text: Observations on Man (6th edition)/Part I/Chapter III/Section IV


text: Observations on Man (6th edition)/Part I/Chapter III/Section V

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text: Observations on Man (6th edition)/Part I/Chapter III/Section VI


text: Observations on Man (6th edition)/Part I/Chapter III/Section VII


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appears, from the whole tenor of the last Section, that assent and dissent, whatever their precise and particular nature may be, must come under the notion of ideas, being only those very complex internal feelings, which adhere by association to such clusters of words as are called propositions in general, or affirmations and negations in particular. The same thing is remarked in the 10th corollary to the 12th proposition.

But in order to penetrate farther into this difficult and important point, I will distinguish assent (and by consequence its opposite, dissent) into two kinds, rational and practical; and define each of these.

Rational assent then to any proposition, may be defined, a readiness to affirm it to be true, proceeding from a close association of the ideas suggested by the proposition, with the idea, or internal feeling, belonging to the word truth; or of the terms of the proposition with the word truth. Rational dissent is the opposite to this. This assent might be called verbal; but as every person supposes himself always to have sufficient reason for such readiness to affirm or deny, I rather choose to call it rational.

Practical assent is a readiness to act in such manner as the frequent vivid recurrency of the rational assent disposes us to act; and practical dissent the contrary.

Practical assent is therefore the natural and necessary consequence of rational, when sufficiently impressed. There are, however, two cautions to be subjoined here, viz. first, that some propositions, mathematical ones for instance, admit only of a rational assent, the practical not being applied to them in common cases. Secondly, that the practical assent is sometimes generated, and arrives at a high degree of strength, without any previous rational assent, and by methods that have little or no connexion with it. Yet still it is in general much influenced by it, and, conversely, exerts a great influence upon it. All this will appear more clearly when we come to the instances.

Let us next inquire into the causes of rational and practical assent, beginning with that given to mathematical conclusions.

Now the cause that a person affirms the truth of the proposition twice two is four, is the entire coincidence of the visible or tangible idea of twice two with that of four, as impressed upon the mind by various objects. We see every where, that twice

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 two and four are only different names for the same impression. And it is mere association which appropriates the word truth, its definition, or its internal feeling, to this coincidence.

Where the numbers are so large, that we are not able to form any distinct visible ideas of them, as when we say that 12 times 12 is equal to 144; a coincidence of the words arising from some method of reckoning up 12 times 12, so as to conclude with 144, and resembling the coincidence of words which attends the just-mentioned coincidence of ideas in the simpler numerical propositions, is the foundation of our rational assent. For we often do, and might always, verify the simplest numerical propositions, by reckoning up the numbers. The operations of addition, subtraction, multiplication, division, and extraction of roots, with all the most complex ones relating to algebraic quantities, considered as the exponents of numbers, are no more than methods of producing this coincidence of words, founded upon and rising above one another. And it is mere association again, which appropriates the word truth to the coincidence of the words, or symbols, that denote the numbers.

It is to be remarked, however, that this coincidence of words is by those who look deeper into things, supposed to be a certain argument, that the visible ideas of the numbers under consideration, as of 12 times 12, and 144, would coincide as much as the visible ideas of twice two and four, were they as clear and distinct. And thus the real and absolute truth is said by such persons to be as great in complex numerical propositions, as in the simplest. All this agrees with what Mr. Locke has observed concerning numbers, viz. that their names are necessary in order to our obtaining distinct ideas of them; for by distinct ideas he must be understood to mean proper methods of distinguishing them from one another, so as to reason justly upon them. He cannot mean distinct visible ideas.

In geometry there is a like coincidence of lines, angles, spaces, and solid contents, in order to prove them equal in simple cases. Afterwards in complex cases, we substitute the terms whereby equal things are denoted for each other, also the coincidence of the terms, for that of the visible ideas, except in the new step advanced in the proposition; and thus get a new equality, denoted by a new coincidence of terms. This resembles the addition of unity to any number, in order to make the next, as of 1 to 20, in order to make 21. We have no distinct visible idea, either of 20 or 21; but we have of the difference between them, by fancying to ourselves a confused heap of things supposed or called 20 in number; and then farther fancying 1 to be added to it. By a like process in geometry we arrive at the demonstration of the most complex propositions.

The properties of numbers are applied to geometry in many cases, as when we demonstrate a line or space to be half or double of any other, or in any other rational proportion to it.

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 And as in arithmetic words stand for indistinct ideas, in order to help us to reason upon them as accurately as if they were distinct; also cyphers for words, and letters for cyphers, both for the same purpose; so letters are put for geometrical quantities also, and the agreements of the first for those of the last. 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. This is upon supposition that the quantities under consideration are to be proved equal. But if they are to be proved unequal, the want of coincidence answers the same purpose. If they are in any numeral ratio, this is only the introduction of a new coincidence. Thus, if, instead of proving A to be equal to B, we are to prove it equal to half B, the two parts of B must coincide with each other, either in idea or terms, and A with one.

And thus it appears, that the use of words is necessary for geometrical and algebraical reasonings, as well as for arithmetical.

We may see also that association prevails in every part of the processes hitherto described.

But these are not the only causes of giving rational assent to mathematical propositions, as this is defined above. 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.

But here a new circumstance arises. For memory and authority are sometimes found to mislead; and this opposite coincidence of terms puts the mind into a state of doubt, so that sometimes truth may recur, and unite itself with the proposition under consideration, sometimes falsehood, according as the memory, authority, &c. in all their peculiar circumstances, have been associated with truth or falsehood. However, the foundation of assent is still the same. I here describe the fact only. And yet, since this fact must always follow from the fixed immutable laws of our frame, the obligation to assent (whatever be meant by this phrase) must coincide with the fact.

And thus a mathematical proposition, with the rational assent or dissent arising in the mind, as soon as it is presented to it, is nothing more than a group of ideas, united by association, i.e. than a very complex idea, as was affirmed above of propositions in general. And this idea is not merely the sum of the ideas belonging to the terms of the proposition, but also includes the ideas, or internal feelings, whatever they be, which belong to

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 equality, coincidence, truth, and in some cases, those of utility, importance, &c.

For mathematical propositions are, in some cases, attended with a practical assent, in the proper sense of these words; as when a person takes this or that method of executing a projected design, in consequence of some mathematical proposition assented to from his own examination, or on the authority of others. Now, that which produces the train of voluntary actions, here denoting the practical assent, is the frequent recurrency of ideas of utility and importance. These operate according to the method laid down in the 20th proposition, i.e. by association; and though the rational assent be a previous requisite, yet the degree of the practical assent is proportional to the vividness of these ideas; and in most cases they strengthen the rational assent by a reflex operation.

Propositions concerning natural bodies are of two kinds, vulgar and scientifical. Of the first kind are, that milk is white, gold yellow, that a dog barks, &c. These are evidently nothing but forming the present complex idea belonging to material objects into a proposition, or adding some of its common associates, so as to make it more complex. There is scarce room for dissent in such propositions, they being all taken from common appearances. Or, if any doubt should arise, the matter must be considered scientifically. The assent given to these propositions arises from the associations of the terms, as well as of the ideas denoted by them.

