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For acquiring a knowledge of facts more recondite, observation and experiment must be employed;* and, accordingly, the use of these media forms one of the characteristical circumstances by which the studies of the philosopher are distinguished from the experience of the multitude. How much the stock of his information must thereby be enlarged is sufficiently manifest. By habits of scientific attention, his accuracy as an observer is improved; and a precision is given to his judgment, essentially different from the vagueness of ordinary perception: by a combination of his own observations with those made by others, he arrives at many conclusions unknown to those who are prevented, by the necessary avocations of human life, from indulging the impulse of a speculative curiosity; while the experiments which his ingenuity devises, enable him to place nature in situations in which she never presents herself spontaneously to view, and to extort from her, secrets, over which she draws a veil to the eyes of others.†

To these, Condorcet adds calculation. "Bacon (he observes) has revealed the true method of studying nature, by employing the three instruments with which she has fur nished us for the discovery of her secrets,-observation, experiment, and calculation." (Tableau Historique des progrès de l'Esprit Humain.) In this enumeration, it appears to me that there is a great defect, in point of logical distinctness. Calculation is certainly not an instrument of discovery at all analogous to experiment and observation: it can accomplish nothing in the study of nature, till they have supplied the materials; and is indeed only one of the many arts by which we are enabled to give a greater degree of ac curacy to their results. The use of optical glasses; of the thermometer and barometer; of time pieces; and of all the various instruments of practical geometry might, with equal propriety, have been added to the list.

The advantages, at the same time, which Natural Philosophy has derived, in modern times, from the arithmetical precision thus given to scientific details, must be allowed to be immense; and they would be well entitled to an ample illustration in a system of inductive logic. To those who may wish to prosecute the subject in this view, I would beg leave to suggest the word mensuration as equally precise, and more comprehensive, than the word calculation, as employed by Condorcet.

+ These primary and essential organs of accurate information (observation and experi ment) which furnish the basis to the whole superstructure of physical science, are very clearly and concisely described by Boscovich, in one of his notes on Stay's poem De Systemate Mundi. "Observationes fiunt spectando id quod natura per se ipsam sponte exhi bet: hujusmodi sunt observationes pertinentes ad astronomiam et historiam naturalem. Experimenta funt ponendo naturam in eas circumstantias, in quibus debeat agere et nobis ostendere id quod quaerimus, quod pertinet ad physicam experimentalem. Porro et ferro et igni utimur, ac dissolvimus per vim compagem corporum, potissimum in chemiâ, et na turanı quodammodo velut torquentes cogimus revelare sua secreta."

I have elsewhere remarked, that the physical discoveries of the moderns have been chiefly owing to the skilful contrivance and conduct of experiments; and that this method of interrogating nature was, in a great measure, unknown to the ancients. (Philosophical Essays, 4to. p. xxxv.) Even Aristotle himself is acknowledged, by one of his most devoted admirers, to have confined himself chiefly to observation; and is, on this very ground, proudly contrasted with the empirical experimentalists of the present times. "Aristotle (says Dr. Gillies) was contented with catching nature in the fact, without attempting, after the modern fashion, to put her to the torture; and in rejecting experiments operose, toilsome, or painful, either to their objects or their authors, he was justified by the habits of thinking, almost universally prevalent in his age and country. Educated in free and

[Observations are made by beholding what nature exhibits of her own accord; of this kind are observations pertaining to astronomy and natural history. Experiments are made by placing nature in circumstances in which she must necessarily act, and show us what we seek. This belongs to experimental philosophy. We moreover make use of iron and fire, and dissolve by their means the union of bodies, especially in chemistry, and compel nature as it were by torture, to reveal her secrets.]

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But the observations and experiments of the philosopher are com monly only a step towards a farther end. This end is, first, to re solve particular facts into other facts more simple and comprehen sive: and, secondly, to apply these general facts (or, as they are usually called, these laws of nature) to a synthetical explanation of particular phenomena. These two processes of the mind, together with that judicious employment of observation and experiment which they presuppose, exhaust the whole business of philosophical investigation; and the great object of the rules of philosophizing is, to show in what manner they ought to be conducted.

I. For the more complete illustration of this fundamental doctrine, How to init is necessary for me to recur to what has been already stated with

respect to our ignorance of efficient causes. As we can, in no investigate

stance, perceive the link by which two successive events are con-
nected, so as to deduce, by any reasoning a priori, the one from the
other as a consequence or effect, it follows, that when we see an
event take place which has been preceded by a combination of diffe.
rent circumstances, it is impossible for human sagacity to ascertain
whether the effect is connected with all the circumstances, or only
with a part of them; and (on the latter supposition) which of the
circumstances is essential to the result, and which are merely acci-

