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Updated: June 1, 2025
If one begins, inductively and horizontally, with mere physical and material order, instead of beginning, deductively and vertically, with man's higher powers of conscience and will, he will end by finding only impersonal force in the universe, and by practically deifying it, as the Hindus deified Brahma.
Only thus can we develop general habits of will and bring the child to know general maxims of conduct inductively, and only thus by judicious boldness and hardihood in command can we bring the child to feel the conscious strength that comes only from doing unpleasant things.
In our ordinary conversation, we speak inductively when we first mention a number of specific facts and then draw from them some general inference; and we speak deductively when we first express a general opinion and then elucidate it by adducing specific illustrations.
When we think inductively, we reason from the particular to the general; and when we think deductively, the process proceeds in the reverse direction and we reason from the general to the particular.
When the phenomena are complex the deductive method must be called in to aid: from the inductively ascertained laws of the action of single causes this deduces the laws of their combined action; and, as a final step, the results of such ratiocination are verified by the proof of their agreement with empirical facts.
The relation of the two modes of reasoning is that, first by observing a sufficient number of instances, we inductively reach the conclusion that a certain principle is of general application, and then we enter upon the deductive process by assuming the truth of this principle and determining what result must follow in a particular case on the hypothesis of its truth.
But the chief object of his ambition, the end and aim of his researches, was to discover a triton and a mermaid, the existence of which he most potently and implicitly believed, and was prepared to demonstrate, a priori, a posteriori, a fortiori, synthetically and analytically, syllogistically and inductively, by arguments deduced both from acknowledged facts and plausible hypotheses.
But, until this organ is established, we have good right to doubt the ipse dixit of self-appointed oracles. When we examine the whole question of miracles inductively and deductively, I think that we must acknowledge that their basis is exceedingly weak.
This is still reasoning from particulars to particulars, but we now reason to the new instance from three distinct sets of former instances: to one only of those sets of instances do we directly perceive the new one to be similar; but from that similarity we inductively infer that it has the attribute by which it is assimilated to the next set, and brought within the corresponding induction; after which by a repetition of the same operation we infer it to be similar to the third set, and hence a third induction conducts us to the ultimate conclusion.
It is worthy of special note in this connection that Hertwig likewise evidently regards as the sole really empirically and inductively serviceable proof of Descent, that which is drawn from palaeontology, from prehistoric animal and plant remains.
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