In scientifical propositions concerning natural bodies, a definition is made, as of gold from its properties, suppose its colour, and specific gravity, and another property or power joined to them, as a constant or common associate. Thus gold is said to be ductile, fixed, or soluble in aqua regia. Now to persons who have made the proper experiments a sufficient number of times, these words suggest the ideas which occur in those experiments, and, conversely, are suggested by them, in the same manner as the vulgar propositions above-mentioned suggest and are suggested by common appearances. But then, if they be scientifical persons, their readiness to affirm that gold is soluble in aqua regia universally, arises also from the experiments of others, and from their own and others’ observations on the constancy and tenor of nature. They know, that the colour, and specific gravity, or almost any two or three remarkable qualities of any natural body, infer the rest, being never found without them. This is a general truth; and as these general terms are observed to coincide, in fact, in a great variety of instances, so they coincide at once in the imagination, when applied to gold, or any other natural body, in particular. The coincidence of general terms is also observed to infer that of the particular cases in many instances, besides those of natural bodies; and this unites the subject and predicate of the proposition, gold is

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 soluble in aqua regia, farther in those who penetrate still deeper into abstract speculations. And hence we may see, as before, First, That terms or words are absolutely necessary to the art of reasoning: Secondly, That our assent is here also, in every step of the process, deducible from association.

The propositions formed concerning natural bodies are often attended with a high degree of practical assent, arising chiefly from some supposed utility and importance, and which is no ways proportionable to the foregoing, or other such like allowed causes of rational assent. And in some cases the practical assent takes place before the rational. But then, after some time the rational assent is generated and cemented most firmly by the prevalence of the practical. This process is particularly observable in the regards paid to medicines, i.e. in the rational and practical assent to the propositions concerning their virtues.

It is to be observed, that children, novices, unlearned persons, &c. give, in many cases, a practical assent upon a single instance; and that this arises from the first and simplest of the associations here considered. 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. These are the usual associates of true past facts, under proper restrictions, and therefore beget the readiness to affirm a past fact to be true, i.e. the rational assent. The integrity and knowledge of the witnesses, being the principal restriction, or requisite, in the accounts of past facts, become principal associates to the assent to them; and the contrary qualities to dissent.

If it be asked, how a narration of an event supposed to be certainly true, supposed doubtful, or supposed entirely fictitious, differs in its effect upon the mind, in the three circumstances here alleged, the words being the same in each, I answer, first, in having the terms true, doubtful, and fictitious, with a variety of usual associates to these, and the corresponding internal feelings of respect, anxiety, dislike, &c. connected with them respectively; whence the whole effects, exerted by each upon the mind, will differ considerably from one another. 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;

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 and it frequently draws after it the rational, as in the other instances above alleged.

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. 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. which intermix themselves in these subjects, and, by doing so, in some cases add great strength to the rational assent; in others destroy it, and convert it into its opposite.

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. For besides the coincidence of ideas and terms, they include, in other cases, ideas of utility, importance, respect, disrespect, ridicule, religious affections, hope, fear, &c. and bear some gross general proportion to the vividness of these ideas.

. I. When a person says, video meliora proboque, deteriora sequor; it shews that the rational and practical assent are at variance, that they have opposite causes, and that neither of these has yet destroyed the other.

. II. The rational and practical faith in religious matters are excellent means of begetting each other.

. III. Vicious men, i.e. all persons who want practical faith, must be prejudiced against the historical and other rational evidences in favour of revealed religion.

. 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

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 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.

. V. As there is a foundation for unity amongst mankind in the use and application of words, so there is for an unity in the assent, or complex ideas belonging to propositions; and a philosophical language, or any other method of bringing about the first unity, would much conduce to this. A careful examination of things, of the world natural, the human mind, the Scriptures, would conduce much also. But candour, simplicity, and an humble sense of our own ignorance, which may be called a religious or christian scepticism, is the principal requisite, and that without which this part of the confusion at Babel can never be remedied. 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. Suppose two persons, A and B, to go together into a crowd, and there each of them to see a variety of persons whom he knew in different degrees, as well as many utter strangers. A would not have the same ideas and associations raised in him from viewing the several faces, dresses, &c. of the persons in the crowd, as B, partly from his having a different knowledge of, and acquaintance with them, partly from different predispositions to approve and disapprove. But let A and B become equally acquainted with them, and acquire, by education and association, the same predispositions of mind, and then they will at last make the same judgment of each of the persons whom they see.

. VI. Religious controversies concerning abstract propositions arise generally from the different degrees of respect paid to terms and phrases, which conduce little or nothing to the generation of practical faith, or of love to God, and trust in Him through Christ.

is done in the doctrine of chances, with respect to the events there considered. And though we seldom have such precise data, in mixed sciences, as are there assumed, yet there are two remarks, of very general use and application, deducible from the doctrine of chances.

Thus, first, If the evidences brought for any proposition,

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 fact, &c. be dependent on each other, so that the first is required to support the second, the second to support the third, &c. i.e. if a failure of any one of the evidences renders all the rest of no value, the separate probability of each evidence must be very great, in order to make the proposition credible; and this holds so much the more, as the dependent evidences are more numerous. For instance, if the value of each evidence be $$\tfrac{1}{a}$$, and the number of evidences be in n, then will the resulting probability be $$\tfrac{1}{a^n}$$. I here suppose absolute certainty to be denoted by 1; and consequently, that a can never be less than 1. Now it is evident, that $$\tfrac{1}{a^n}$$ decreases with every increase both of a and n.

Secondly, If the evidences brought for any proposition, fact, &c. be independent on each other, i.e. if they be not necessary to support each other, but concur, and can, each of them, when established upon its own proper evidences, be applied directly to establish the proposition, fact, &c. in question, the deficiency in the probability of each must be very great, in order to render the proposition perceptibly doubtful; and this holds so much the more, as the evidences are more numerous. For instance, if the evidences be all equal, and the common deficiency in each be $$\tfrac{1}{a}$$, if also the number of evidences be n as before, the deficiency of the resulting probability will be no more than $$\tfrac{1}{a^n}$$, which is practically nothing, where a and n are considerable. Thus if a and n be each equal to 10, $$\tfrac{1}{a^n}$$ will be $$\tfrac{1}{10,000,000,000}$$, 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. Thus a report passing from one original author through a variety of successive hands loses much of its credibility, and one attested by a variety of original witnesses gains, in both cases, according to the number of successive reporters, and original witnesses, though by no means proportionably thereto. This is the common judgment of mankind, verified by observation and experience. But the mathematical method of considering these things is much more precise and satisfactory, and differs from the common one, just as the judgment made of the degrees of heat by the thermometer does from that made by the hand.

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

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text: Author:Christopher Brooke

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 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. For, if $$\tfrac{1}{a}$$ be equal to 1, $$\tfrac{1}{a^n}$$ will be equal to 1 also; and if the deficiency of $$\tfrac{1}{a}$$ from 1 be extremely small, that of $$\tfrac{1}{a^n}$$ will be extremely small also, unless n be extremely great. And for the same reason a large number of weak arguments proves little; for $$\tfrac{1}{a}$$ the deficiency of each argument, being extremely great, $$\tfrac{1}{a}$$, the resulting deficiency of independent evidences, will be extremely great also.

It appears likewise, that the inequality of the separate evidences does not much affect this reasoning. In like manner, if the number of evidences, dependent or independent, be great, we may make great concessions as to the separate values of each. Again, a strong evidence in dependent ones can add nothing, but must weaken a little; and, after a point is well settled by a number of independent ones, all that come afterwards are useless, because they can do no more than remove the imperceptible remaining deficiency, &c. 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.

If it be asked, upon what authority absolute certainty is represented by unity, and the several degrees of probability by fractions less than unity, in the doctrine of chances? also, upon what authority the reasoning used in that doctrine is transferred to other subjects, and made general, as here proposed? I answer, that no person who weighs these matters carefully, can avoid giving his assent; and that this precludes all objections. No sceptic would, in fact, be so absurd as to lay two to one, where the doctrine of chances determines the probability to be equal on each side; and therefore we may be sure, that he gives a practical assent at least to the doctrine of chances.