martial republics, careless of wealth, because uncorrupted by luxury, the whole tribe of
ancient philosophers dedicated themselves to agreeable only and liberal pursuits, with too
proud a disdain of arts merely useful or lucrative. They ranked with the first class of
citizens; and as such, were not to be lightly subjected to unwholesome or disgusting em-
ployments. To bend over a furnace, inhaling noxious 'steams, to torture animals, or to
touch dead bodies, appeared to them operations not more misbecoming their humanity,
than unsuitable to their dignity. For such discoveries as the heating and mixing of bodies
offers to inquisitive curiosity, the naturalists of Greece trusted to slaves and mercenary
mechanics, whose poverty or avarice tempted them to work in metals and minerals; and
to produce, by unwearied labour, those coloured and sculptured ornaments, those gems,
rings, cups, and vases, and other admired but frivolous elegancies, of which (in the opinion
of good judges of art) our boasted chemistry cannot produce the materials; nor, were the
materials at hand, supply us with the instruments fit to shape. The work-shops of trades-
men then revealed those mysteries which are now sought for in colleges and laboratories;
and useful knowledge, perhaps, was not the less likely to be advanced, while the
arts were confined to artists only; nor facts the more likely to be perverted, in order
to support favourite theories, before the empiric had yet assumed the name, and usurped
the functions of the philosopher." (Translation of Aristotle's Ethics and Politics, Vol. I.
p. 161. 2d ed.)

In another passage, we are told by the same author, that "the learning of Greece pro-
perly terminates in the Stagirite, by whom it was finally embodied into one great work;
a work rather impaired than improved by the labours of succeeding ages." (Ibid. p. x. of
the Preface)

Notwithstanding the length of this note, I must beg leave to add to it a short extract from one of the aphorisms of Lord Bacon.-" Of the criteria for guiding our judgment among so many different and discordant schools, there is none more to be relied on, than that which is exhibited by their fruits; for the fruits of any speculative doctrine, or the inventions which it has really produced, are, as it were, sponsers or vouchers for the truths which it contains. Now, it is well known, that from the philosophy of the Greeks, with its numerous derivative schools, hardly one experimental discovery can be collected which has any tendency to aid or to ameliorate the condition of man, or which is entitled to rank with the acknowledged principles of genuine science." Wherefore, as in religion, faith is proved by its works, so in philosophy, it were to be wished, that those theories should be accounted vain, which, when tried by their fruits, are barren ;-much more those, which, instead of grapes and olives, have produced only the thorns and thistles of controversy."-Nov. Org. Lib. i. Aph. Ixiii.






dental accessories or concomitants. The only way, in such a case, of coming at the truth, is to repeat over the experiment again and again, leaving out all the different circumstances successively, and observing with what particular combinations of them the effect is conjoined. If there be no possibility of making this separation, and if, at the same time, we wish to obtain the same result, the only method of insuring success is to combine together all the various circumstances which were united in our former trials. It is on this principle, that I have attempted, in a former chapter of this work, to account for the superstitious observances which always accom pany the practice of medicine among rude nations. These are commonly ascribed to the influence of imagination, and the low state of reason in the earlier periods of society; but the truth is, that they are the necessary and unavoidable consequences of a limited experience, and are to be corrected, not by mere force of intellect, but by a more enlarged acquaintance with the established order of nature.*

Observations perfectly similar to those which I made with respect to medicine are applicable to all the other branches of philosophy. Wherever an interesting change is preceded by a combination of different circumstances, it is of importance to vary our experiments in such a manner as to distinguish what is essential from what is accessory; and when we have carried the decomposition as far as we can, we are entitled to consider this simplest combination of indispensable conditions, as the physical cause of the event.

When by thus comparing a number of cases, agreeing in some circumstances, but differing in others, and all attended with the same result, a philosopher connects, as a general law of nature, the event with its physical cause, he is said to proceed according to the method of induction. This, at least, appears to me to be the idea which, in general, Bacon himself annexes to the phrase:† although I will not venture to affirm, that he has always employed it with uniform precision. I acknowledge, also, that it is often used by very accurate writers, to denote the whole of that system of rules, of which the process just mentioned forms the most essential and characteristical part.

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The same word induction is employed by mathematicians in a sense not altogether different. In that general formula (for instance) if bet: in-known by the name of the Binomial Theorem, having found that it duction in corresponds with the table of powers raised from a Binomial root, as far, as it is carried by actual multiplication, we have no scruple math: & in to conclude, that it holds universally. Such a proof of a mathemaphysical scitical theorem is called a proof by induction;—a mode of speaking


• Elements of the Philosophy of the Human Mind, Vol. I. chap. v. Part ii. sect. i. + Inductio, quae ad inventionem et demonstrationem scientiarum et artium erit utilis, naturam separare debet, per rejectiones et exclusiones debitas, &c. &c.-Nov. Org. Lib. i. Aph. cv.

