A System of Logic: Ratiocinative and Inductive by John Stuart Mill (popular e readers .txt) 📕
3. Some of the first principles of geometry are axioms, and these are not hypothetical 256
4. --but are experimental truths 258
5. An objection answered 261
6. Dr. Whewell's opinions on axioms examined 264
CHAPTER VI.
The same Subject continued.
Sec. 1. All deductive sciences are inductive 281
2. The propositions of the science of number are not verbal, but generalizations from experience 284
3. In what sense hypothetical 289
4. The characteristic property of demonstrative science is to be hypothetical 290
5. Definition of demonstrative evidence 292
CHAPTER VII.
Examination of some Opinions opposed to the preceding doctrines.
Sec. 1. Doctrine of the Universal Postulate 294
2. The test of inconceivability does not
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[30] In the words of Fontenelle, another celebrated Cartesian, "les philosophes aussi bien que le peuple avaient cru que l'âme et le corps agissaient réellement et physiquement l'un sur l'autre. Descartes vint, qui prouva que leur nature ne permettait point cette sorte de communication véritable, et qu'ils n'en pouvaient avoir qu'une apparente, dont Dieu était le Médiateur."—Œuvres de Fontenelle, ed. 1767, tom. v. p. 534.
[31] I omit, for simplicity, to take into account the effect, in this latter case, of the diminution of pressure, in diminishing the flow of water through the drain; which evidently in no way affects the truth or applicability of the principle, since when the two causes act simultaneously the conditions of that diminution of pressure do not arise.
[32] Unless, indeed, the consequent was generated not by the antecedent, but by the means employed to produce the antecedent. As, however, these means are under our power, there is so far a probability that they are also sufficiently within our knowledge, to enable us to judge whether that could be the case or not.
[33] Discourse on the Study of Natural Philosophy, p. 179.
[34] For this speculation, as for many other of my scientific illustrations, I am indebted to Professor Bain, of Aberdeen, who has since, in his profound treatises entitled "The Senses and the Intellect," and "The Emotions and the Will," carried the analytic investigation of the mental phenomena according to the methods of physical science, to the most advanced point which it has yet reached, and has worthily inscribed his name among the successive constructors of an edifice to which Hartley, Brown, and James Mill had each contributed their part.
[35] This view of the necessary coexistence of opposite excitements involves a great extension of the original doctrine of two electricities. The early theorists assumed that, when amber was rubbed, the amber was made positive and the rubber negative to the same degree; but it never occurred to them to suppose that the existence of the amber charge was dependent on an opposite charge in the bodies with which the amber was contiguous, while the existence of the negative charge on the rubber was equally dependent on a contrary state of the surfaces that might accidentally be confronted with it; that, in fact, in a case of electrical excitement by friction, four charges were the minimum that could exist. But this double electrical action is essentially implied in the explanation now universally adopted in regard to the phenomena of the common electric machine.
[36] Pp. 159-162.
[37] Infra, book iv. ch. ii. On Abstraction.
[38] I must, however, remark, that this example, which seems to militate against the assertion we made of the comparative inapplicability of the Method of Difference to cases of pure observation, is really one of those exceptions which, according to a proverbial expression, prove the general rule. For in this case, in which Nature, in her experiment, seems to have imitated the type of the experiments made by man, she has only succeeded in producing the likeness of man's most imperfect experiments; namely, those in which, though he succeeds in producing the phenomenon, he does so by employing complex means, which he is unable perfectly to analyse, and can form therefore no sufficient judgment what portion of the effects may be due, not to the supposed cause, but to some unknown agency of the means by which that cause was produced. In the natural experiment which we are speaking of, the means used was the clearing off a canopy of clouds; and we certainly do not know sufficiently in what this process consists, or on what it depends, to be certain à priori that it might not operate upon the deposition of dew independently of any thermometric effect at the earth's surface. Even, therefore, in a case so favourable as this to Nature's experimental talents, her experiment is of little value except in corroboration of a conclusion already attained through other means.
