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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[8] Or rather, all objects except itself and the percipient mind; for, as we shall see hereafter, to ascribe any attribute to an object, necessarily implies a mind to perceive it.
The simple and clear explanation given in the text, of relation and relative names, a subject so long the opprobrium of metaphysics, was given (as far as I know) for the first time, by Mr. James Mill, in his Analysis of the Phenomena of the Human Mind.
[9] Philosophy of the Inductive Sciences, vol. i. p. 40.
[10] Discussions on Philosophy, &c. Appendix I. pp. 643-4.
[11] It is to be regretted that Sir William Hamilton, though he often strenuously insists on this doctrine, and though, in the passage quoted, he states it with a comprehensiveness and force which leave nothing to be desired, did not consistently adhere to his own doctrine, but maintained along with it opinions with which it is utterly irreconcileable. See the third and other chapters of An Examination of Sir William Hamilton's Philosophy.
[12] "Nous savons qu'il existe quelque chose hors de nous, parceque nous ne pouvons expliquer nos perceptions sans les rattacher à des causes distinctes de nous-mêmes; nous savons de plus que ces causes, dont nous ne connaissons pas d'ailleurs l'essence, produisent les effets les plus variables, les plus divers, et même les plus contraires, selon qu'elles rencontrent telle nature ou telle disposition du sujet. Mais savons-nous quelque chose de plus? et même, vu le caractère indéterminé des causes que nous concevons dans les corps, y a-t-il quelque chose de plus à savoir? Y a-t-il lieu de nous enquérir si nous percevons les choses telles qu'elles sont? Non évidemment.... Je ne dis pas que le problème est insoluble, je dis qu'il est absurde et enferme une contradiction. Nous ne savons pas ce que ces causes sont en elles-mêmes, et la raison nous défend de chercher à le connaître: mais il est bien évident à priori, qu'elles ne sont pas en elles-mêmes ce qu'elles sont par rapport à nous, puisque la présence du sujet modifie nécessairement leur action. Supprimez tout sujet sentant, il est certain que ces causes agiraient encore puisqu'elles continueraient d'exister; mais elles agiraient autrement; elles seraient encore des qualités et des propriétés, mais qui ne ressembleraient à rien de ce que nous connaissons. Le feu ne manifesterait plus aucune des propriétés que nous lui connaissons: que serait-il? C'est ce que nous ne saurons jamais. C'est d'ailleurs peut-être un problème qui ne répugne pas seulement à la nature de notre esprit, mais à l'essence même des choses. Quand même en effet on supprimerait par la pensée tous les sujets sentants, il faudrait encore admettre que nul corps ne manifesterait ses propriétés autrement qu'en relation avec un sujet quelconque, et dans ce cas ses propriétés ne seraient encore que relatives: en sorte qu'il me paraît fort raisonnable d'admettre que les propriétés déterminées des corps n'existent pas indépendamment d'un sujet quelconque, et que quand on demande si les propriétés de la matière sont telles que nous les percevons, il faudrait voir auparavant si elles sont en tant que déterminées, et dans quel sens il est vrai de dire qu'elles sont."—Cours d'Histoire de la Philosophie Morale au 18me siècle, 8me leçon.
[13] An attempt, indeed, has been made by Reid and others, to establish that although some of the properties we ascribe to objects exist only in our sensations, others exist in the things themselves, being such as cannot possibly be copies of any impression upon the senses; and they ask, from what sensations our notions of extension and figure have been derived? The gauntlet thrown down by Reid was taken up by Brown, who, applying greater powers of analysis than had previously been applied to the notions of extension and figure, pointed out that the sensations from which those notions are derived, are sensations of touch, combined with sensations of a class previously too little adverted to by metaphysicians, those which have their seat in our muscular frame. His analysis, which was adopted and followed up by James Mill, has been further and greatly improved upon in Professor Bain's profound work, The Senses and the Intellect, and in the chapters on "Perception" of a work of eminent analytic power, Mr. Herbert Spencer's Principles of Psychology.
On this point M. Cousin may again be cited in favour of the better doctrine. M. Cousin recognises, in opposition to Reid, the essential subjectivity of our conceptions of what are called the primary qualities of matter, as extension, solidity, &c., equally with those of colour, heat, and the remainder of the so-called secondary qualities.—Cours, ut supra, 9me leçon.
