[SUBSECTION] II.-Critical Remarks on the vague Use, among Modern Writers, of the Terms Analysis and Synthesis.

The foregoing observations on the Analysis and Synthesis of the Greek Geometers may, at first sight, appear somewhat out of place, in a disquisition concerning the principles and rules of the Inductive Logic. As it was, however, from the Mathematical Sciences that these words were confessedly borrowed by the experimental inquirers of the Newtonian school, an attempt to illustrate their original technical import seemed to form a necessary introduction to the strictures which I am about to offer, on the loose and inconsistent applications of them, so frequent in the logical phraseology of the present times.

Sir Isaac Newton himself has, in one of his Queries, fairly brought into comparison the Mathematical and the Physical Analysis, as if the word, in both cases, conveyed the same idea. "As in Mathematics, so in Natural Philosophy, the investigation of difficult things, by the method of analysis, ought ever to precede the method of Composition. This analysis consists in making experiments and observations, and in drawing conclusions from them by induction, and admitting of no objections against the conclusions, but such as are taken from experiments, or other certain truths. For hypotheses are not to be regarded in experimental philosophy. And although the arguing from experiments and observations by induction be no demonstration of general conclusions, yet it is the best way of arguing which the nature of things admits of, and may be looked upon as so much the stronger, by how much the induction is more general. And if no exception occur from phenomena, the conclusion may be pronounced generally. But if, at any time afterwards, any exception shall occur from experiments, it may then begin to be pronounced, with such exceptions as occur. By this way of analysis we may proceed from compounds to ingredients; and from motions to the forces producing them; and, in general, from effects to their causes; and from particular causes to more general ones, till the argu

ment end in the most general. This is the method of analysis. And the synthesis consists in assuming the causes discovered, and established as principles, and by them explaining the phenomena proceeding from them, and proving the explanations."

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It is to the first sentence of this extract (which has been repeated over and over by subsequent writers) that I would more particularly request the attention of my readers. Mr. Maclaurin, one of the most illustrious of Newton's followers, has not only sanctioned it by transcribing it in the words of the author, but has endeavoured to illustrate and enforce the observation which it contains. "It is evident, that as in Mathematics, so in Natural Philosophy, the investigation of difficult things by the method of analysis ought ever to precede the method of composition, or the synthesis. For, in any other way, we can never be sure that we assume the principles which really obtain in nature; and that our system, after we have composed it with great labour, is not mere dream or illusion."2 The very reason here stated by Mr. Maclaurin, one should have thought, might have convinced him, that the parallel between the two kinds of analysis was not strictly correct; inasmuch as this reason ought, according to the logical interpretation of his words, to be applicable to the one science as well as to the other, instead of exclusively applying (as is obviously the case) to inquiries in Natural Philosophy.

After the explanation which has been already given of geometrical, and also of physical analysis, it is almost superfluous to remark, that there is little, if anything, in which they resemble each other, excepting this-that both of them are methods of investigation and discovery; and that both happen to be called by the same name. This name is, indeed, from its literal or etymological import, very happily significant of the notions conveyed by it in both instances; but, notwithstanding this accidental coincidence, the wide and essential difference between the subjects to which the two kinds of analysis are 1 See the concluding paragraphs of Newton's Optics.

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2 Account of Newton's Discoveries.

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applied, must render it extremely evident, that the analogy of the rules which are adapted to the one can be of no use in illustrating those which are suited to the other.

Nor is this all: The meaning conveyed by the word Analysis, in Physics, in Chemistry, and in the Philosophy of the Human Mind, is radically different from that which was annexed to it by the Greek Geometers, or which ever has been annexed to it by any class of modern Mathematicians. In all the former sciences, it naturally suggests the idea of a decomposition of what is complex into its constituent elements. It is defined by Johnson, "a separation of a compound body into the several parts of which it consists." He afterwards mentions, as another signification of the same word, "a solution of any thing, whether corporeal or mental, to its first elements; as of a sentence to the single words; of a compound word to the particles and words which form it; of a tune, to single notes; of an argument, to single propositions." In the following sentence, quoted by the same author from Glanvill, the word Analysis seems to be used in a sense precisely coincident with what I have said of its import, when applied to the Baconian method of investigation. "We cannot know anything of nature, but by an analysis of its true initial causes."1

In the Greek geometry, on the other hand, the same word evidently had its chief reference to the retrograde direction of this method, when compared with the natural order of didactic demonstration. Τὴν τοιαύτην ἔφοδον (says Pappus) ανάλυσιν καλοῦμεν, οἷον ἀνάπαλιν λύσιν ; a passage which Halley thus translates: hic processus Analysis vocatur, quasi dicas, inversa solutio. That this is the primitive and genuine import

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By the true initial causes of a phenomenon, Glanvill means (as might be easily shewn by a comparison with other parts of his works) the simple laws from the combination of which it results, and from a previous knowledge of which, it might have been synthetically deduced as a consequence.

