Finite and infinite

Preface

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Our Heavenly Father has endowed us with the powers of observing, thinking, and reasoning. Therefore we owe Him the duty to discern and think as well as we are able, and to teach with such clearness as is given us ; holding to what appears as Truth, with such firmness and such humility that conscience and judgment shall always be in accord with word and deed, and preserving such unfailing trust in His wisdom and love that we shall never be dismayed because what seems folly to-day was thought to be science yesterday. In the search for truth, error detected becomes the lamp of experience, folly an honest effort to obtain wisdom. To know the one truth is well, but is not the highest moral

6 PREFACE

flight. We must also know the many things that are false or only in part true ; for to know them is wisdom, and having wisdom we shall the more readily find other truth. Thus truth and wisdom wax stronger, subsisting upon each other, and the moral nature of man is subjected to the divine method of evolution.

T. C. R.

Wausau, Wisconsin, October, 1905.

Chapter I

What is the sky? — The author's views sent to Popular Astronomy in 1 894 ; synopsis thereof published and comments of the editor — Herschel, Tyndall, Wallace, and Spring agree that its color proves the sky to be matter of some sort 165

Chapter II

The components of the color of the sky, — matter and light ; where is the matter ; whence comes the light, — from our sun, or from the distant suns? — The Herschel theory and Tyndall' s experiment, —a bottle of sky — The impregnable wall of the Sidereal City — Spring's criticism of Tyndall' s experiment ; the oxygen theory I77 lo CONTENTS

Chapter III Page

"Man's Place in the Universe " — Wallace's theory of a dust-sky — The constant sky and the fickle wind — Inconceivable elements in the Wallace theory — Its self-contradictions — A transparent, opaque cloud that you see through and cannot see through, as you wish — Density in the line of vision — Possible significance of the fact that oxygen is blue l88

Chapter IV

The prevailing idea that the universe is finite — Views of Miss Clerke — Professor Newcomb's mathematical demonstration that an infinite star-system would give us a blazing sky — The tentative attitude of those who hesitate to accept this view — Other possible explanations why the whole sky is not as bright as the sun — Ether may not be a perfect light carrier ; dark suns and other opaque matter might intercept light — Tyndall's experiment with light, and his theory of its transmission 20i

Chapter V

Necessity of examining science as to its views about the ether — Sloane' s statement of the ether theory — Professor Comstock's description of wave-radiation- Humboldt's history of the ether idea ; the akasa of the ancient Hindu philosophers ; transplanted from India to Greece, — " precisely similar to the vibrating light-ether of Huygens, Hooke, and modern physicists " — Irving' s remarks about ether — Has the real question been asked? — The worthless half of experimental science 220

CONTENTS II

Chapter VI Pagb

The other side of the ether question — Spencer heaves a metaphysical rock — Fiske makes a bull's-eye — The French school of physicists is heard in protest — A metaphysical bogie 236

Chapter VII

Is the universe finite ? — Inferences from the phenomenon of star "magnitude" — Newcomb's researches in this field — Young's statement of the facts — The absolute persistence of light ; light from nebulae, and comets' tails — The discovery of light pressure — Going into the realm of the inconceivable to find the problematical effect of a dubious cause — Wallace speaks to the point — Carl Snyder adds a new suggestion — Wallace sums up, and in fancy paints a blue sky upon a "dark background." 249

Chapter VIII

A finite universe and an infinite mass of matter — Opinions of Newcomb, Irving, and Comstock — No disagreement as to the infinite spacial extent of matter — That which is created is necessarily of finite spacial extent — That which is of infinite spacial extent is, of necessity, self-existent 270

Chapter IX

Shape of the star-system ; opinions of Wallace, Young, Newcomb, Comstock, and others — The experiment made by Herschel and Celoria — The camera has reached the farthest boundary of the star-system —

I 2 CONTENTS

PAGB

Our sun's central location among the stars, indicating that stellar evolution began in our neighborhood — Gravitation as a factor in the evolution of the star-system — History of the idea that bodies of matter attract each other — Newton's predecessors in this field of inquiry ; he proved yfha.t o^ers suggested . . 280

Chapter X

The law of gravitation as formulated by Newton ; its three subdivisions — How the energy of gravitation acts ; its mysterious behavior — Why the law of gravitation is inoperative in an infinite mass 293