[39] In his subsequent work, Outlines of Astronomy (§ 570), Sir John Herschel suggests another possible explanation of the acceleration of the revolution of a comet.
[40] Discourse, pp. 156-8, and 171.
[41] Outlines of Astronomy, § 856.
[42] Philosophy of Discovery, pp. 263, 264.
[43] See, on this point, the second chapter of the present Book.
[44] Ante, ch. vii. § 1.
[45] It seems hardly necessary to say that the word impinge, as a general term to express collision of forces, is here used by a figure of speech, and not as expressive of any theory respecting the nature of force.
[46] Essays on some Unsettled Questions of Political Economy, Essay V.
[47] Vide Memoir by Thomas Graham, F.R.S., Master of the Mint, "On Liquid Diffusion Applied to Analysis," in the Philosophical Transactions for 1862, reprinted in the Journal of the Chemical Society, and also separately as a pamphlet.
[48] It was an old generalization in surgery, that tight bandaging had a tendency to prevent or dissipate local inflammation. This sequence, being, in the progress of physiological knowledge, resolved into more general laws, led to the important surgical invention made by Dr. Arnott, the treatment of local inflammation and tumours by means of an equable pressure, produced by a bladder partially filled with air. The pressure, by keeping back the blood from the part, prevents the inflammation, or the tumour, from being nourished: in the case of inflammation, it removes the stimulus, which the organ is unfit to receive; in the case of tumours, by keeping back the nutritive fluid, it causes the absorption of matter to exceed the supply, and the diseased mass is gradually absorbed and disappears.
[49] Since acknowledged and reprinted in Mr. Martineau's Miscellanies.
[50] Dissertations and Discussions, vol. i., fourth paper.
[51] Written before the rise of the new views respecting the relation of heat to mechanical force; but confirmed rather than contradicted by them.
END OF VOL. I.
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Spelling irregularities where there was no obviously preferred version were left as is. Variants include: "alkalies" and "alkalis;" "apprise" and "apprize;" "coexistent" and "co-existent" (along with derivatives); "coextensive" and "co-extensive;" "e. g." and "e.g."; "encumbered" and "incumbered;" "formulæ" and "formulas;" "i. e." and "i.e."; "nonentity" and "non-entity;" "recal" and "recall" (and derivatives); "rectilinear" and "rectilineal;" "stopt" and "stopped."
Volume I. contains "το ὄν," while Volume II. spells it "τὸ ὄν." The spellings were left as is, in each case.
Changed "3" to "4" on page xiii: "4. —and from descriptions."
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Moved the semi-colon inside the quotation marks in the footnote on page 14: "the Science of the Formal Laws of Thought;".
Changed "sub-divisions" to "subdivisions" on page 59: "three subdivisions."
Changed "pre-supposed" to "presupposed" on page 75: "they are presupposed."
In the footnote to page 122, changed the Greek character upsilon with dasia and oxia to upsilon with psili and oxia, making the transliteration "deuterai ousiai."
Changed "he" to "be" on page 189: "to which it may be reduced."
Changed "cb." to "ch." in footnote on page 227: "Theory of Reasoning, ch. iv."
Changed "reconcilable" to "reconcileable" on page 240: "not easily reconcileable."
Preserved the hyphen in "counter-acting" on page 280. Usually this is spelled without the hyphen, but this instance is in a quotation.
Moved parenthesis that was after "to" to before it on page 321: "(to return to a former example)."
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Changed "paralyzed" to "paralysed" on page 389: "nerves of motion were paralysed."
The footnote from page 396 refers to the footnote on page 270. There is no such footnote. The intent may be to refer to the footnote on page 268. However, the text was not changed.
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Added the dropped "l" to "essential" on page 515: "an essential requisite."
Removed extra opening quotation mark before "gum" on page 532: "vegetable gum is not digested."
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