Induction, which will be useful for the finding out and demonstration of sciences and arts, ought to separate what is united, by means of proper rejections and exclusions, &c.]


obviously suggested by the previous application of this term to our inferences concerning the laws of nature. There is, at the same time, notwithstanding the obvious analogy between the two cases, one very essential circumstance by which they are discriminated ;that in mathematical induction, we are led to our conclusion (as I shall afterwards endeavour to shew) by a process of thought, which, although not conformable to the rules of legitimate demonstration, involves, nevertheless, a logical inference of the understanding with respect to an universal truth or theorem; whereas, in drawing a general physical conclusion from particular facts, we are guided merely by our instinctive expectation of the continuance of the laws of nature; an expectation which, implying little, if any, exercise of the reasoning powers, operates alike on the philosopher and on the savage.

To this belief in the permanent uniformity of physical laws, Dr. Reid long ago gave the name of the inductive principle. "It is "from the force of this principle (he observed) that we immediate"ly assent to that axiom upon which all our knowledge of nature "is built, That effects of the same kind must have the same cause. "For effects and causes, in the operations of nature, mean nothing "but signs, and the things signified by them. We perceive no pro"per causality or efficiency in any natural cause; but only a con"nexion established by the course of nature between it and what is "called its effects."*

A late celebrated writer, more distinguished by the singular variety and of his talents than by the or soundness of

his understanding, was pleased to consider Reid's inductive principle dr. Trusttay, as a fit subject of ridicule; asserting that the phenomenon in ques-correction. tion was easily explicable by the common principles of experience, and the association of ideas. "Though no man (says he) has had "any experience of what is future, every man has had experience "of what was future." Of the shallowness of this solution philosophers are, I believe, now very generally convinced; but even if the case were otherwise, the fact remarked by Reid would be equally entitled to the attention of logicians as the basis of all physical science, nor would it be easy to distinguish it by a name less liable to objection than that which he has selected.

In all Bacon's logical rules, the authority of this law of belief is virtually recognized, although it is no where formally stated in his writings; and although the doctrines connected with it do not seem to be easily reconcilable with some of his occasional expressions.

It is indeed only of late that natural philosophers have been fully aware of its importance as the ground-work of the inductive logic; the earlier writers under whose review it fell having been led to

• Inquiry into the Human Mind, Chap. vi. Sect. 24.

Priestley's Examination of Reid, Beattie and Oswald, p. 85. Some very judicious and decisive strictures on this theory of Priestley may be found in Dr. Campbell's Philosophy of Rhetoric. See note at the end of the sixth chapter of Book i.

of Reid & Jur.

Not tho't consider it chiefly by its supposed subserviency to their metaphysical or to their theological speculations. Dr. Reid and M. Turgot original were, so far as I know, the first who recognized its existence as an ultimate original and ultimate law of the understanding; the source of all law of mind that experimental knowledge which we begin to acquire from the till moment of our birth, as well as of those more recondite discoveries ブ which are dignified by the name of science. It is but justice to Mr. Hume to acknowledge, that his Treatise of Human Nature furnished to Dr. Reid all the premises from which his conclusions were drawn; and that he is therefore fairly entitled to the honour of having reduced logicians to the alternative of either acquiescing in his sceptical inferences, or of acknowledging the authority of some instinctive principles of belief, overlooked in Locke's Analysis.*


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II. There is another circumstance which frequently adds to the difficulty of tracing the laws of nature; and which imposes on the philosopher, while carrying on the process of induction, the necessity of following a still more refined logic than has been hitherto described. -When a uniformity is observed in a number of different events, the curiosity is roused the coincidence, and is sometimes led insensi

bly to a general conclusion. In a few other cases, a multiplicity of


difficulty in tracing I laws of




events, which appear to common observers to be altogether anomalous, are found, upon a more accurate and continued examination of them, to be subjected to a regular law. The cycles by which the ancients predicted eclipses of the sun and moon; the two laws inferred by Kepler from the observations of Tycho Brahe; the law of refraction inferred by Snellius from the tables of Kircher and Scheiner, are instances of very comprehensive and most important rules obtained by the mere examination and comparison of particulars. Such purely empirical discoveries, however, are confined almost entirely to optics and astronomy, in which the physical laws combined together are comparatively few, and are insulated from the influence of those incalculable accidents which, in general, disturb the regularity of terrestrial phenomena. In by far the greater several laus number of instances, the appearances of nature depend on a variety of different laws, all of which are often combined together in producing one single event: And, wherever such a combination happens, although each law may take place with the most complete uniformity, it is likely that nothing but confusion will strike the mere observer. A collection of such results, therefore, would not advance us one step in the knowledge of nature; nor would it enable us to anticipate the issue of one new experiment. In cases of this These must description, before we can avail ourselves of our past experience, we must employ our reasoning powers in comparing a variety of instances together, in order to discover by a sort of analysis or decom

be examined yanalysis position, the simple laws which are concerned in the phenomenon

*Note (0.)

Philosophy of the Human Mind, Vol. I. Chap. vi. Sect. iv.

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