M. De Moivre has shewn, that where the causes of the happening of an event bear a fixed ratio to those of its failure, the happenings must bear nearly the same ratio to the failures, if the number of trials be sufficient; and that the last ratio approaches to the first indefinitely, as the number of trials increases. This

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 may be considered as an elegant method of accounting for that order and proportion, which we every where see in the phænomena of nature. The determinate shapes, sizes, and mutual actions of the constituent particles of matter, fix the ratios between the causes for the happenings, and the failures; and therefore it is highly probable, and even necessary, as one may say, that the happenings and failures should perpetually recur in the same ratio to each other nearly, while the circumstances are the same. When the circumstances are altered, then new causes take place; and consequently there must be a new, but fixed ratio, between the happenings and the failures. Let the first circumstances be called A, the new ones B. If now the supposition be made so general, as equally to take in both A and B, the ratio of the happenings and failures will not be such as either A or B required. But still it will tend to a preciseness, just as they did, since the sum of the causes of the happenings must bear a fixed ratio to the sum of the causes of the failures.

An ingenious friend has communicated to me a solution of the inverse problem, in which he has shewn what the expectation is, when an event has happened p times, and failed q times, that the original ratio of the causes for the happening or failing of an event should deviate in any given degree from that of p to q. And it appears from this solution, that where the number of trials is very great, the deviation must be inconsiderable; which shews that we may hope to determine the proportions, and, by degrees, the whole nature, of unknown causes, by a sufficient observation of their effects.

The inferences here drawn from these two problems are evident to attentive persons, in a gross general way, from common methods of reasoning.

Let us, in the next place, consider the Newtonian differential method, and compare it with that of arguing from experiments and observations, by induction and analogy. This differential method teaches, having a certain number of the ordinates of any unknown curve given with the points of the absciss on which they stand, to find out such a general law for this curve, i.e. such an equation expressing the relation of an ordinate and absciss in all magnitudes of the absciss, as will suit the ordinates and points of the absciss given, in the unknown curve under consideration. Now here we may suppose the given ordinates standing upon given points to be analogous to effects, or the results of various experiments in given circumstances, the absciss analogous to all possible circumstances, and the equation afforded by the differential method to that law of action, which, being supposed to take place in the given circumstances, produces the given effects. And as the use of the differential method is to find the lengths of ordinates not given, standing upon points of the absciss that are given, by means of the equation, so the use of attempts to make general conclusions by induction and

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 analogy, from particular effects or phænomena, in different given circumstances, by applying the general law conclusion to these circumstances.

This parallel is the more pertinent and instructive, inasmuch as the mathematical conclusion drawn by the differential method, though formed in a way that is strictly just, and so as to have the greatest possible probability in its favour, is, however, liable to the same uncertainties, both in kind and degree, as the general maxims of natural philosophy drawn from natural history, experiments, &c.

If many ordinates be given; if the distances of the points of the absciss, on which they stand, be equal and small; if the ordinate required lie amongst them, or near them; and if there be reason to think, that the curve itself is formed according to some simple, though unknown law; then may we conclude, that the new ordinate, determined by the equation, does not vary far from the truth. And if the resulting equation be simple, and always the same, from whatever given ordinates it be extracted, there is the greatest reason to think this to be the real original law or equation of the curve; and consequently that all its points and properties may be determined with perfect exactness by means of it: whereas, if the given ordinates be few, their distances great or unequal, the ordinate required considerably distant from many or most of them, the unknown curve be a line drawn at hazard, and the resulting equation different, where different ordinates are given, though their number be the same, there will be little probability of determining the new ordinate with exactness; however, still the differential method affords us the greatest probability which the data permit in such cases.

In like manner, if the experiments or observations be many, their circumstances nearly related to each other, and in a regular series, the circumstances of the effect to be investigated nearly related to them; also, if the real cause may be supposed to produce these effects, by the varieties of some simple law, the method of induction and analogy will carry great probability with it. And if the general conclusion or law be simple, and always the same, from whatever phænomena it be deduced, such as the three laws of nature, the doctrines of gravitation, and of the different refrangibility of light; or to go still higher, by taking a mathematical instance, the law for finding the coefficients of the integral powers of a binomial, deduced from mere trials in various powers; there can scarce remain any doubt, but that we are in possession of the true law inquired after, so as to be able to predict with certainty, in all cases where we are masters of the method of computation, or applying it; and have no reason to suspect, that other unknown laws interfere. But, if the given phænomena be few, their circumstances very different from each other, and from those of the effect to be predicted; if there be reason to suppose, that many causes concur in the producing

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 these phænomena, so that the law of their production must be very complex; if a new hypothesis be required to account for every new combination of these phænomena; or, at least, one that differs considerably from itself; the best hypothesis which we can form, i.e. the hypothesis which is most conformable to all the phænomena, will amount to no more than an uncertain conjecture; and yet still it ought to be preferred to all others, as being the best that we can form.

That instantaneous and necessary coalescence of ideas, which makes intuitive evidence, may be considered as the highest kind of induction, and as amounting to a perfect coincidence of the effect concluded with those from which it is concluded. This takes place only in mathematics. Thus we infer, that 2 and 2 make 4, only from prior instances of having actually perceived this, and from the necessary coincidence of all these instances with all other possible ones of 2 and 2. Mathematical demonstrations are made up of a number of these, as was observed above.

Where the instances from whence the induction is made are alike, as far as we know, to that under consideration, at least in all things that affect the present inquiry, it affords the highest probability, and may be termed induction, in the proper sense of the word. Thus we infer, that the bread before us is nutritive and wholesome, because its smell, taste, ingredients, manner of composition, &c. are the same as those of other bread, which has often before been experienced to be so.

But, if the instance under consideration be in some respects like the foregoing ones, in others not, this kind of proof is generally termed one taken from analogy. Thus, if we argue from the use and action of the stomach in one animal to those in another, supposed to be unknown, there will be a probable hazard of being mistaken, proportional in general to the known difference of the two animals, as well as a probable evidence for the truth of part, at least, of what is advanced, proportional to the general resemblance of the two animals. But if, upon examination, the stomach, way of feeding, &c. of the second animal should be found, to sense, the same as in the first, the analogy might be considered as an induction properly so called, at least as approaching to it; for precise limits cannot be fixed here. 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; this lessens the difference theoretically also.

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 It is often in our power to obtain an analogy where we cannot have an induction; in which case reasoning from analogy ought to be admitted; however, with all that uncertainty which properly belongs to it, considered as more or less distant from induction, as built upon more or fewer dependent or independent evidences, &c. Analogy may also, in all cases, be made use of as a guide to the invention. But coincidence in mathematical matters, and induction in others, wherever they can be had, must be sought for as the only certain tests of truth. However, induction seems to be a very sufficient evidence in some mathematical points, affording at least as much evidence there as in natural philosophy; and may be safely relied on in perplexed cases, such as complex series, till satisfactory demonstrations can be had.

The analogous natures of all the things about us are a great assistance in decyphering their properties, powers, laws, &c. inasmuch as what is minute or obscure in one may be explained and illustrated by the analogous particular in another, where it is large and clear. And thus all things become comments on each other in an endless reciprocation.

