Chemists From The United States

"Since space is continuous, it follows that there must be an immediate community of feeling between parts of mind infinitesimally close together. Without this, I believe it would have been impossible for any co-ordination to be established in the action of the nerve-matter of one brain."

"Accordingly, time logically supposes a continuous range of intensity of feeling. It follows then, from the definition of continuity, that when any particular kind of feeling is present, an infinitesimal continuum of all feelings differing infinitesimally from that, is present."

"In the case of colors, there is a tridimensional spread of feelings. Originally all feelings may have been connected in the same way, and the presumption is that the number of dimensions was endless. For development essentially involves a limitation of possibilities. But given a number of dimensions of feeling, all possible varieties are obtainable by varying the intensities of the different elements."

"The development of the human mind has practically extinguished all feelings, except a few sporadic kinds, [like] sound, colors, smells, warmth, etc., which now appear to be disconnected and separate."

"Time with its continuity logically involves some other kind of continuity than its own. Time, as the universal form of change, cannot exist unless there is something to undergo change, and to undergo a change continuous in time, there must be a continuity of changeable qualities."

"One of the most marked features about the law of mind is that it makes time to have a definite direction of flow from past to future. ...This makes one of the great contrasts between the law of mind and the law of physical force, where there is no more distinction between the two opposite directions in time than between moving northward and moving southward."

"Suppose a surface to be part red and part blue; so that every point on it is either red or blue, and of course, no part can be both red and blue. What then, is the color of the surface in the immediate neighborhood of the point. ...it follows that the boundary is half red and half blue. In like manner, we find it necessary to hold that consciousness essentially occupies time... Thus, the present is half past and half time to come. ...Take another case: the velocity of a particle at any instant of time is its mean velocity during an infinitesimal instant in which that time is consumed. Just so, my immediate feeling is my feeling through an infinitesimal duration containing the present instant."

"Indeed, even this last moment will be recognized like the rest, at least, be just beginning to be so."

"Now, let there be an indefinite succession of these inferential acts of comparative perception; and it is plain that the last moment will contain objectively the whole series. Let there be, not merely an indefinite succession, but a continuous flow of inference through a finite time; and the result will be a mediate objective consciousness of the whole time in the last moment. In this last moment, the whole series will be recognized, or known as known before."

"From these two immediate perceptions, we gain a mediate, or inferential perception of the relation of all four instants. This mediate perception is objectively, or as to the object being represented, spread over the four instants; but subjectively, or as itself the subject of duration, it is completely embraced in the second moment. (The reader will observe that I use the word instant to mean a point in time, and moment to mean an infinitesimal duration."

"Professor Klein then speaks of "that artistic finish that we admire in Euclid's Elements," and mentions Allman's important historical work. I heartily concur in this estimate of Euclid, and desire to contrast it with the error of Charles S. Peirce, in the Nation, where he speaks of "Euclid's proof (Elements Bk. I., props. 16 and 17)" as "really quite fallacious, because it uses no premises not as true in the case of spherics." Our bright American seems to have forgotten Euclid's Postulate 6 (Axiom 12 in Gregory, Axiom 9 in Heiberg), "Two straight lines cannot enclose a space;" that is, two straights having crossed never recur."

"Conceptual graphs are system of logic based on the existential graphs of Charles Sanders Peirce and the semantic networks of artificial intelligence. The purpose of the system is to express meaning in a form that is logically precise, humanly readable, and computationally tractable."

"Ultimately, the last word is never ours. Peirce said: the meaning of my life is entrusted to others. [...] Which proves that truth is never something definitive; we are always mistaken. On a journey. It is no coincidence that I speak of the “transit of truth.”"

"One of the greatest philosophers of all time."

"Beyond doubt ... he was one of the most original minds of the later nineteenth century and certainly the greatest American thinker ever."

"Peirce was a man of tremendous energy, producing a multitude of ideas, good, bad, and indifferent. He reminds on of a volcano spouting vast masses of rock, of which some, on examination, turn out to be nuggets of pure gold. He holds―and I confess that an examination of scientific inference has made me feel the force of this view―that man is adapted, by his congenital constitution, to the apprehension of natural laws which cannot be proved by experience, although experience is in conformity with them."

