David Hartley

“ IV. It is impossible any person should be so sceptical, as not to have the complex ideas denoted by assent and dissent associated with a great variety of propositions, in the same manner, as in other persons; just as he must have the same ideas in general affixed to the words of his native language, as other men have. A pretended sceptic is therefore no more than a person who varies from the common usage in his application of a certain set of words, viz. truth, certainty, assent, dissent, &c. ”

“ It is of the highest use to us in practical matters, that the properties of bodies are so closely connected with each other. Thus the colour and specific gravity of a metal, the visible idea of a plant, also its taste or smell, give us a practical certainty in respect of all the other properties. This close connexion of the properties follows undoubtedly from the powers and mutual actions of the small parts ”

“ It seems also, that as logic is required for the basis of the other sciences, so a logic of a second order is required for a basis to that of the first, of a third for that of a second, and so on sine limite: which, if it were true, would, from the nature of dependent evidences, prove that logic is either absolutely certain, or absolutely void of all probability. For, if the evidence for it be ever so little inferior to unity, it will, by the continual infinite multiplication required in dependent evidences infinitely continued, bring itself down to nothing. ”

“ For instance, if the evidences be all equal, and the common deficiency in each be , if also the number of evidences be n as before, the deficiency of the resulting probability will be no more than , which is practically nothing, where a and n are considerable. Thus if a and n be each equal to 10, will be , or only one in ten thousand millions; a deficiency from certainty, which is utterly imperceptible to the human mind.
It is indeed evident, without having recourse to the doctrine of chances, that the dependency of evidences makes the resulting probability weak, their independency strong. ”

“ And thus we see the foundation upon which the whole doctrine of quantity is built; for all quantity is expounded either by number or extension, and their common and sole exponent is algebra. The coincidence of ideas is the foundation of the rational assent in simple cases; and that of ideas and terms together, or of terms alone, in complex ones. ”

“ The materials for natural history, which any single person can collect from his own observation, being very inconsiderable, in respect of those which he wants, he is obliged to have recourse to others; and therefore must depend upon their testimony, just as in civil history. And our assent, in each case, being excited by a variety of concurrent proofs, and of coincident circumstances, transfers part of its authority upon the other. ”

“ The evidence for future facts is of the same kind with that for the propositions concerning natural bodies, being like it, taken from induction and analogy. This is the cause of the rational assent. The practical depends upon the recurrency of the ideas, and the degree of agitation produced by them in the mind. Hence reflection makes the practical assent grow for a long time after the rational is arisen to its height; or if the practical arise without the rational, in any considerable degree, which is often the case, it will generate the rational. ”

“ If it be reasonable to suppose many orders of particles, it is also reasonable to suppose, that their powers and properties are somewhat analogous to one another; and that those of the larger particles arise from, and are compounded of, those of the next less in size, and so on; just as the whole gravity of the moon is compounded of the gravity of all its parts. ”

“ Till our knowledge be applied to the predicting or producing future facts, no sort of it is of use or importance to us; and the application of mathematical knowledge is just as much exposed to the several kinds and degrees of uncertainty, as that of any other. That the evidence for principal historical facts is not, in general, considered as equal to mathematical certainty, arises partly from the just mentioned ill-grounded affirmations of learned men ”

“ We may thus also see in a shorter and simpler way that the resulting probability may be sufficiently strong in dependent evidences, and of little value in independent ones, according as the separate probability of each evidence is greater or less. Thus the principal facts of ancient history are not less probable practically now, than ten or fifteen centuries ago, nor less so then, than in the times immediately succeeding; because the diminution of evidence in each century is imperceptible. ”

“ When religion has equally and fully absorbed different persons, so that God is, in respect of them, all in all, as far as the present condition of mortality will permit, their practical assent must be the same; and therefore their rational cannot differ long or widely.
The ideas and internal feelings which arise in the mind, from words and propositions, may be compared to, and illustrated by, those which the appearances of different persons excite. ”

“ And thus it appears, that rational assent has different causes in propositions of different kinds, and practical likewise; that the causes of rational are also different from those of practical; that there is, however, a great affinity, and general resemblance, in all the causes; that rational and practical assent exert a perpetual reciprocal effect upon one another; and consequently, that the ideas belonging to assent and dissent, and their equivalents and relatives, are highly complex ones, unless in the cases of very simple propositions, such as mathematical ones. ”

“ Sixthly, Natural philosophy, or the application of the arts of mathematics and logic to the phænomena of natural and civil history communicated to us by means of our previous skill in philology, in order to decypher the laws by which the external world is governed, and thereby to predict or produce such phænomena, as we are interested in. Its parts are mechanics, hydrostatics, pneumatics, optics, astronomy, chemistry, the theories of the several manual arts and trades, medicine and psychology, or the theory of the human mind, with that of the intellectual principles of brute animals. ”

“ Things that are quite unknown have often fixed relations to one another, and sometimes relations to things known, which, though not determinable with certainty and precision, may yet be determined in some probable manner, or within certain limits. Now as in algebra it is impossible to express the relation of the unknown quantity to other quantities known or unknown, till it has a symbol assigned to it of the same kind with those that denote the others ”

“ The memory of having once examined and assented to each step of a demonstration, the authority of an approved writer, &c. are sufficient to gain our assent, though we understand no more than the import of the proposition; nay, even though we do not proceed so far as this. Now this is mere association again; this memory, authority, &c. being, in innumerable instances, associated with the before-mentioned coincidence of ideas and terms. ”