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; and vice versâ. And the more analogies, and mutual connexions, between the understanding and affections, were produced, so many more independent or concurrent evidences would there be for this prevalence of association in one, admitting it in the other. But, if now it be shewn farther, that the understanding and affections are not really distinct things, but only different names, which we give to the same kind of motions in the nervous system, on account of a difference in degree, and other differences which it would be tedious here to enumerate, but which make no difference in respect of the power of association, then all the arguments from analogy are transformed into one of induction; which, however, is stronger than the united force of them all. For now it may be shewed, that association must prevail in each motion in the brain, by which affection is expounded, from a large induction of particulars, in which it prevails in the generation of ideas, or of the motions by which they are expounded, and which we suppose to be proved to be of the same kind with those that expound the affections. Thus also inductions may be taken from the smell and taste of bread, to prove it wholesome; which would both be transformed into one simple argument stronger

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 than both, could we see the internal constitution of the small parts of the bread, from whence its smell, and taste, and wholesomeness, are all derived. Thus, again, all the arguments of induction for the manner of extracting the square root in numbers vanish into the single demonstrative proof, as soon as this is produced. And the great business in all branches of knowledge is thus to reduce, unite, and simplify our evidences; so as that the one resulting proof, by being of a higher order, shall be more than equal in force to all the concurrent ones of the inferior orders.

Having now considered in what manner the doctrine of chances, and the Newtonian differential method, may serve to shew in general the value of dependent and independent or concurrent evidences, and the probability of general conclusions formed by induction and analogy; let us next inquire by what means we are to form these general conclusions, and discover their evidences. Now the different methods of doing this may be said to resemble respectively the rule of false in common arithmetic; the algebraic methods of bringing the unknown quantity into an equation, under a form capable of all the algebraic operations, addition, subtraction, &c.; the algebraic methods of finding the roots of equations of the higher orders by approximation; and the art of decyphering: all which four methods bear also a considerable resemblance to each other. I will consider them in order, and endeavour to shew how analogous methods may be introduced into the sciences in general to advantage.

First, then, As according to the rule of false, the arithmetician supposes a certain number to be that which is sought for; treats it as if it was that; and finding the deficiency or overplus in the conclusion, rectifies the error of his first position by a proportional addition or subtraction, and thus solves the problem; so it is useful in inquiries of all kinds to try all such suppositions as occur with any appearance of probability, to endeavour to deduce the real phænomena from them; and if they do not answer in some tolerable measure, to reject them at once; or if they do, to add, expunge, correct, and improve, till we have brought the hypothesis as near as we can to an agreement with nature. After this it must be left to be farther corrected and improved, or entirely disproved, by the light and evidence reflected upon it from the contiguous, and even, in some measure, from the remote branches of other sciences.

Were this method commonly used, we might soon expect a great advancement in the sciences. It would much abate that unreasonable fondness, which those who make few or no distinct hypotheses, have for such confused ones as occur accidentally to their imaginations, and recur afterwards by association. For the ideas, words, and reasonings, belonging to the favourite hypothesis, by recurring, and being much agitated in the brain, heat

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 it, unite with each other, and so coalesce in the same manner, as genuine truths do from induction and analogy. Verbal and grammatical analogies and coincidences are advanced into real ones; and the words which pass often over the ear, in the form of subject and predicate, are from the influence of other associations made to adhere together insensibly, like subjects and predicates, that have a natural connexion. It is in vain to bid an inquirer form no hypothesis. Every phænomenon will suggest something of this kind: and, if he do not take care to state such as occur fully and fairly, and adjust them one to another, he may entertain a confused inconsistent mixture of all, of fictitious and real, possible and impossible: and become so persuaded of it, as that counter-associations shall not be able to break the unnatural bond. But he that forms hypotheses from the first, and tries them by the facts, soon rejects the most unlikely ones; and, being freed from these, is better qualified for the examination of those that are probable. He will also confute his own positions so often, as to fluctuate in equilibrio, in respect of prejudices, and so be at perfect liberty to follow the strongest evidences.

In like manner, the frequent attempts to make an hypothesis that shall suit the phænomena, must improve a man in the method of doing this; and beget in him by degrees an imperfect practical art, just as algebraists and decypherers, that are much versed in practice, are possessed of innumerable subordinate artifices, besides the principal general ones, that are taught by the established rules of their arts; and these, though of the greatest use to themselves, can scarce be explained or communicated to others. These artifices may properly be referred to the head of factitious sagacity, being the result of experience, and of impressions often repeated, with small variations from the general resemblance.

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.

But this method of making definite hypotheses, and trying them, is far too laborious and mortifying for us to hope that inquirers will in general pursue it. It would be of great use to such as intend to pursue it, to make hypotheses for the phænomena, whose theories are well ascertained; such as those of the circulation of the blood, of the pressure of the air, of the different refrangibility of the rays of light, &c. and see how they

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 are gradually compelled into the right road, even from wrong suppositions fairly compared with the phænomena. This would habituate the mind to a right method, and beget the factitious sagacity above-mentioned.

The second of the four methods proposed is, that of bringing the unknown quantity to an equation, and putting it into a form susceptible of all the algebraic operations. Now to this answers, in philosophy, the art of giving names, expressing nothing definite, as to manner, quantity, &c. and then inserting these names, or indefinite terms, in all the enunciations of the phænomena, to see whether, from a comparison of these enunciations with each other, where the terms are used in the greatest latitude, some restrictions, something definite in manner, degree, or mutual relation, will not result. 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; so in philosophy we must give names to unknown quantities, qualities, causes, &c. not in order to rest in them, as the Aristotelians did, but to have a fixed expression, under which to treasure up all that can be known of the unknown cause, &c. in the imagination and memory, or in writing for future inquirers.

But then it is necessary, for the same reasons, that these terms should have no more of secondary ideas from prior associations, than the terms x and y in algebra.—Whence, if we use old terms excluding the old associations, the reader should be made aware of this at first, and incidentally reminded of it afterwards. Sir Isaac Newton has used the words æther, attraction, and some others, in this way, not resting in them, but enumerating a great variety of phænomena; from the due comparison of which with each other, and with such as farther observation and experiments shall suggest, their laws and action will, perhaps, be discovered hereafter; so that we may be able to predict the phænomena. There is also an instance of the proper manner of reasoning concerning the knowable relations of unknown things in Mr. Mede’s Clavis Apocalyptica.

The third method is that of approximating to the roots of equations. Here a first position is obtained, which, though not accurate, approaches, however, to the truth. From this, applied to the equations, a second position is deduced, which approaches nearer to the truth than the first; from the second, a third, &c. till the analyst obtains the true root, or such an approximation as is practically equivalent, every preceding discovery being made the foundation for a subsequent one, and the equation resolving itself, as it were, gradually. Now this is indeed the way, in

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 which all advances in science are carried on; and scientific persons are in general aware, that it is and must be so. However, I thought it not improper to illustrate this general process by a parallel taken from algebra, in which there is great exactness and beauty. Besides, writers do not often dispose their arguments and approximations in this way, though for want of it they lose much of their clearness and force; and, where the writer does this, the reader is frequently apt to overlook the order of proofs and positions.

Sir Isaac Newton’s Optics, Chronology, and Comment on Daniel, abound with instances to this purpose: and it is probable, that his great abilities and practice in algebraic investigations led him to it insensibly. In his Chronology he first shews in gross, that the technical chronology of the ancient Greeks led them to carry their authorities higher than the truth; and then, that the time of the Sesostris mentioned by the Greek historians was near that of Sesac mentioned in the Old Testament; whence it follows, that these two persons were the same; and consequently, that the exact time of Sesostris’s expedition may now be fixed by the Old Testament. And now, having two points absolutely fixed, viz. the expeditions of Sesostris and Xerxes, he fixes all the most remarkable intermediate events; and these being also fixed, he goes on to the less remarkable ones in the Greek history. And the chronology of the Greeks being rectified, he makes use of it to rectify the cotemporary affairs of the Egyptians, Assyrians, Babylonians, Medes, and Persians, making use of the preceding step every where, for the determination of the subsequent one. He does also, in many cases, cast light and evidence back from the subsequent ones upon the precedent. But the other is his own order of proof, and ought to be that in which those who call his chronology in question should proceed to inquire into it.