"Peirce held that the continuity of space, time, ideation, feeling, and perception is an irreducible deliverance of science, and that an adequate conception of the continuous is an extremely important part of all the sciences. This doctrine he called “synechism,” a word deriving from the Greek preposition that means “(together) with.”"

"James called Peirce the most original thinker of their generation; Peirce placed himself somewhere near the rank of Leibniz. This much is now certain; he is the most original and versatile of America's philosophers and America's greatest logician."

"Peirce was concerned to explicate the idea of meaning whereas James was concerned to explicate the meaning of ideas."

"The principle of interpretation says that "a sign is something by knowing which we know something more" (Peirce). The Peircean idea of semiosis is the idea of an infinite process of interpretation."

"Pierce wrote as a logician and James as a humanist."

"Peirce, to my knowledge, is original and unique in stressing the problem of studying the rules that limit the class of possible theories. Of course, his concept of abduction, like Lorenz’s biological a priori, has a strongly Kantian flavor, and all derive from the rationalist psychology that concerned itself with the forms, the limits, and the principles that provide “the sinews and connections” for human thought, that underlie “that infinite amount of knowledge of which we are not always conscious,” of which Leibnitz spoke. It is therefore quite natural that we should link these developments to the revival of philosophical grammar, which grew from the same soil as an attempt, quite fruitful and legitimate, to explore one basic facet of human intelligence."

"Our whole past experience is continually in our consciousness, though most of it sunk to a great depth of dimness. I think of consciousness as a bottomless lake, whose waters seem transparent, yet into which we can clearly see but a little way."

"Mere imagination would indeed be mere trifling; only no imagination is mere."

"All the evolution we know of proceeds from the vague to the definite."

"Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object."

"Let us not pretend to doubt in philosophy what we do not doubt in our hearts."

"To say, therefore, that thought cannot happen in an instant, but requires a time, is but another way of saying that every thought must be interpreted in another, or that all thought is in signs."

"Every man is fully satisfied that there is such a thing as truth, or he would not ask any question."

"It is ...easy to be certain. One has only to be sufficiently vague."

"The ordinary logic has a great deal to say about genera and species, or in our nineteeth century dialect, about classes. Now a class is a set of objects comprising all that stand to one another in a special relation of similarity. But where ordinary logic talks of classes the logic of relatives talks of systems. A system is a set of objects comprising all that stands to one another in a group of connected relations. Induction according to ordinary logic rises from the contemplation of a sample of a class to that of a whole class; but according to the logic of relatives it rises from the comtemplation of a fragment of a system to the envisagement of the complete system."

"Effort supposes resistance."

"The idea does not belong to the soul; it is the soul that belongs to the idea."

"Do not block the way of inquiry."

"If we endeavor to form our conceptions upon history and life, we remark three classes of men. The first consists of those for whom the chief thing is the qualities of feelings. These men create art. The second consists of the practical men, who carry on the business of the world. They respect nothing but power, and respect power only so far as it [is] exercized. The third class consists of men to whom nothing seems great but reason. If force interests them, it is not in its exertion, but in that it has a reason and a law. For men of the first class, nature is a picture; for men of the second class, it is an opportunity; for men of the third class, it is a cosmos, so admirable, that to penetrate to its ways seems to them the only thing that makes life worth living."

"My original essay, having been written for a popular monthly, assumes, for no better reason than that real inquiry cannot begin until a state of real doubt arises and ends as soon as Belief is attained, that "a settlement of Belief," or, in other words, a state of satisfaction, is all that Truth, or the aim of inquiry, consists in. The reason I gave for this was so flimsy, while the inference was so nearly the gist of Pragmaticism, that I must confess the argument of that essay might with some justice be said to beg the question. The first part of the essay, however, is occupied with showing that, if Truth consists in satisfaction, it cannot be any actual satisfaction, but must be the satisfaction which would ultimately be found if the inquiry were pushed to its ultimate and indefeasible issue. This, I beg to point out, is a very different position from that of Mr Schiller and the pragmatists of to-day. I trust I shall be believed when I say that it is only a desire to avoid being misunderstood in consequence of my relations with pragmatism, and by no means as arrogating any superior immunity from error which I have too good reason to know that I do not enjoy, that leads me to express my personal sentiments about their tenets. Their avowedly undefinable position, if it be not capable of logical characterisation, seems to me to be characterised by an angry hatred of strict logic, and even some disposition to rate any exact thought which interferes with their doctrines as all humbug. At the same time, it seems to me clear that their approximate acceptance of the Pragmaticist principle, and even that very casting aside of difficult distinctions (although I cannot approve of it), has helped them to a mightily clear discernment of some fundamental truths that other philosophers have seen but through a mist, and most of them not at all. Among such truths — all of them old, of course, yet acknowledged by few — I reckon their denial of necessitarianism; their rejection of any "consciousness" different from a visceral or other external sensation; their acknowledgment that there are, in a Pragmatistical sense, Real habits (which Really would produce effects, under circumstances that may not happen to get actualised, and are thus Real generals); and their insistence upon interpreting all hypostatic abstractions in terms of what they would or might (not actually will) come to in the concrete. It seems to me a pity they should allow a philosophy so instinct with life to become infected with seeds of death in such notions as that of the unreality of all ideas of infinity and that of the mutability of truth, and in such confusions of thought as that of active willing (willing to control thought, to doubt, and to weigh reasons) with willing not to exert the will (willing to believe)."