Chapter XI

Gravitation and the Finite — The potentiality of a zone of empty space — The beginning of evolution, — a boundary between the Finite and the Infinite — Birth of the first sun — Probability that star evolution progresses from within outward — More evidence that the universe is finite — What lies beyond the star system ? . . 304

Chapter XII

The lesson to be learned from a finite universe ; its refutation of the fundamental tenet of Idealism — The fallacies of Idealism ; the danger to Christianity. . . 316

PART I ACTUS DEI

" Every good gift and every perfect gift is from above, and cometh down from the Father of lights, writh whom is no variableness, neither shadow of turning. ' ' — J amis i. 17

Introduction

Destiny is evolution ; evolution is trend ; trend is infinite. Destiny comprehends an infinite number of finite conditions ; it is the new ever replacing the old ; it was, it is, it is to be ; it came ages ago ; it comes to-day ; it is in the future, — waiting. Every mile-stone on the endless thoroughfare of Time is Destiny. Do these mile-stones belong to Man? Or is he only one of them? We cannot answer apart from God. No general system of philosophy has been deemed complete that did not seek after a First Cause. Hence it is that all great philosophers have given to the world their ideas of God, or of something they chose to put in His place.

The effect cannot antedate the cause.

Therefore, as destiny is limitless its cause can have neither end nor beginning. The conditions of to-day, having been caused by those of the past, are themselves to be the causes of future conditions. There was no initial time, no beginning of destiny, no first cause ; for these expressions imply limits,— finites ; but cause, time, destiny, are among the eternals. This little word "first" has sometimes led science and philosophy upon a search for the beginnings of things eternal, the causes of things that were not caused but are self-existent There is no first cause, but there is an Eternal Cause ; all other /^ causes are secondary. As infinites can- xy^ not be caused, the Eternal produces only finites, — forms. These are subject to the laws of evolution. Evolution, therefore, comprehends the destiny of all things which God has caused, — it is the divine method. Man is interested in evolution because it is a revelation of God's methods and purposes. The more man is intellectually trained and morally enlightened the less is his satisfaction with existing knowledge concerning the Creator. He wants to know more, — all that possibly can be learned concerning God. He hopes to obtain from that knowledge inference of God's purpose concerning the human race.

From year to year, the tree of knowledge of good and evil, nurtured in the hopes and fears, the smiles and tears, of Humanity, bears better harvest. Behold, afar, the faint but sure promise of a day when its richest fruit, evolved in the heart-travail and soul-struggle of the ages, will be gathered : — a theology that shall be an all-inclusive philosophy, — a philosophy embracing God and all evidences of what He has done, is doing, and intends to do, with His creation, and for His creatures, — a theology that will convince the intellect, thereby awakening to full fruition in the spirit of man the divine seeds of faith, hope, and love.

Thus our minds o-q out into the future, — the far future, it may be. Yet we are advised by some well-meaning souls that, as we can live only in the present, our best preparation for the future is to devote ourselves solely to present duties, " leaving the future to care for itself until we reach it," These good people believe themselves intensely practical, yet their advice is of a sort that will brinof certain failure to any business man who follows it.

The future must be considered in all that goes to make up earthly life. We take food to satisfy present craving and to preserve ourselves for coming tasks. We care for the child that it may be happy day by day and live to a vigorous and useful manhood. We educate our youths to prepare them for a future which ignorance might find unsolvable. It is only by knowing what may reasonably be expected from to-morrow that we are able to discern our whole duty for to-day.

No argument is to be made here, save incidentally, in support of belief that God exists. Such an argument I hope to present in another book. My purpose now, is to consider, first, such evidences of God's disposition toward the world, as may be found in the history of nature ; and, second, as to whether, in the light of science and philosophy, we may conceive of Him as other than a Person, having such attributes as are, to human understanding, inseparable from personality. Is God a comprehensible and real friend who has imparted to human nature His own standard of right and wrong ? Or is He an inconceivable, unapproachable, unknowable something, of infinite spacial extent and therefore necessarily formless, — the cause of things that we call Evil and Good, Right and Wrong, which, judged by His standard, may be neither, but something not given us to know ?