The fourth and last method is that used by decypherers, in investigating words written in unknown characters, or in known ones substituted for one another, according to secret and complex laws. The particular methods by which this is done are only known to those who study and practise this art: however, it is manifest in general, that it is an algebra of its own kind, and that it bears a great resemblance to the three foregoing methods; also, that it may be said, with justness and propriety in general, that philosophy is the art of decyphering the mysteries of nature; that criticism bears an obvious relation to decyphering; and that every theory which can explain all the phænomena, has all the same evidence in its favour, that it is possible the key of a cypher can have from its explaining that cypher. And if the cause assigned by the theory have also its real existence proved, it may be compared to the explanation of a cypher; which may be verified by the evidence of the person who writes in that cypher.

These speculations may seem uncouth to those who are not

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 conversant in mathematical inquiries; but to me they appear to cast light and evidence upon the methods of pursuing knowledge in other matters, to sharpen the natural sagacity, and to furnish loci for invention. 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.

I will add two more remarks relating to the present subject.

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; also whether the ratios be simple or compound, direct or inverse. For though it will seldom happen, that one can bring the practical problems that occur in real life, to an exact estimate in this way, yet one may avoid part of that uncertainty and confusion, to which persons who take things merely in the gross are liable. Or, in other words, it is better in every thing to have probable or tolerable limits for the data, with a regular method of computation, or even an approximation thereto, than to have only such gross and general conceptions, as result from the more or less frequent recurrency of impressions, even though they be somewhat improved by natural or acquired sagacity, arising, in a kind of implicit indefinite way, from experience.

Secondly, it seems to me, that the rays of light may be considered as a kind of fluxions in respect of the biggest component particles of matter; I mean those upon which Sir Isaac Newton supposes the colours of natural bodies, and the changes effected in chemical processes, to depend. For, as the increments of variable quantities, when diminished so as to bear no finite ratio to the quantities of which they are the increments, shew, in a simple way, the velocities with which these quantities are increased; and so give rise to the determination of fluxions from fluents, and fluents from fluxions, and to all the applications of these determinations to real quantities, all which is entirely grounded upon the supposition, that the fluxions are not increments, but relative nothings; so, since the rays of light are so small in respect of the biggest component particles, as to be relatively and practically nothing in respect of them, to bear no relation to any of them, all the differences observable in the actions of light upon these particles, and of these particles upon

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 light, will depend purely upon the differences of these particles in respect of one another; it not being possible that any part of them should arise from the comparative magnitude of light, which is equally nothing in respect of them all. And thus it seems, that optics and chemistry will, at last, become a master-key for unlocking the mysteries in the constitution of natural bodies, according to the method recommended by Sir Isaac Newton.

Let A, B, C, be three particles, whose magnitude are 3, 2, and 1, respectively. It is evident, that the mutual influences between A and C, B and C, cannot correspond entirely to the ratio which A and B bear to each other, because C bears a different ratio to A from that which it bears to B; and this difference of ratios must have its share in the effects of A and B upon C: whereas had C been a particle of light, it would have been equally nothing in respect both of A and B; and so the mutual influences between A and C, B and C, would entirely correspond to the difference between A and B, and decypher it. Thus the particles of light, by being infinitely smaller than the biggest component ones of natural bodies, may become a kind of communis norma, whereby to measure their active powers.

the sciences, knowledge of all kinds, may be reduced to the seven general heads following, when they are understood in the latitude here expressed.

First, Philology, or the knowledge of words, and their significations. It comprehends under it the arts of grammar and criticism. Rhetoric and poetry may be referred to it.

Secondly, Mathematics, or the doctrine of quantity. It may be divided into three branches; viz. arithmetic, which makes use of numbers as the exponents of quantity; geometry, which uses figures for the same purpose; and algebra, which comprehends both these, and whose symbols are accordingly so general, as to represent the symbols of the two foregoing parts.

Thirdly, Logic, or the art of using words, considered as symbols, for making discoveries in all the branches of knowledge. It presupposes philology to a certain degree; and must evidently, in the view here given of it, receive great illustrations from mathematics, which is the art of making discoveries in the single category of quantity, by means of the simplest kinds of symbols.

Fourthly, Natural history, or regular and well-digested accounts of the phænomena of the natural world. It may be distributed into six parts, i.e. into the natural histories of animals, plants, minerals, the earth considered as a terraqueous globe, the atmosphere, and the heavenly bodies.

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 Fifthly, Civil history, or regular accounts of the transactions of the world politic. To this head must be referred that part of geography which treats of the present manners, customs, laws, religion, &c. of the several nations of the world.

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.

Seventhly, Religion, which might also be called divine philosophy. This requires the application of all the foregoing branches of knowledge to each other in an endless reciprocation, in order to discover the nature of the invisible world, of God, of good and evil spirits, and of the future state, which commences at death, with all the duties that result from these considerations. The arts of ethics, and politics, are to be referred to this head. For, though these arts are supposed to teach individuals, and bodies politic, how to arrive at their summum bonum in the present world, yet, since the rules given for this purpose either are or ought to be the same with those which teach mankind how to secure a happy futurity, it is plain, that these arts are included within the precepts of religion.

All these branches of knowledge are very much involved in each other; so that it is impossible to make any considerable progress in any one, without the assistance of most or all the rest. However, each has also an independent part, which being laid down as a foundation, we may proceed to improve it by the light afforded from the independent parts of the other branches. I will here subjoin a few hints concerning the proper manner of proceeding in each branch.

Of Philology.

The rudiments of the native language are learnt in infancy, by the repeated impressions of the sounds, at the same time that the things signified are presented to the senses, as has been already explained. Words standing for intellectual things, particles, &c., are decyphered by their connexion with other words, by their making parts of sentences, whose whole import is known. Grammatical analogy and derivation do also, in many cases, discover the import of words. And many words may be explained by definitions. Where these several ways concur, the sense is soon learnt, and steadily fixed; where they oppose each other, confusion arises for a time, but the strongest authority prevails at last. Translations and dictionaries explain the words

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 of unknown languages by those of known ones. Afterwards we decypher by the context, deduce the sense from analogy, &c. These last methods reflect authority upon the translations and dictionaries, where they agree with them. In living languages the import of the principal words may be ascertained with ease and certainty; and these being fixed, the rest become determinable and decypherable by proper care and caution, so that no practical errors can remain. 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. And the fixing the senses of words, by all the methods here enumerated, may be called the art of making dictionaries. It receives great assistance from the art of grammar; and is at the same time the main foundation of it. This last art has also the same connexions with the other branches of knowledge; as that of fixing the senses of words. The same may be said of criticism; which may be defined the art of restoring the corrupted passages of authors, and ascertaining their genuine sense, and method of reasoning.

In all these things there seems to be a sufficient foundation for unity of opinion amongst those that are truly learned and candid; at least in all important points. And, in fact, the differences here amongst the literati, are plainly owing, in great measure, to ambition, envy, affectation of singularity and novelty, &c. All these things magnify the ideas and coalescences, which a man calls his own; those of his party, &c. associate ideas of truth, excellence, genius, &c. to them, and opposite ones to all that the supposed adversary delivers.