"The third argument, enclosing and defending the other two, consists in the development of those principles of logic according to which the humble argument is the first stage of a scientific inquiry into the origin of the three Universes, but of an inquiry which produces, not merely scientific belief, which is always provisional, but also a living, practical belief, logically justified in crossing the Rubicon with all the freightage of eternity."

"The difference between a pessimistic and an optimistic mind is of such controlling importance in regard to every intellectual function, and especially for the conduct of life, that it is out of the question to admit that both are normal, and the great majority of mankind are naturally optimistic."

"Unless man have a natural bent in accordance with nature's, he has no chance of understanding nature at all."

"The hypothesis of God is a peculiar one, in that it supposes an infinitely incomprehensible object, although every hypothesis, as such, supposes its object to be truly conceived in the hypothesis. This leaves the hypothesis but one way of understanding itself; namely, as vague yet as true so far as it is definite, and as continually tending to define itself more and more, and without limit. The hypothesis, being thus itself inevitably subject to the law of growth, appears in its vagueness to represent God as so, albeit this is directly contradicted in the hypothesis from its very first phase. But this apparent attribution of growth to God, since it is ineradicable from the hypothesis, cannot, according to the hypothesis, be flatly false. Its implications concerning the Universes will be maintained in the hypothesis, while its implications concerning God will be partly disavowed, and yet held to be less false than their denial would be. Thus the hypothesis will lead to our thinking of features of each Universe as purposed; and this will stand or fall with the hypothesis. Yet a purpose essentially involves growth, and so cannot be attributed to God. Still it will, according to the hypothesis, be less false to speak so than to represent God as purposeless."

"An "Argument" is any process of thought reasonably tending to produce a definite belief. An "Argumentation" is an Argument proceeding upon definitely formulated premisses. If God Really be, and be benign, then, in view of the generally conceded truth that religion, were it but proved, would be a good outweighing all others, we should naturally expect that there would be some Argument for His Reality that should be obvious to all minds, high and low alike, that should earnestly strive to find the truth of the matter; and further, that this Argument should present its conclusion, not as a proposition of metaphysical theology, but in a form directly applicable to the conduct of life, and full of nutrition for man's highest growth. What I shall refer to as the N.A. — the Neglected Argument — seems to me best to fulfil this condition, and I should not wonder if the majority of those whose own reflections have harvested belief in God must bless the radiance of the N.A. for that wealth. Its persuasiveness is no less than extraordinary; while it is not unknown to anybody. Nevertheless, of all those theologians (within my little range of reading) who, with commendable assiduity, scrape together all the sound reasons they can find or concoct to prove the first proposition of theology, few mention this one, and they most briefly. They probably share those current notions of logic which recognise no other Arguments than Argumentations."

"Of the three Universes of Experience familiar to us all, the first comprises all mere Ideas, those airy nothings to which the mind of poet, pure mathematician, or another might give local habitation and a name within that mind. Their very airy-nothingness, the fact that their Being consists in mere capability of getting thought, not in anybody's Actually thinking them, saves their Reality. The second Universe is that of the Brute Actuality of things and facts. I am confident that their Being consists in reactions against Brute forces, notwithstanding objections redoubtable until they are closely and fairly examined. The third Universe comprises everything whose being consists in active power to establish connections between different objects, especially between objects in different Universes. Such is everything which is essentially a Sign — not the mere body of the Sign, which is not essentially such, but, so to speak, the Sign's Soul, which has its Being in its power of serving as intermediary between its Object and a Mind."

