an universal doubt, not only of all our former opinions and principles, but also of our very faculties; of whose veracity, say they, we must assure ourselves, by a chain of reasoning, deduced from some original principle, which cannot possibly be fallacious or deceitful.

Part 1

1 The passion for philosophy, like that for religion, seems liable to this inconvenience, that, though it aims at the correction of our manners, and extirpation of our vices, it may only serve, by imprudent management, to foster a predominant inclination, and push the mind, with more determined resolution, towards that side which already draws too much, by the bias and propensity of the natural temper. It is certain that, while we aspire to the magnanimous firmness of the philosophic sage, and endeavour to confine our pleasures altogether within our own minds, we may, at last, render our philosophy like that of Epictetus, and other Stoics, only a more refined system of selfishness, and reason ourselves out of all virtue as well as social enjoyment. While we study with attention the vanity of human life, and turn all our thoughts towards the empty and transitory nature of riches and honours, we are, perhaps, all the while flattering our natural indolence, which, hating the bustle of the world, and drudgery of business, seeks a pretence of reason to give itself a full and uncontrolled indulgence. There is, however, one species of philosophy which seems little liable to this inconvenience, and that because it strikes in with no disorderly passion of the human mind, nor can mingle itself with any natural affection or propensity; and that is the Academic or Sceptical philosophy.

1 Moral philosophy, or the science of human nature, may be treated after two different manners; each of which has its peculiar merit, and may contribute to the entertainment, instruction, and reformation of mankind. The one considers man chiefly as born for action; and as influenced in his measures by taste and sentiment; pursuing one object, and avoiding another, according to the value which these objects seem to possess, and according to the light in which they present themselves. As virtue, of all objects, is allowed to be the most valuable, this species of philosophers paint her in the most amiable colours; borrowing all helps from poetry and eloquence, and treating their subject in an easy and obvious manner, and such as is best fitted to please the imagination, and engage the affections. They select the most striking observations and instances from common life; place opposite characters in a proper contrast; and alluring us into the paths of virtue by the views of glory and happiness, direct our steps in these paths by the soundest precepts and most illustrious examples. They make us feel the difference between vice and virtue; they excite and regulate our sentiments; and so they can but bend our hearts to the love of probity and true honour, they think, that they have fully attained the end of all their labours.

One considerable advantage, that arises from philosophy, consists in the sovereign antidote, which it affords to superstition and false religion. All other remedies against that pestilent distemper are vain, or, at least, uncertain. Plain good sense, and the practice of the world, which alone serve most purposes of life, are here found ineffectual: History, as well as daily experience, affords instances of men, endowed with the strongest capacity for business and affairs, who have all their lives crouched under slavery to the grossest superstition. Even gaiety and sweetness of temper, which infuse a balm into every other wound, afford no remedy to so virulent a poison; as we may particularly observe of the fair sex, who, though commonly possessed of these rich presents of nature, feel many of their joys blasted by this importunate intruder. But when sound philosophy has once gained possession of the mind, superstition is effectually excluded; and one may safely affirm, that her triumph over this enemy is more complete than over most of the vices and imperfections, incident to human nature. Love or anger, ambition or avarice, have their root in the temper and affections, which the soundest reason is scarce ever able fully to correct. But superstition, being founded on false opinion, must immediately vanish, when true philosophy has inspired juster sentiments of superior powers. The contest is here more equal between the distemper and the medicine: And nothing can hinder the latter from proving effectual, but its being false and sophisticated.

Part 1

1 The great advantage of the mathematical sciences above the moral consists in this, that the ideas of the former, being sensible, are always clear and determinate, the smallest distinction between them is immediately perceptible, and the same terms are still expressive of the same ideas, without ambiguity or variation. An oval is never mistaken for a circle, nor an hyperbola for an ellipsis. The isosceles and scalenum are distinguished by boundaries more exact than vice and virtue, right and wrong. If any term be defined in geometry, the mind readily, of itself, substitutes, on all occasions, the definition for the term defined: Or even when no definition is employed, the object itself may be presented to the senses, and by that means be steadily and clearly apprehended. But the finer sentiments of the mind, the operations of the understanding, the various agitations of the passions, though really in themselves distinct, easily escape us, when surveyed by reflection; nor is it in our power to recall the original object, as often as we have occasion to contemplate it. Ambiguity, by this means, is gradually introduced into our reasonings: Similar objects are readily taken to be the same: And the conclusion becomes at last very wide of the premises.

2 One may safely, however, affirm, that, if we consider these sciences in a proper light, their advantages and disadvantages nearly compensate each other, and reduce both of them to a state of equality.