Such an inquiry, not based upon divine revelation, does not belong to theology in the commonly accepted sense of that word. It pertains, rather, to philosophy. Let us then prepare for it by an acquaintance with some basal principles of philosophy which should govern the method, and mental attitude, of all searchers for truth. This preliminary study will occupy the next four chapters.

Chapter II Truth And Knowledge

Philosophy has expended much wordy war upon the questions, What is Truth ? What is the test of Truth ? The centre of this battle-field in modern times seems to have been the inquiry, Is there or can there be any conscious truth dissociated from experience ? Truth may exist without knowledge, but knowledge cannot be separated from truth. We cannot know what is untrue, and we know only a part of what is true.

Human life and its environments and limitations are such that the sort of knowledge discussed by philosophers is often lacking when one is required to act. In these cases we are compelled to act with only the lamp of probability to guide our footsteps. Thus acting, we acquire further knowledge. We do not seem, however, to be nearing any goal. The search after knowledge does not present to our minds any promise of complete achievement. On the contrary, it impresses us, more and more, as being a process which must go on forever, as new questions, before Unsuspected, are thrust upon us. An illustration of this is the fact that just now science is beginning to concede the necessity of investigating matters occurring, or said to be occurring, in the field known as " Psychic phenomena ;" though it was only a very short time ago that a suggestion of such investigation coming from scientists of repute, such as Crookes and ZoUner, and some others, was received with derision. Thus as we journey on in our search for truth and knowledge an everwidening vista in the infinite realm of the Unknown opens before us. And this is the means whereby Intellect is subjected to the universal law of evolution.

The battle between Hume and Kant seems like many of the contests fought over doctrinal questions in the religious world. Hume insisted that the only way of reaching truth is through uniformity of experience. Kant alleged that no amount of experience can justly be termed uniform, since there is an eternity before us during which exceptions may arise, — that uniformity up to the present time does not make it a " necessary " or "absolute" truth, but only a " contingent " truth, — a truth upon probation, as it were, — a probation which, however, cannot culminate in proof. Kant had his own test of truth, which was to inquire whether its negation is conceivable. For example, I assert that I exist ; can my mind conceive a negation, — that I do not exist? I assert that two straight lines cannot enclose a space ; can my mind conceive that two straight Hnes may enclose a space ? In each case, negation being inconceivable, the assertion becomes a "necessary" or "absolute" truth.

I do not like the idea of coupling adjectives with truth. It does not appear to be an accurate mode of expressing what is meant, for it is not supposable that there are really different sorts of truth, and what is meant is only the attitude of our mind toward the evidences presented, or found, and appearing relevant to the question whether a statement or proposition is or is not the truth. We know that the answer of Truth lies beyond every inquiry. But how will it answer? It it be a question that can be answered "yes" or "no," which of these answers will Truth make? If it be Kant's question, "Can two straight lines enclose a space?" the answer of Truth is instantaneous, —

"No." Why this instantaneous answer? "Experience," replies Hume; "Negation is inconceivable," says Kant.

But suppose we ask a question to which there is no such obvious answer : suppose we ask, "What is the sky?" Can we conceive that there is no answer? No. We know, as well as we know there is a sun, that there is a something which we call sky, and so we can no more conceive that this thing does not exist than we can conceive the possibility of there being no answer to the question, What is it? But how is Truth going to answer this question? In this case, as in a great many others, like the indicted Irishman when asked by the judge, "Are you guilty or not guilty?" we must wait until we hear the evidence. But shall we know then ? Possibly, but more likely all we shall know will be that if Truth made answer, the answer would quite probably be thus, or so. And we should have a "contingent" truth. Now why call this any sort of truth? Why not say it is a hypothesis that has a greater or less appearance of truth ? Truth is one of those exact thincrs which can never assume but one shape. To call it contingent is to compound two incongruous ideas into one which means neither truth nor anything else.

John Fiske, after reviewing the arguments of Hume and Kant, and finding neither of them satisfactory nor complete, joined both together in one universal canon of truth, as follows: —

"A necessary truth is one that is expressed in a proposition of which the negation is inconceivable, after all disturbing conditions have been eliminated.

"A proposition of which the negation is inconceivable is necessarily true in relation to human intelligence.

" This test of inconceivability is the only ultimate test of truth which philosophy can accept as valid.