No sceptic can proceed so far as to disclaim the sense of the words of his native tongue, or of a foreign one, which he understands. The things signified thereby must and will be suggested by, and coalesce with, the sounds; so that he cannot but understand what he hears and reads. And this is all the truth that belongs to philology as such. The truth of the things expressed in words is a consideration belonging to the several other branches of knowledge respectively.

As the plain didactic style is intended merely to inform the understanding, so the rhetorical and poetical styles are intended to excite the passions by the associations which figurative terms and forms of expression, flowing periods, numbers, rhymes, similes, fables, fictions, &c. draw after them.

Painting and music produce a like effect upon the passions, as rhetoric and poetry, and by means that are not very unlike. But I shall have occasion hereafter to say something more concerning all these imaginative arts.

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 Of Mathematics.

Mathematics are that branch of knowledge which is the most independent of any, and the least liable to uncertainty, difference of opinion, and sceptical doubts. However, uncertainties, differences, and doubts, have arisen here; but then they have been chiefly about such parts of mathematics as fall under the consideration of the logician. For, it seems impossible that a man who has qualified himself duly, should doubt about the justness of an arithmetical, algebraical, or fluxional operation, or the conclusiveness of a geometrical demonstration.

The words point, line, surface, infinitely great, infinitely little, are all capable of definitions, at least of being explained by other words. But then these words cannot suggest any visible ideas to the imagination, but what are inconsistent with the very words themselves. However, this inconsistency has no effect upon the reasoning. It is evident, that all that can be meant by the three angles of a triangle being equal to two right ones, or the parabolic area to $$\tfrac{2}{3}$$ of the circumscribing parallelogram, or deduced from these positions, must always hold in future fact; and this, as observed above, is all the truth that any thing can have. In fluxional conclusions it is demonstratively evident, that the quantity under consideration cannot be greater or less by any thing assignable, than according to the fluxional conclusion; and this seems to me entirely the same thing as proving it to be equal.

I cannot presume to suggest any particular methods by which farther discoveries may be made in mathematical matters, which are so far advanced, that few persons are able to comprehend even what is discovered and unfolded already. 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.

Of Logic.

It is the purport of this and the foregoing section, to give imperfect rudiments of such an art of logic, as is defined above, i.e. as should make use of words in the way of mathematical symbols, and proceed by mathematical methods of investigation and computation in inquiries of all sorts. Not that the data in the sciences are as yet, in general, ripe for such methods; but

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 they seem to tend to this more and more perpetually, in particular branches, so that it cannot be amiss to prepare ourselves, in some measure, previously.

Logic, and metaphysics, which are nearly allied to logic, seem more involved in obscurity and perplexity, than any other part of science. This has probably been the chief source of scepticism, since it appears necessary, that that part of knowledge, which is the basis of all others, which is to shew wherein certainty, probability, possibility, improbability, and impossibility, consist, should itself be free from all doubt and uncertainty.

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. Therefore, e converso, since no one can say, that the rules of logic are void of all probability, the summum genus of them must be certain. This summum genus is the necessary coalescence of the subject with the predicate. But the argument here alleged is merely one ad hominem, and not the natural way of treating the subject. The necessary coalescence just spoken of carries its own evidence with it. It is necessary from the nature of the brain, and that in the most confirmed sceptic, as well as in any other person. And we need only inquire into the history of the brain, and the physiological influences of words and symbols upon it by association, in order to see this. I am also inclined to believe, that the method here proposed of considering words and sentences as impressions, whose influence upon the mind is entirely to be determined by the associations heaped upon them in the intercourses of life, and endeavouring to determine these associations, both analytically and synthetically, will cast much light upon logical subjects, and cut off the sources of many doubts and differences.

As the theories of all other arts and sciences must be extracted from them, so logic, which contains the theory of all these theories, must be extracted from these theories; and yet this is not to reason in a circle in either case, since the theory is first extracted from self-evident or allowed particulars, and then applied to particulars not yet known, in order to discover and prove them.

It may not be amiss here to take notice how far the theory of these papers has led me to differ in respect of logic, from Mr. Locke’s excellent Essay on Human Understanding, to which the world are so much indebted for removing prejudices and incumbrances, and advancing real and useful knowledge.

First, then, It appears to me, that all the most complex ideas

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 arise from sensation; and that reflection is not a distinct source, as Mr. Locke makes it.

Secondly, Mr. Locke ascribes ideas to many words, which, as I have defined idea, cannot be said to have any immediate and precise ones; but only to admit of definitions. However, let definition be substituted instead of idea, in these cases, and then all Mr. Locke’s excellent rules concerning words, delivered in his third book, will suit the theory of these papers.

As to the first difference, which I think may be called an error in Mr. Locke, it is, however, of little consequence. We may conceive, that he called such ideas as he could analyse up to sensation, ideas of sensation; the rest ideas of reflection, using reflection, as a term of art, denoting an unknown quantity. Besides which, it may be remarked, that the words which, according to him, stand for ideas of reflection, are in general words, that, according to the theory of these papers, have no ideas, but definitions only. And thus the first difference is, as it were, taken away by the second; for, if these words have no immediate ideas, there will be no occasion to have recourse to reflection as a source of ideas; and, upon the whole, there is no material repugnancy between the consequences of this theory, and any thing advanced by Mr. Locke.

The ingenious Bishop Berkeley has justly observed against Mr. Locke, that there can be no such thing as abstract ideas, in the proper sense of the word idea. However, this does not seem to vitiate any considerable part of Mr. Locke’s reasoning. Substitute definition for idea in the proper places, and his conclusions will hold good in general.

Of Natural History.

Natural history is a branch of knowledge, which, at the first view, appears to have a boundless extent, and to be capable of the utmost practical precision and certainty, if sufficient care and industry be employed. And, in fact, the doubts and differences here are not very considerable; they do also grow less and less every day, by the great quantity of knowledge of this kind, which is poured in from all quarters, as learning and inquisitiveness diffuse themselves more and more amongst all nations, and all orders of men.

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. We believe testimony in natural history, because we do in civil, and vice versâ: and have a variety of concurrent confirmations in both cases.

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 However, as the general facts are thus practically certain, so the subordinate ones are, in many cases, liable to doubts. And it is evident, that, for the resolution of these doubts in natural history, we must borrow the assistance of all the other branches of science; and that some skill in philology must be attained, before we can hope to arrive at any tolerable perfection in natural or civil history. 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.

The ancient history of the kingdoms of Asia Minor, Egypt, and Greece, will probably be much better understood, when the inhabitants of those countries become learned.

He that would search into the first ages of the world, must take the Scriptures for his guide, lay down the truth of these as unquestionable, and force all other evidences into that position. This seems to have been the method taken by Sir Isaac Newton in his Chronology, and which at last unfolded to him the proper method of detecting and correcting the mistakes in the ancient technical chronology of the Greeks by itself.

The concurrent independent evidences in the grand points of history are so much more numerous than the dependent ones, and most of them so strong, singly taken, that the deficiency from certainty in these grand points cannot be distinguished by the human mind. And therefore it is a practical error of great importance to suppose, that such kind of historical evidences are inferior to mathematical ones. They are equal, as far as we have any thing to do with them; i.e. can judge of them, or be influenced by them. All future facts depending on them have as good a basis, as those depending on mathematical evidences. I speak here of principal matters, such as the conquests of Alexander and Julius Caesar, and the main history, common and miraculous, of the Old and New Testaments. 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; partly from the complexness of the historical proofs, which require time and consideration to digest them; and partly because the uncertainty

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 attending subordinate facts has diluted the evidence of the principal and unquestionable ones, since the same general forms of expression are, and must be used in both cases.

Of Natural Philosophy.