1 It is evident, that there is a principle of connexion between the different thoughts or ideas of the mind, and that, in their appearance to the memory or imagination, they introduce each other with a certain degree of method and regularity. In our more serious thinking or discourse, this is so observable, that any particular thought, which breaks in upon the regular tract or chain of ideas, is immediately remarked and rejected. And even in our wildest and most wandering reveries, nay in our very dreams, we shall find, if we reflect, that the imagination ran not altogether at adventures, but that there was still a connexion upheld among the different ideas, which succeeded each other. Were the loosest and freest conversation to be transcribed, there would immediately be observed something which connected it in all its transitions. Or where this is wanting, the person, who broke the thread of discourse, might still inform you, that there had secretly revolved in his mind a succession of thought, which had gradually led him from the subject of conversation. Among different languages, even where we cannot suspect the least connexion or communication, it is found, that the words, expressive of ideas, the most compounded, do yet nearly correspond to each other: A certain proof that the simple ideas, comprehended in the compound ones, were bound together by some universal principle, which had an equal influence on all mankind.

I have long entertained a suspicion, with regard to the decisions of philosophers upon all subjects, and found in myself a greater inclination to dispute, than assent to their conclusions. There is one mistake, to which they seem liable, almost without exception; they confine too much their principles, and make no account of that vast variety, which nature has so much affected in all her operations. When a philosopher has once laid hold of a favourite principle, which perhaps accounts for many natural effects, he extends the same principle over the whole creation, and reduces to it every phenomenon, though by the most violent and absurd reasoning. Our own mind being narrow and contracted, we cannot extend our conception to the variety and extent of nature; but imagine, that she is as much bounded in her operations, as we are in our speculation.

But if ever this infirmity of philosophers is to be suspected on any occasion, it is in their reasonings concerning human life, and the methods of attaining happiness. In that case, they are led astray, not only by the narrowness of their understandings, but by that also of their passions. Almost every one has a predominant inclination, to which his other desires and affections submit, and which governs him, though, perhaps, with some intervals, through the whole course of his life.

The main feature of a spiral or S0 galaxy is its conspicuous extended stellar disk. Stars in the disk of a large spiral galaxy, like our Milky Way, follow nearly circular orbits with very little random motion. Ordered rotation accounts for almost all the energy of motion, with random speeds contributing less than ~5%: the disk is dynamically ‘cold’. In smaller galaxies, random motions are proportionally larger, but most of the disk's kinetic energy is still in rotation. Because the stars have little vertical motion perpendicular to the disk plane, the disk can be quite thin.

Spiral galaxies are distinguished from S0 systems by the multi-armed spiral pattern in the disk. The disks of spiral galaxies still retain some gas, whereas S0 systems have lost their disk gas, or converted it into stars. Both S0 and spiral galaxies can show a central linear bar; in Figure 1.11, the sequence of barred galaxies SB0, SBa, …, SBm runs parallel to the ‘unbarred’ sequence S0, Sa, … Apart from the bar and spiral arms, the stellar disks of large galaxies are usually fairly round; but many smaller systems are quite asymmetric.

We begin this chapter by discussing galaxies with an active nucleus, a compact central region from which we observe substantial radiation that is not the light of stars or emission from the gas heated by them. Active nuclei emit strongly over the whole electromagnetic spectrum, including the radio, X-ray, and γ-ray regions where most galaxies hardly radiate at all. The most powerful of them, the quasars, easily outshine their host galaxies. With luminosities exceeding 1012L ☉, many are bright enough to be seen most of the way across the observable Universe. But the emitting region may be no bigger than the solar system; its power source is probably the energy released by gas falling into a central black hole. Very luminous active nuclei, such as the quasars, were far more common when the Universe was 20%–40% of its present age than they are today; nuclear activity seems to be characteristic of a galaxy's early life.

In many bright quasars, narrow twin jets are seen to emerge from the nucleus; they are probably launched and kept narrow by strong magnetic fields that build up in the surrounding disk of inflowing matter. In some cases, the jets appear to move outward faster than the speed of light. This is an illusion: the motion is slower than, but close to, light speed.

About half the galaxies in the Universe are found in groups and clusters, complexes where typically half the member galaxies are packed into a region ≲1 Mpc across. Groups and clusters no longer expand with the cosmic flow: mutual gravitational attraction is strong enough that the galaxies are moving inward, or have already passed through the core. Clusters are the denser and richer structures. Within the central megaparsec, they typically contain at least 50 luminous galaxies: those with L ≳ L * ~ 2 × 1010L ☉. Poorer associations are called groups; they are generally less massive than ~ 1014M ☉.

Galaxies and clusters are not simply concentrations of galaxies: the fact that a galaxy is a member significantly affects its development. The most common inhabitants of groups are spiral and irregular galaxies. The Local Group is typical; its three bright members are all spirals. Almost all the large galaxies of the Ursa Major group, featured in Figures 5.6, 5.8, and 5.23, are disk systems; there are no more than two ellipticals among the brightest 79 galaxies. Elliptical and S0 galaxies predominate in dense clusters. Curiously, both the most luminous giant ellipticals and the dwarfs with L ≲ 3 × 109L ☉ are concentrated more strongly into clusters than the midsized ellipticals.

By contrast with groups, which we discuss in Section 7.1, we will see in Section 7.2 that most of the baryonic (‘normal’) matter in galaxy clusters is not in the galaxies themselves.