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Updated: May 13, 2025
And therefore the conclusions of all deductive sciences were said by the ancients to be necessary propositions. We have observed already that to be predicated necessarily was characteristic of the predicable Proprium, and that a proprium was any property of a thing which could be deduced from its essence, that is, from the properties included in its definition.
Such, I say, is the theological method, deductive; however, the history of the last three centuries is only one long course of attempts, on the part of the partisans of the Baconian Philosophy, to get rid of the method proper to Theology and to make it an experimental science.
What authority had the boundary man or I to dogmatise on the Coming Australian? Just the same authority as Marcus Clarke, or Trollope, or Froude, or Francis Adams and that is exactly none. Deductive reasoning of this kind is seldom safe.
It was thus that Descartes and Clairaut made geometry, which was already partially deductive, still more so, by pointing out the correspondence between geometrical and algebraical properties.
And inasmuch as the partly deductive and partly experimental methods of treatment to which Newton and others subjected these branches of human knowledge, showed that the phenomena of nature which belonged to them were susceptible of explanation, and thereby came within the reach of what was called "philosophy" in those days; so much of this kind of knowledge as was not included under astronomy came to be spoken of as "natural philosophy" a term which Bacon had employed in a much wider sense.
When the separate studies into which mathematics is divided have each been viewed as a logical whole, as a natural growth from the propositions which constitute their principles, the learner will be able to understand the fundamental science which unifies and systematises the whole of deductive reasoning.
Exact Science in its largest sense, that which extends to all domains in which the proper Deductive Method has been or may hereafter be rightly employed is therefore a system or series of truths relating to the whole Universe, or to some department of it, consecutively and necessarily resulting from, and dependent upon, each other, in a definite chain or series; and resting primarily upon some fundamental truth or truths so simple and self-evident, that, when clearly stated, all men must, by the natural constitution of the human mind, perceive them and recognize them as true.
Such a test however there is: and its application forms, under the name of Verification, the third essential component part of the Deductive Method; without which all the results it can give have little other value than that of guess-work.
Such a test, however, there is: and its application forms, under the name of Verification, the third essential component part of the Deductive Method; without which all the results it can give have little other value than that of conjecture.
To Astronomy, on the other hand, the pupils of Euclid turned naturally, as to the science which required the greatest amount of their favourite geometry: but even that they were content to let pass from its inductive to its deductive stage not as we have done now, after two centuries of inductive search for the true laws, and their final discovery by Kepler and Newton: but as soon as Hipparchus had propounded any theory which would do instead of the true laws, content there to stop their experiments, and return to their favourite work of commenting, deducing, spinning notion out of notion, ad infinitum.
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