"Some words shall herein be capitalised when used, not as vernacular, but as terms defined. Thus an "idea" is the substance of an actual unitary thought or fancy; but "Idea," nearer Plato's idea of ἰδέα, denotes anything whose Being consists in its mere capacity for getting fully represented, regardless of any person's faculty or impotence to represent it."

"The word "God," so "capitalised" (as we Americans say), is the definable proper name, signifying Ens necessarium; in my belief Really creator of all three Universes of Experience."

"All nature abounds in proofs of other influences than merely mechanical action, even in the physical world. They crowd in upon us at the rate of several every minute. And my observation of men has led me to this little generalization. Speaking only of men who really think for themselves and not of mere reporters, I have not found that it is the men whose lives are mostly passed within the four walls of a physical laboratory who are most inclined to be satisfied with a purely mechanical metaphysics. On the contrary, the more clearly they understand how physical forces work the more incredible it seems to them that such action should explain what happens out of doors. A larger proportion of materialists and agnostics is to be found among the thinking physiologists and other naturalists, and the largest proportion of all among those who derive their ideas of physical science from reading popular books."

"The third category of which I come now to speak is precisely that whose reality is denied by nominalism. For although nominalism is not credited with any extraordinarily lofty appreciation of the powers of the human soul, yet it attributes to it a power of originating a kind of ideas the like of which Omnipotence has failed to create as real objects, and those general conceptions which men will never cease to consider the glory of the human intellect must, according to any consistent nominalism, be entirely wanting in the mind of Deity."

"Philosophy, as I understand the word, is a positive theoretical science, and a science in an early stage of development. As such it has no more to do with belief than any other science. Indeed, I am bound to confess that it is at present in so unsettled a condition, that if the ordinary theorems of molecular physics and of archaeology are but the ghosts of beliefs, then to my mind, the doctrines of the philosophers are little better than the ghosts of ghosts. I know this is an extremely heretical opinion."

"There never was a sounder logical maxim of scientific procedure than Ockham's razor: Entia non sunt multiplicanda praeter necessitatem. That is to say; before you try a complicated hypothesis, you should make quite sure that no simplification of it will explain the facts equally well. No matter if it takes fifty generations of arduous experimentation to explode the simpler hypothesis, and no matter how incredible it may seem that that simpler hypothesis should suffice, still fifty generations are nothing in the life of science, which has all time before it; and in the long run, say in some thousands of generations, time will be economized by proceeding in an orderly manner, and by making it an invariable rule to try the simpler hypothesis first. Indeed, one can never be sure that the simpler hypothesis is not the true one, after all, until its cause has been fought out to the bitter end. But you will mark the limitation of my approval of Ockham's razor. It is a sound maxim of scientific procedure. If the question be what one ought to believe, the logic of the situation must take other factors into account. Speaking strictly, belief is out of place in pure theoretical science, which has nothing nearer to it than the establishment of doctrines, and only the provisional establishment of them, at that. Compared with living belief it is nothing but a ghost. If the captain of a vessel on a lee shore in a terrific storm finds himself in a critical position in which he must instantly either put his wheel to port acting on one hypothesis, or put his wheel to starboard acting on the contrary hypothesis, and his vessel will infallibly be dashed to pieces if he decides the question wrongly, Ockham's razor is not worth the stout belief of any common seaman. For stout belief may happen to save the ship, while Entia non sunt multiplicanda praeter necessitatem would be only a stupid way of spelling Shipwreck. Now in matters of real practical concern we are all in something like the situation of that sea-captain."

"Thus far, gentlemen, I have been insisting very strenuously upon what the most vulgar common sense has every disposition to assent to and only ingenious philosophers have been able to deceive themselves about. But now I come to a category which only a more refined form of common sense is prepared willingly to allow, the category which of the three is the chief burden of Hegel's song, a category toward which the studies of the new logico-mathematicians, Georg Cantor and the like, are steadily pointing, but to which no modern writer of any stripe, unless it be some obscure student like myself, has ever done anything approaching to justice."

"Understand me well. My appeal is to observation — observation that each of you must make for himself."