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multitude (who are unacquainted with many of those Premises) strictly “ New Truths,” hence it is, that men in general give to the general facts, and to them, most peculiarly, the name of Discoveries; for to themselves they are such, in the strictest sense; the Premises from which they were inferred being not only originally unknown to them, but frequently remaining unknown to the very last ; e.g. the general conclusion concerning cattle, which Bakewell made known, is what most Agriculturists and many others also) are acquainted with ; but the Premises he set out with, viz. the facts respecting this, that, and the other, individual ox, (the ascertainment of which facts was his first Discovery,) these are what few know, or care to know, with any exact particularity.
And it may be added, that these discoveries of particular facts, which are the immediate result of observation, are, in themselves, uninteresting and insignificant, till they are combined so as to lead to a grand general result; those who on each occasion watched the motions, and registered the times of occultation of Jupiter's satellites, little thought, perhaps, themselves, what magnificent results they were preparing the way for. * So that
Observation and experiment.
* Hence, Bacon urges us to pursue Truth, without always requiring to perceive its practical application.
there is an additional cause which has confined the term Discovery to these grand general conclusions; and, as was just observed, they are, to the generality of men, perfectly New Truths in the strictest sense of the word, not being implied in any previous knowledge they possessed. Very often it will happen, indeed, that the conclusion thus drawn will amount only to a probable conjecture; which conjecture will dictate to the inquirer such an experiment, or course of experiments, as will fully establish the fact : thus Sir H. Davy, from finding that the flame of hydrogen gas was not communicated through a long slender tube, conjectured that a shorter but still slenderer tube would answer the same purpose; this led him to try the experiments, in which, by continually shortening the tube, and at the same time lessening its bore, he arrived at last at the wire-gauze of his safety-lamp.
It is to be observed also, that whatever credit is conveyed by the word “Discovery,” to him who is regarded as the author of it, is well deserved by those who skilfully select and combine known Truths (especially such as have been long and generally known) so as to elicit important, and hitherto unthoughtof, conclusions; their's is the master-mind:αρχιτεκτονική φρόνησις. Whereas men of very inferior powers may sometimes, by immediate
observation, discover perfectly new facts, empirically; and thus be of service in furnishing materials to the others; to whom they stand in the same relation (to recur to a former illustration) as the brickmaker or stonequarrier to the architect.
It is peculiarly creditable to Adam Smith, and to Mr. Malthus, that the data from which they drew such important Conclusions had been in every one's hands for centuries.
As for Mathematical Discoveries, they (as we have before said) must always be of the description to which we have given the name of “Logical Discoveries ;" since to him who properly comprehends the meaning of the Mathematical terms, (and to no other are the Truths themselves, properly speaking, intelligible) those results are implied in his previous knowledge, since they are Logically deducible therefrom. It is not, however, meant to be implied, that Mathematical Discoveries are effected by pure Reasoning, and by that singly. For though there is not here, as in Physics, any exercise of judgment as to the degree of evidence of the Premises, nor any experiments and observations, yet there is the same call for skill in the selection and combination of the Premises in such a manner as shall be best calculated to lead to a new, that is, unperceived and unthought-of Conclusion.
In following, indeed, and taking in a demonstration, nothing is called for but pure Reasoning; but the assumption of Premises is not a part of Reasoning, in the strict and technical sense of that term. Accordingly, there are many who can follow a Mathematical demonstration, or any other train of argument, who would not succeed well in framing one of their own. *
connected with Reason
For both kinds of Discovery then, the Lo-Operations gical, as well as the Physical, certain opera- mig tions are requisite, beyond those which can fairly be comprehended under the strict sense of the word “Reasoning;” in the Logical, is required a skilful selection and combination of known Truths: in the Physical, we must employ, in addition (generally speaking) to that process, observation and experiment. It will generally happen, that in the study of nature, and, universally, in all that relates to matters of fact, both kinds of investigation will be united; i. e. some of the facts or principles you reason from as Premises, must be ascertained by observation; or, as in the case of the safety-lamp, the ultimate Conclusion will
* Hence, the Student must not confine himself to this passive kind of employment, if he would truly become a Mathematician.
need confirmation from experience; so that both Physical and Logical Discovery will take place in the course of the same process: we need not, therefore, wonder, that the two are so perpetually confounded. In Mathematics, on the other hand, and in great part of the discussions relating to Ethics and Jurisprudence, there being no room for any
Physical Discovery whatever, we have only L to make a skilful use of the propositions in our possession, to arrive at every attainable result.
The investigation, however, of the latter class of subjects differs in other points also from that of the former. For, setting aside the circumstance of our having, in these, no question as to facts,—no room for observation,
there is also a considerable difference in what may be called, in both instances, the process of Logical investigation; the Premises on which we proceed being of so different a nature in the two cases.
To take the example of Mathematics, the Reasoning. Definitions, which are the principles of our
Reasoning, are very few, and the Axioms still fewer; and both are, for the most part, laid down and placed before the student in the outset ; the introduction of a new Definition or Axiom, being of comparatively rare occurrence, at wide intervals, and with a formal statement; besides which, there is no room
Mathematical and other