It may be observed of natural philosophy, that in the parts where the ideas are simple, clear, and of the visible kind, or adequately expounded by such, and the method of investigation and computation mathematical, as in mechanics, hydrostatics, pneumatics, optics, and astronomy, the doubts and diversities of opinion which arise, are inconsiderable. But in the theories of chemistry, of manual arts and trades, of medicine, and, in general, of the powers and mutual actions of the small parts of matter, the uncertainties and perplexities are as great as in any part of science. 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; and how far the number of orders may go, is impossible to say. I see no contradiction in supposing it infinite, and a great difficulty in stopping at any particular size.

Suppose the number of orders of particles infinite, or at least very great; and that particles of all orders are perpetually flying off from all bodies with great velocity. First, This may occasion the gravitation of the great bodies of the universe to each other, by the impulse of the smaller corpuscles upon particles of sizes equal to each other in the greater bodies, the impulses of the larger corpuscles, and upon particles, of unequal size, being evanescent in respect of the foregoing impulses. But where particles approach near to one another, and the corpuscles bear some finite ratio to the particles so as not to pervade them freely, before they come to particles of equal size to each other, but affect them in proportion to their surfaces, not solid content, and I suppose from many other causes, attractions of other kinds may arise; and if one or both of the contiguous particles send out many corpuscles with great force; also if these corpuscles effervesce together in the intermediate space, and gain new forces thence, &c. repulsive powers may rise. 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. But these are all very gross and uncertain conjectures.

In the mean time, it seems proper to use the words magnetism,

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 electricity, attraction of cohesion, spiritus rector, acrimony of the animal juices, &c. as terms of art, as unknown causes of known effects. But then they ought always to be defined, the definitions rigorously kept to, and all secondary ideas from prior associations excluded. Were this done in chemistry and medicine, it would produce a great reformation, and at once cut off many incumbrances, perplexities, and obscurities. The vis inertiæ of bodies, and the equivalent terms, were once terms of this kind, standing for the unknown cause of known phænomena. By degrees these phænomena were digested into order, the terms contributing thereto, and the three several kinds of them, classed respectively under the three laws of nature, which have been applied synthetically since, and given rise to the greatest mechanical discoveries. The same may be observed of gravity. And if the laws of magnetism, electricity, and the attraction of cohesion, could be ascertained in the same manner as the laws of the vis inertiæ and gravity, we should be enabled to predict and produce many effects of great importance to us.

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; so that, if we could arrive at the knowledge of these last, we should immediately see not only the reason of all the properties of bodies, which are known at present, but be able to discover innumerable other relative ones. In the mean time we must endeavour to discover, digest, and register, the various properties of natural bodies, as they rise to view from suitable experiments; and thus prepare the way for those who shall hereafter decypher their internal constitution.

Of Religion.

All the foregoing branches of knowledge ought to be considered as mere preparatories and preliminaries to the knowledge of religion, natural and revealed. They all, in their several orders and degrees, concur to establish the principal doctrines and duties of it; and these, when established, become the best means for attaining knowledge. The benevolence of the Deity, and the doctrine of final causes, are the best clew for guiding us through the labyrinths of natural phænomena, and particularly of those which relate to animals. The Scriptures are the only book which can give us any just idea of ancient times, of the original of mankind, their dispersion, &c. or of what will befall them in future generations. As to future things, predicted in the Scriptures, we can as yet collect nothing more than general intimations; but there is reason to believe, that succeeding generations

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 may arrive at a far more precise interpretation of prophecy. It may also be, that much philosophical knowledge is concealed in the Scriptures; and that it will be revealed in its due time. 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; at the same time that where there is a morally good disposition, a very small portion of other knowledge is sufficient for the attainment of all that is necessary for virtue and comfort here, and eternal happiness hereafter.

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.

Section III
OF THE AFFECTIONS IN GENERAL.

we may observe,

First, That our passions or affections can be no more than aggregates of simple ideas united by association. For they are excited by objects, and by the incidents of life. But these, if we except the impressed sensations, can have no power of affecting us, but what they derive from association; just as was observed above of words and sentences.

Secondly, Since therefore the passions are states of considerable pleasure or pain, they must be aggregates of the ideas, or traces of the sensible pleasures and pains, which ideas make up by their number, and mutual influence upon one another, for the faintness and transitory nature of each singly taken. This may be called a proof à priori. The proof à posteriori will be given, when I come to analyse the six classes of intellectual affections, viz. imagination, ambition, self-interest, sympathy, theopathy, and the moral sense.

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 Thirdly, As sensation is the common foundation of all these, so each in its turn, when sufficiently generated, contributes to generate and model all the rest. We may conceive this to be done in the following manner. Let sensation generate imagination; then will sensation and imagination together generate ambition; sensation, imagination, and ambition, self- interest; sensation, imagination, ambition, and self-interest, sympathy; sensation, imagination, ambition, self-interest, and sympathy, theopathy; sensation, imagination, ambition, self-interest, sympathy, and theopathy, the moral sense: and, in an inverted order, imagination will new model sensation; ambition, sensation and imagination; self-interest, sensation, imagination, and ambition; sympathy, sensation, imagination, ambition, and self-interest; theopathy, sensation, imagination, ambition, self-interest, and sympathy; and the moral sense, sensation, imagination, ambition, self-interest, sympathy, and theopathy: till at last, by the numerous reciprocal influences of all these upon each other, the passions arrive at that degree of complexness, which is observed in fact, and which makes them so difficult to be analysed.

Fourthly, As all the passions arise thus from pleasure and pain, their first and most general distribution may be into the two classes of love and hatred, i.e. we may term all those affections of the pleasurable kind, which objects and incidents raise in us, love; all those of the painful kind, hatred. Thus we are said to love not only intelligent agents of morally good dispositions, but also sensual pleasures, riches, and honours; and to hate poverty, disgrace, and pain, bodily and mental.

Fifthly, When our love and hatred are excited to a certain degree, they put us upon a variety of actions, and may be termed desire and aversion; by which last word I understand an active hatred. Now the actions which flow from desire and aversion, are entirely the result of associated powers and circumstances, agreeable to the twentieth, twenty-first, and twenty-second propositions, with their corollaries. The young child learns to grasp and go up to the play-thing that pleases him, and to withdraw his hand from the fire that burns him, at first from the mechanism of his nature, and without any deliberate purpose of obtaining pleasure, and avoiding pain, or any explicit reasoning about them. By degrees he learns, partly from the recurrency of these mechanical tendencies, inspired by God, as one may say, by means of the nature which He has given us, and partly from the instruction and imitation of others, to pursue every thing which he loves and desires, fly from every thing which he hates; and to reason about the method of doing this, just as he does upon other matters. And, because mankind are for the most part pursuing or avoiding something or other, the desire of happiness, and the aversion to misery, are supposed to be inseparable from, and essential to, all intelligent natures. But this does not seem to be an exact or correct way of speaking. The

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 most general of our desires and aversions are factitious, i.e. generated by association; and therefore admit of intervals, augmentations, and diminutions. And, whoever will be sufficiently attentive to the workings of his own mind, and the actions resulting therefrom, or to the actions of others, and the affections which may be supposed to occasion them, will find such differences and singularities in different persons, and in the same person at different times, as no way agree to the notion of an essential, original, perpetual desire of happiness, and endeavour to attain it; but much rather to the factitious associated desires and endeavours here asserted. And a due regard to this, will, as it seems to me, solve many difficulties and perplexities found in treatises upon the passions. The writers upon this subject have begun in the synthetical method prematurely, and without having premised the analytical one. For it is very true that, after general desires and endeavours are generated, they give rise in their turn to a variety of particular ones. But the original source is in the particular ones, and the general ones never alter and new-model the particular ones so much, as that there are not many traces and vestiges of their original mechanical nature and proportions remaining.