That Bacon, when he speaks of those separations of nature, by means of com

parison, exclusions, and rejections, which form essential steps in the inductive process, had a view to the analytical operations of the chemical laboratory, appears sufficiently from the following words, before quoted: "Itaque naturæe facienda est prorsus solutio et separatio; non per ignem certe, sed per mentem, tanquam ignem divinum."

of the preposition avà, is very generally admitted by Grammarians; and it accords, in the present instance, so happily with the sense of the context, as to throw a new and strong light on the justness of their opinion.1

In farther proof of what I have here stated with respect to the double meaning of the words analysis and synthesis, as employed in physics and in mathematics, it may not be superfluous to add the following considerations. In mathematical analysis, we always set out from a hypothetical assumption, and our object is to arrive at some known truth, or some datum, by reasoning synthetically, from which we may afterwards return, on our own footsteps, to the point where our investigation began. In all such cases the synthesis is infallibly obtained by reversing the analytical process; and as both of them have in view the demonstration of the same theorem, or the solution of the same problem, they form, in reality, but different parts of one and the same investigation. But in natural philosophy, a synthesis which merely reversed the analysis would be absurd. On the contrary, our analysis necessarily sets out from known facts; and after it has conducted us to a general principle, the synthetical reasoning which follows consists always of an application of this principle to phenomena, different from those comprehended in the original induction.

In some cases, the natural philosopher uses the word Analysis where it is probable that a Greek geometer would have used the word Synthesis. Thus, in astronomy, when we attempt from the known phenomena to establish the truth of the Copernican system, we are said to proceed analytically. But

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The force of this preposition, in its primitive sense, may, perhaps, without any false refinement, be traced more or less palpably, in every instance to which the word analysis is with any propriety applied. In what Johnson calls (for example) "the separation of a compound body into the several parts of which it consists," we proceed on the supposition, that these parts have previously been combined, or put together, so as to

make up the aggregate who'e, submitted to the examination of the chemist; and, consequently, that the analytic process follows an inverted or retrograde direction, in respect of that in which the compound is conceived to have been originally formed. A similar remark will be found to apply (mutatis mutandis) to other cases, however apparently different.

the analogy of ancient geometry would apply this word to a process directly the reverse; a process which, assuming the system as true, should reason from it to the known phenomena: After which, if the process could be so reversed as to prove that this system, and this system alone, is consistent with these facts, it would bear some analogy to a geometrical synthesis.

These observations had occurred to me, long before I had remarked that the celebrated Dr. Hooke (guided also by what he conceived to be the analogy of the Greek geometry) uses the words analysis and synthesis in physics, precisely in the contrary acceptations to those assigned to them in the definitions of Sir Isaac Newton. "The methods," he observes, "of attaining a knowledge in nature may be two; either the Analytic or the Synthetic. The first is the proceeding from the causes to the effects. The second, from the effects to the causes. The former is the more difficult, and supposes the thing to be already done and known, which is the thing sought and to be found out. This begins from the highest, most general and universal principles or causes of things, and branches itself out into the more particular and subordinate. The second is the more proper for experimental inquiry, which, from a true information of the effect by a due process, finds out the immediate cause thereof, and so proceeds gradually to higher and more remote causes and powers effective, founding its steps upon the lowest and more immediate conclusions."1

1 Hooke's Posthumous Works, p. 330. As this volume is now become extremely rare, I shall transcribe the paragraph which immediately follows the above quotation.

"An inquisition by the former (or analytic) method, is resembled fitly enough by the example of an architect, who hath a full comprehension of what he designs to do, and acts accordingly: But the latter (or synthetic) is more properly resembled to that of a husbandman or gardener, who prepares his ground, and sows his seed, and diligently cherishes the growing vegetable, supply

ing it continually with fitting moisture, food, and shelter-observing, and cherishing its continual progression, till it comes to its perfect ripeness and maturity, and yields him the fruit of his labour. Nor is it to be expected, that a production of such perfection as this is designed, should be brought to its complete ripeness in an instant; but as all the works of nature, if it be naturally proceeded with, it must have its due time to acquire its due form and full maturity, by gradual growth and a natural progression; not but that the other method is also of excellent and