The answer I conceive to be, that this character of necessity, ascribed to the truths of mathematics, and (even with some reservations to be hereafter made) the peculiar certainty attributed to them, is an illusion; in order to sustain which, it is necessary to suppose that those truths relate to, and express the properties of, purely imaginary objects. It is acknowledged that the conclusions of geometry are deduced, partly at least, from the so-called Definitions, and that those definitions are assumed to be correct representations, as far as they go, of the objects with which geometry is conversant. Now we have pointed out that, from a definition as such, no proposition, unless it be one concerning the meaning of a word, can ever follow; and that what apparently follows from a definition, follows in reality from an implied assumption that there exists a real thing conformable thereto. This assumption, in the case of the definitions of geometry, is not strictly true: there exist no real things exactly conformable to the definitions. There exist no points without magnitude; no lines without breadth, nor perfectly straight; no circles with all their radii exactly equal, nor squares with all their angles perfectly right. It will perhaps be said that the assumption does not extend to the actual, but only to the possible, existence of such things. I answer that, according to any test we have of possibility, they are not even possible. Their existence, so far as we can form any judgment, would seem to be inconsistent with the physical constitution of our planet at least, if not of the universe. To get rid of this difficulty, and at the same time to save the credit of the supposed system of necessary truth, it is customary to say that the points, lines, circles, and squares which are the subject of geometry, exist in our conceptions merely, and are part of our minds; which minds, by working on their own materials, construct ana priori science, the evidence of which is purely mental, and has nothing whatever to do with outward experience. By howsoever high authorities this doctrine may have been sanctioned, it appears to me psychologically incorrect. The points, lines, circles, and squares which any one has in his mind, are (Iapprehend) simply copies of the points, lines, circles, and squares which he has known in his experience. Our idea of a point, I apprehend to be simply our idea of the minimum visibile, the smallest portion of surface which we can see. A line, as defined by geometers, is wholly inconceivable. We can reason about a line as if it had no breadth; because we have a power, which is the foundation of all the control we can exercise over the operations of our minds; the power, when a perception is present to our senses, or a conception to our intellects, of attending to a part only of that perception or conception, instead of the whole. But we can not conceive a line without breadth; we can form no mental picture of such a line: all the lines which we have in our minds are lines possessing breadth. If any one doubts this, we may refer him to his own experience. I much question if any one who fancies that he can conceive what is called a mathematical line, thinks so from the evidence of his consciousness: I suspect it is rather because he supposes that unless such a conception were possible, mathematics could not exist as a science: a supposition which there will be no difficulty in showing to be entirely groundless. I hope to be pardoned for adding, that Dr. Whewell himself has both confirmed by his testimony the effect of habitual association in giving to an experimental truth the appearance of a necessary one, and afforded a striking instance of that remarkable law in his own person. In hisPhilosophy of the Inductive Sciences he continually asserts, that propositions which not only are not self-evident, but which we know to have been discovered gradually, and by great efforts of genius and patience, have, when once established, appeared so self-evident that, but for historical proof, it would have been impossible to conceive that they had not been recognized from the first by all persons in a sound state of their faculties. We now despise those who, in the Copernican controversy, could not conceive the apparent motion of the sun on the heliocentric hypothesis; or those who, in opposition to Galileo, thought that a uniform force might be that which generated a velocity proportional to the space; or those who held there was something absurd in Newtons doctrine of the different refrangibility of differently colored rays; or those who imagined that when elements combine, their sensible qualities must bemanifest in the compound; or those who were reluctant to give up the distinction of vegetables into herbs, shrubs, and trees. We can not help thinking that men must have been singularly dull of comprehension, to find a difficulty in admitting what is to us so plain and simple. We have a latent persuasion that we in their place should have been wiser and more clear-sighted; that we should have taken the right side, and given our assent at once to the truth. Yet in reality such a persuasion is a mere delusion. The persons who, in such instances as the above, were on the losing side, were very far, in most cases, from being persons more prejudiced, or stupid, or narrow-minded, than the greater part of mankind now are; and the cause for which they fought was far from being a manifestly bad one, till it had been so decided by the result of the war.... So complete has been the victory of truth in most of these instances, that at present we can hardly imagine the struggle to have been necessary. The very essence of these triumphs is, that they lead us to regard the views we reject as not only false but inconceivable.[81] So, tell me, he said, ‘what happened after Jack decided to play baseball with my head?’ § 3. The first and most obvious distinction between Observation and Experiment is, that the latter is an immense extension of the former. It not only enables us to produce a much greater number of variations in the circumstances than nature spontaneously offers, but also, in thousands of cases, toproduce the precisesort of variation which we are in want of for discovering the law of the phenomenon; a service which nature, being constructed on a quite different scheme from that of facilitating our studies, is seldom so friendly as to bestow upon us. For example, in order to ascertain what principle in the atmosphere enables it to sustain life, the variation we require is that a living animal should be immersed in each component element of the atmosphere separately. But nature does not supply either oxygen or azote in a separate state. We are indebted to artificial experiment for our knowledge that it is theformer, and not the latter, which supports respiration; and for our knowledge of the very existence of the two ingredients. This was the opening epigraph of the first volume, and my father read it with portentous intonations proper to the magical proceedings that would follow. Macintosh said:You ready, Connell.We are. In one of the three cases, Mr. Spencer, to my no small surprise, thinks that the belief of mankindcan not be rightly said to have undergone the change I allege. Mr. Spencer himself still thinks we are unable to conceive gravitation acting through empty space. “If an astronomer avowed that he could conceive gravitative force as exercised through space absolutely void, my private opinion would be that he mistook the nature of conception. Conception implies representation. Here the elements of the representation are the two bodies and an agency by which either affects the other. To conceive this agency is to represent it in some terms derived from our experiences—that is, from our sensations. As this agency gives us no sensations, we are obliged (if we try to conceive it) to use symbols idealized from our sensations—imponderable units forming a medium. No, I didnt say... He doesnt say anything. He isn’t there. But the man who works for him and has charge of the dogs when Trenton is away, said Trenton drove this car home and left it in the driveway. In the morning it was gone. Trenton started out in his station wagon and hasn’t been heard from since. He’s just back from a European trip. I telephoned Customs to see if they knew anything about the car and they told me Trenton had been subjected to quite a search because of association with a man by the name of Ostrander who was thought to have been mixed up in smuggling drugs. I said:Everything is okey in the outside office. Get ready to come in when I sing out. Bring her in with you. The girl in the harlequin glasses screamed. Not loud. Just as Rob Trenton dared to make an estimate as to the time he would arrive at the little farmhouse where he maintained his kennels, he felt the car swerve to the right, heard the bang of a blown-out tire and then was fighting the wheel to hold the machine straight on the road while he angled off to one side, touching the brakes at intervals very gently until he had the car well over on the verge. Youre doing all right the way you are, buddy. It won’t be long now. This is doubtless a true statement of the leading idea in the classification. The CategoryΟὐσία was certainly understood by Aristotle to be a general name for all possible answers to the question Quid sit? when asked respecting a concrete individual; as the other Categories are names comprehending all possible answers to the questions Quantum sit? Quale sit? etc. In Aristotlesconception, therefore, the Categories may not have been a classification of Things; but they were soon converted into one by his Scholastic followers, who certainly regarded and treated them as a classification of Things, and carried them out as such, dividing down the Category Substance as a naturalist might do, into the different classes of physical or metaphysical objects as distinguished from attributes, and the other Categories into the principal varieties of quantity, quality, relation, etc. It is, therefore, a just subject of complaint against them, that they had no Category of Feeling. Feeling is assuredly predicable as a summum genus, of every particular kind of feeling, for instance, as in Mr. Bain’s example, of Hope: but it can not be brought within any of the Categories as interpreted either by Aristotle or by his followers. Whats the matter? the other trooper asked. Suddenly got a cramp, or is it an inspiration? The man smiled and shook his head with easy good nature.No, Rob, he said, “that isnt going to do. We weren’t dumb enough to let the car sit there without having someone to keep an eye on it. To tell you the truth, we were good and worried when you didn’t come down to drive it away. It bothered us a bit. It was an explanation that would fit, but it didnt make allowance for the dead French girl in any way, shape, or form. It did offer a possible explanation for the shooting at me angle. The operators might have some notion I was on that; coming from the City and all. I went back to the room and thought it over, right from the start. This preliminary inquiry we have prosecuted to a definite result. Assertion, in the first place, relates either to the meaning of words, or to some property of the things which words signify. Assertions respecting the meaning of words, among which definitions are the most important, hold a place, and an indispensable one, in philosophy; but as the meaning of words is essentially arbitrary, this class of assertions are not susceptible of truth or falsity, nor therefore of proof or disproof. Assertions respecting Things, or what may be called Real Propositions, in contradistinction to verbal ones, are of various sorts. We have analyzed the import of each sort, and have ascertained the nature of the things they relate to, and the nature of what they severally assert respecting those things. We found that whatever be the form of the proposition, and whatever its nominal subject or predicate, the real subject of every proposition is some one or more facts or phenomena of consciousness, or some one or more of the hidden causes or powers to which we ascribe those facts; and that what is predicated or asserted, either in the affirmative or negative, of those phenomena or those powers, is always either Existence, Order in Place, Order in Time, Causation, or Resemblance. This, then, is the theory of the Import of Propositions, reduced to its ultimate elements: but there is another and a less abstruse expression for it, which, though stopping short in an earlier stage of the analysis, is sufficiently scientific for many of the purposes for which such a general expression is required. This expression recognizes the commonly received distinction between Subject and Attribute, and gives the following as the analysis of the meaning of propositions:—Every Propositionasserts, that some given subject does or does not possess some attribute; or that some attribute is or is not (either in all or in some portion of the subjects in which it is met with) conjoined with some other attribute. I wouldnt! Or do as you like! He had never thought of her as a big woman, though she had been firm in his arms. But a flaccid thickness of arm poked through the pulled-up sleeves, a greenish pallor of skin tones— and the magic was gone..