“ The influence of the practical assent over the rational arises plainly from their being joined together in so many cases. The vividness of the ideas arising from the supposed utility, importance, &c. does also unite the subject and predicate sooner and closer, agreeably to what has been observed in the general account of association.
The evidences for past facts are a man’s own memory, and the authority of others. ”

“ Secondly, If the event be of an interesting nature, as a great advantage accruing, the death of a near friend, the affecting related ideas will recur oftener, and by so recurring agitate the mind more, in proportion to the supposed truth of the event. And it confirms this, that the frequent recurrency of an interesting event, supposed doubtful, or even fictitious, does, by degrees, make it appear like a real one, as in reveries, reading romances, seeing plays, &c. This affection of mind may be called the practical assent to past facts ”

“ However, it may not be amiss to observe, that all the operations of arithmetic, geometry, and algebra, should be applied to each other in every possible way, so as to find out in each something analogous to what is already known and established in the other two. The application of the arithmetical operations of division and extraction of roots to algebraic quantities, and of the method of obtaining the roots of numeral equations by approximation to specious ones, as taught by Sir Isaac Newton, have been the sources of the greatest fluxional discoveries. ”

“ And it will be of great use to pursue these and such like deductions, both mathematically, and by applying them to proper instances selected from the sciences, and from common life, in order to remove certain prejudices, which the use of general terms, and ways of speaking, with the various associations adhering to them, is apt to introduce and fix upon the mind. It cannot but assist us in the art of reasoning, thus to take to pieces, recompose, and ascertain our evidences. ”

“ For the small parts of matter, with their actions, are too minute to be the objects of sight; and we are as yet neither possessed of a detail of the phænomena sufficiently copious and regular, whereon to ground an investigation; nor of a method of investigation, subtle enough to arrive at the subtlety of nature even in the biggest component particles, much less in the particles of the smaller orders ”

“ In dead languages the difficulty is greater; but the certainty that ultimately results, is not less practically in respect of the bulk of the language, on account of the number of coincidences. But much remains undone yet, particularly in respect of the Hebrew language. Logic, natural and civil history, philosophical and religious knowledge, may all, in their several ways, contribute to fix the true sense of words. ”

“ The great differences of opinion, and contentions which happen in religious matters, are plainly owing to the violence of men’s passions, more than to any other cause. Where religion has its due effect in restraining these, and begetting true candour, we may expect an unity of opinion, both in religious and other matters, as far as is necessary for useful practical purposes. ”

“ Thus the sanguine are apt to believe and assert what they hope, and the timorous what they fear.
There are many speculative abstracted propositions in logic, metaphysics, ethics, controversial divinity, &c. the evidence for which is the coincidence or analogy of the abstract terms, in certain particular applications of them, or as considered in their grammatical relations. This causes the rational assent. As to the practical assent or dissent, it arises from the ideas of importance, reverence, piety, duty, ambition, jealousy, envy, self-interest, &c. ”

“ Lastly, The frequent making of hypotheses, and arguing from them synthetically, according to the several variations and combinations of which they are capable, would suggest numerous phænomena, that otherwise escape notice, and lead to experimenta crucis, not only in respect of the hypothesis under consideration, but of many others. The variations and combinations just mentioned suggest things to the invention, which the imagination unassisted is far unequal to; just as it would be impossible for a man to write down all the changes upon eight bells, unless he had some method to direct him. ”

“ The analogy between the word and works of God, which is a consideration of the religious kind, seems to comprehend the most important truths. To all this it must be added, that the temper of mind prescribed by religion, viz. modesty, impartiality, sobriety, and diligence, are the best qualifications for succeeding in all inquiries. Thus religion comprehends, as it were, all other knowledge, advances, and is advanced by all ”

“ Natural history is the only sure basis of natural philosophy, and has some influence upon all the other sciences.
Of Civil History. The general evidences upon which civil history is grounded, have been just hinted at. It is manifest, that the discoveries of natural historians, astronomers, linguists, antiquaries, and philosophers of all kinds, have brought great light and evidence upon this branch of knowledge within the last two centuries; and are likely to do so more and more. ”

“ When there are various arguments for the same thing taken from induction or analogy, they may all be considered as supporting one another in the same manner as independent evidences. Thus, if it could be shewed, that the human understanding is entirely dependent on association, (as is remarked in this and the last section,) the many analogies and connexions between the understanding and affections, as these terms are commonly understood and contradistinguished by writers, would make it very probable, that association presides in the same manner in the generation of the affections ”

“ It appears also not impossible, that future generations should put all kinds of evidences and inquiries into mathematical forms; and, as it were, reduce Aristotle’s ten Categories, and Bishop Wilkins’s forty Summa Genera, to the head of quantity alone, so as to make mathematics and logic, natural history and civil history, natural philosophy and philosophy of all other kinds, coincide omni ex parte. ”

“ If the second animal be of the same species, also of the same age, sex, &c. with the first, the induction becomes perpetually of a higher and a higher order, approaching more and more to the coincidence, which obtains in mathematical evidences, and yet never being able entirely to arrive at it. But then the difference, being only an infinitesimal fraction, as it were, becomes nothing to all practical purposes whatsoever. And if a man considers farther, that it would be hard to find a demonstration, that he does not mistake the plainest truths ”

“ First, then, as in many mechanical problems, which fall strictly under the consideration of mathematicians, the quantities considered depend on several others, so as to increase in the simple or compound, direct or inverse, ratio of several others, and not to be greatest or least, when one or two of these are so, but when the factum of the proper powers of all is so; so throughout natural philosophy, in physic, in the analysis of the mind, &c., it is necessary to inquire, as carefully as we can, upon how many considerable causes each effect depends ”