Sixthly, The will appears to be nothing but a desire or aversion sufficiently strong to produce an action that is not automatic primarily or secondarily. At least it appears to me, that the substitution of these words for the word will may be justified by the common usage of language. The will is therefore that desire or aversion, which is strongest for the then present time. For if any other desire was stronger, the muscular motion connected with it by association would take place, and not that which proceeds from the will, or the voluntary one, which is contrary to the supposition. Since therefore all love and hatred, all desire and aversion, are factitious, and generated by association, i.e. mechanically, it follows that the will is mechanical also.

Seventhly, Since the things which we pursue do, when obtained, generally afford pleasure, and those which we fly from affect us with pain, if they overtake us, it follows that the gratification of the will is generally attended or associated with pleasure, the disappointment of it with pain. Hence a mere associated pleasure is transferred upon the gratification of the will; a mere associated pain upon the disappointment of it. And if the will was always gratified, this mere associated pleasure would, according to the present frame of our natures, absorb, as it were, all our other pleasures; and thus by drying up the source from whence it sprung, be itself dried up at last: and the first disappointments, after a long course of gratification, would be intolerable. Both which things are sufficiently observable, in an inferior degree, in children that are much indulged, and in adults, after a series of successful events. Gratifications of the

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 will without the consequent expected pleasure, and disappointments of it without the consequent expected pain, are particularly useful to us here. And it is by this amongst other means, that the human will is brought to a conformity with the divine; which is the only radical cure for all our evils and disappointments, and the only earnest and medium for obtaining lasting happiness.

Eighthly, We often desire and pursue things which give pain rather than pleasure. Here it is to be supposed, that at first they afforded pleasure, and that they now give pain on account of a change in our nature and circumstances. Now, as the continuance to desire and pursue such objects, notwithstanding the pain arising from them, is the effect of the power of association, so the same power will at last reverse its own steps, and free us from such hurtful desires and pursuits. The recurrency of pain will at last render the object undesirable and hateful. And the experience of this painful process, in a few particular instances, will at last, as in other cases of the same kind, beget a habit of ceasing to pursue things, which we perceive by a few trials, or by rational arguments, to be hurtful to us upon the whole.

Ninthly, A state of desire ought to be pleasant at first, from the near relation of desire to love, and of love to pleasure and happiness. But in the course of a long pursuit, so many fears and disappointments, apparent or real, in respect of the subordinate means, and so many strong agitations of mind passing the limits of pleasure, intervene, as greatly to chequer a state of desire with misery. For the same reasons states of aversion are chequered with hope and comfort.

Tenthly, Hope and fear are, as just now observed, the attendants upon desire and aversion. These affect us more or less, according to the more or less frequent recurrency of the pleasing and painful ideas, according to the greater or less probability of the expected event, according to the greater or less distance of time, &c. the power of association displaying itself every where in the agitations of mind excited by these passions. It is particularly remarkable here that our hopes and fears rise and fall with certain bodily dispositions, according as these favour or oppose them.

Eleventhly, Joy and grief take place when the desire and aversion, hope and fear, are at an end; and are love and hatred, exerted towards an object which is present either in a sensible manner, or in a rational one, i.e. so as to occupy the whole powers of the mind, as sensible objects, when present, and attended to, do the external senses. It is very evident, that the objects of the intellectual pleasures and pains derive their power of thus affecting the mind from association.

Twelfthly, After the actual joy and grief are over, and the object withdrawn, there generally remains a pleasing or

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  recollection or resentment, which recurs with every recurrency of the idea of the object, or of the associated ones. This recollection keeps up the love or hatred. In like manner the five grateful passions, love, desire, hope, joy, and pleasing recollection, all enhance one another; as do the five ungrateful ones, hatred, aversion, fear, grief, and displeasing recollection. And the whole ten, taken together, comprehend, as appears to me, all the general passions of human nature.

Section IV
OF MEMORY.

was defined in the introduction to be that faculty by which traces of sensations and ideas recur, or are recalled, in the same order and proportion, accurately or nearly, as they were once presented.

Now here we may observe,

First, That memory depends entirely or chiefly on the state of the brain. For diseases, concussions of the brain, spirituous liquors, and some poisons, impair or destroy it; and it generally returns again with the return of health, from the use of proper medicines and methods. And all this is peculiarly suitable to the notion of vibrations. If sensations and ideas arise from peculiar vibrations, and dispositions to vibrate, in the medullary substance of the brain, it is easy to conceive, that the causes above alleged may so confound the sensations and ideas, as that the usual order and proportion of the idea shall be destroyed.

Secondly, The rudiments of memory are laid in the perpetual recurrency of the same impressions, and clusters of impressions. How these leave traces, in which the order is preserved, may be understood from the eighth, ninth, tenth, and eleventh propositions.

The traces which letters, and words, i.e. clusters of letters, leave, afford an instance and example of this. And, as in languages the letters are fewer than the syllables, the syllables than the words, and the words than the sentences, so the single sensible impressions, and the small clusters of them, are comparatively few in respect of the large clusters; and, being so, they must recur more frequently, so as the sooner to beget those traces which I call the rudiments or elements of memory. When these traces or ideas begin to recur frequently, this also

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 to fix them, and their order, in the memory, in the same manner as the frequent impression of the objects themselves.

Thirdly, Suppose now a person so far advanced in life, as that he has learnt all these rudiments, i.e. that he has ideas of the common appearances and occurrences of life, under a considerable variety of subordinate circumstances, which recur to his imagination from the slightest causes, and with the most perfect facility; and let us ask, how he can be able to remember or recollect a past fact, consisting of one thousand single particulars, or of one hundred such clusters as are called the rudiments of memory; ten single particulars being supposed to constitute a rudiment? First, then, We may observe, that there are only one hundred links wanting in the chain; for he has already learnt considerable exactness in the subordinate circumstances of the one hundred clusters; and perfect exactness is not to be supposed or required.—Secondly, The one hundred clusters recur again and again to the imagination for some time after the fact, in a quick and transient manner, as those who attend sufficiently to what passes in their own minds may perceive; and this both makes the impression a little deeper, and also serves to preserve the order. If the person attempts to recollect soon after the impression, the effect remaining in the brain is sufficient to enable him to do this with the accuracy required and experienced; if a longer time intervene, before he attempts to recollect, still the number of involuntary recurrences makes up in some measure for the want of this voluntary recollection. However, the power of recollection declines in general, and is entirely lost by degrees. It confirms this reasoning, that a new set of strong impressions destroys this power of recollection. For this must both obliterate the effects of the foregoing impressions, and prevent the recurrency of the ideas.—Thirdly, As the single impressions, which make the small clusters, are not combined together at hazard, but according to a general tenor in nature, so the clusters which make facts succeed each other according to some general tenor likewise. Now this both lessens the number of varieties, and shews that the association between many of the clusters, or rudiments, or one hundred links supposed to be wanting, is cemented already. This may be both illustrated and exemplified by the observation, that it is difficult to remember even well-known words that have no connexion with each other, and more so to remember collections of barbarous terms; whereas adepts in any science remember the things of that science with a surprising exactness and facility.—Fourthly, Some clusters are excluded from succeeding others, by ideas of inconsistency, impossibility, and by the methods of reasoning, of which we become masters as we advance in life.—Fifthly, The visible impressions which concur in the past fact, by being vivid, and preserving the order of place, often contribute greatly to preserve the order of time, and to suggest the clusters which may be

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