[14] This doctrine, which is the most complete form of the philosophical theory known as the Relativity of Human Knowledge, has, since the recent revival in this country of an active interest in metaphysical speculation, been the subject of a greatly increased amount of discussion and controversy; and dissentients have manifested themselves in considerably greater number than I had any knowledge of when the passage in the text was written. The doctrine has been attacked from two sides. Some thinkers, among whom are the late Professor Ferrier, in his Institutes of Metaphysic, and Professor John Grote in his Exploratio Philosophica, appear to deny altogether the reality of Noumena, or Things in themselves—of an unknowable substratum or support for the sensations which we experience, and which, according to the theory, constitute all our knowledge of an external world. It seems to me, however, that in Professor Grote's case at least, the denial of Noumena is only apparent, and that he does not essentially differ from the other class of objectors, including Mr. Bailey in his valuable Letters on the Philosophy of the Human Mind, and (in spite of the striking passage quoted in the text) also Sir William Hamilton, who contend for a direct knowledge by the human mind of more than the sensations—of certain attributes or properties as they exist not in us, but in the Things themselves.
With the first of these opinions, that which denies Noumena, I have, as a metaphysician, no quarrel; but, whether it be true or false, it is irrelevant to Logic. And since all the forms of language are in contradiction to it, nothing but confusion could result from its unnecessary introduction into a treatise, every essential doctrine of which could stand equally well with the opposite and accredited opinion. The other and rival doctrine, that of a direct perception or intuitive knowledge of the outward object as it is in itself, considered as distinct from the sensations we receive from it, is of far greater practical moment. But even this question, depending on the nature and laws of Intuitive Knowledge, is not within the province of Logic. For the grounds of my own opinion concerning it, I must content myself with referring to a work already mentioned—An Examination of Sir William Hamilton's Philosophy; several chapters of which are devoted to a full discussion of the questions and theories relating to the supposed direct perception of external objects.
[15] Analysis of the Human Mind, i. 126 et seq.
[16] It may, however, be considered as equivalent to an universal proposition with a different predicate, viz. "All wine is good quâ wine," or "is good in respect of the qualities which constitute it wine."
[17] Dr. Whewell (Philosophy of Discovery, p. 242) questions this statement, and asks, "Are we to say that a mole cannot dig the ground, except he has an idea of the ground, and of the snout and paws with which he digs it?" I do not know what passes in a mole's mind, nor what amount of mental apprehension may or may not accompany his instinctive actions. But a human being does not use a spade by instinct; and he certainly could not use it unless he had knowledge of a spade, and of the earth which he uses it upon.
[18] "From hence also this may be deduced, that the first truths were arbitrarily made by those that first of all imposed names upon things, or received them from the imposition of others. For it is true (for example) that man is a living creature, but it is for this reason, that it pleased men to impose both these names on the same thing."—Computation or Logic, ch. iii. sect. 8.
[19] "Men are subject to err not only in affirming and denying, but also in perception, and in silent cogitation.... Tacit errors, or the errors of sense and cogitation, are made by passing from one imagination to the imagination of another different thing; or by feigning that to be past, or future, which never was, nor ever shall be; as when by seeing the image of the sun in water, we imagine the sun itself to be there; or by seeing swords, that there has been, or shall be, fighting, because it uses to be so for the most part; or when from promises we feign the mind of the promiser to be such and such; or, lastly, when from any sign we vainly imagine something to be signified which is not. And errors of this sort are common to all things that have sense."—Computation or Logic, ch. v. sect. 1.
[20] Ch. iii. sect. 3.
[21] To the preceding statement it has been objected, that "we naturally construe the subject of a proposition in its extension, and the predicate (which therefore may be an adjective) in its intension, (connotation): and that consequently coexistence of attributes does not, any more than the opposite theory of equation of groups, correspond with the living processes of thought and language." I acknowledge the distinction here drawn, which, indeed, I had myself laid down and exemplified a few pages back (p. 104). But though it is true that we naturally "construe the subject of a proposition in its extension," this extension, or in other words, the extent of the class denoted by the name, is not apprehended or indicated directly. It is both apprehended and indicated solely through the attributes. In the "living processes of thought and language" the extension, though in this case really thought of (which in the case of the predicate it is not), is thought of only through the medium of what my acute and courteous critic terms the "intension."
For further illustrations of this subject, see Examination of Sir William Hamilton's Philosophy, ch. xxii.
[22] Book iv. ch. vii.
[23] The doctrines which prevented the real meaning of Essences from being understood, had not assumed so settled a shape in the time of Aristotle and his immediate followers, as was afterwards given to them by the Realists of the middle ages. Aristotle himself (in his Treatise on the Categories) expressly denies that the δεύτεραι οὔσιαι, or Substantiæ Secundæ, inhere in a subject. They are only, he says, predicated of it.
[24] The always acute and often profound author of An Outline of Sematology (Mr. B. H. Smart) justly says, "Locke will be much more intelligible if, in the majority of places,
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