"Thus the uniformity-test of Hume and the inconceivability-test of Kant are fused together in a deeper synthesis, — the deepest which philosophy can reach. As Mr. Spencer forcibly states it : * Conceding the entire truth of the position that, during any phase of human progress, the ability or inability to form a specific conception wholly depends on the experience men have had; and that, by a widening of their experiences, they may by-and-by be enabled to conceive things before inconceivable to them; it may still be argued, that as at any time the best warrant men can have for a belief is the perfect agreement of all pre-existing experience in support of it, it follows that, at any time, the inconceivableness of its negation is the deepest test any belief admits of. Objective facts are ever impressing themselves upon us ; our experience is a register of these objective facts ; and the inconceivableness of a thing implies that it is wholly at variance with the register. Even were this all, it is not clear how, if every truth is primarily inductive, any better test of truth could exist. But it must be remembered, that whilst many of these facts impressing themselves upon us are occasional; whilst others again are very general ; some are universal, and are unchanging. These universal and unchanging facts are, by the hypothesis, certain to establish beliefs of which the negations are inconceivable.' "

From this it will be seen that Hume, Spencer, and Fiske do not disagree with Kant as to the existence of truth which is " self-evident." They differ merely as to the causes which induce this mental attitude toward that class of truths.

Philosophy, in so far as it attempts to deal with the human mind, is handicapped very much as astronomy was before the invention of the telescope, the camera, and the spectroscope. It has only been able to examine those mental processes which are so very slow that they give plenty of time for observation. It has been forced to recognize the fact of a subconscious condition of mind which acts with inconceivable rapidity, dreaming in an instant such a host of events as would occupy a week of normal thinking. We do not know but that all this truth which we call "self-evident" may come to our objective consciousness through this subconscious mill. Probably we shall never find out in the present life the secrets of this class of mental phenomena. We may find out more or less about them, but when It comes to finding them, laboratories are useless. The tangible cannot measure the intangible.

Chapter III The Absolute Persistence Of Truth

"Absolute" or "necessary" truths, says Fiske, "can be recognized by a simple act of consciousness, as self-evident." And for this very reason they are not susceptible of demonstration or proof. " You believe in your own existence, of which, however, you can furnish no logical demonstration, simply because it is an ultimate fact in your consciousness which underlies and precedes all demonstration," When Fiske follows up this with the statement that, if asked why we believe two straight lines cannot enclose a space, we can only reply that we believe it simply because we must believe it, perhaps a trivial issue might be joined with him. I am, myself, conscious of a momentary 30 process of reasoning when answering" this class of questions; while, when answering such questions as, Do I exist? Is something nothing ? Is there space ? Is there time ? Is the beginning before the end ? Is there a boundary to space, or an end to time ? Is design the same as chance ? Are there such things as motion, heat, light, matter, mind, life? and thousands or tens of thousands of similar questions that might be asked, I am conscious of no mental process or act whatever, save the mere fact that I already possess the answer of Truth. In other words, I am conscious that I am conscious, and that is all.

Nevertheless, whether we become conscious of the truth through demonstration, or have it already in our consciousness, as one of those truths too self-evident to admit of demonstration, we are not conscious that these are different sorts or degrees of truth. The result of demonstration and the ipse dixit of consciousness are equally truth to us, and we are as ready to swear by one as the other. Having pictured to ourselves the two straight lines, and satisfied ourselves that their shape is such that we cannot enclose a space with them, unless we destroy our proposition by changing the shape of one or both lines, we are as fully convinced that it cannot be done as we are of our own existence. So with more elaborate demonstrations. When truth is demonstrated, whether by the elimination of one, two, or twenty inconceivable propositions running counter to the successive steps by which the demonstration is reached, the converse of the result attained is found to be absolutely inconceivable, and we know that Truth has made its answer, — not "relative" truth, not even "absolute" truth, but simply truth. Anything short of this may cause in our minds the attitude of belief. It points, maybe, to the truth, in which case it may lead us to the truth. It points, maybe, to error, in which case its believers will sooner or later find themselves upon the wrong path, and abandon it.

Let the foundation of inconceivability be named experience, or intuition, or what you will ; the fact of inconceivability is the all-important thing. It is, of course, true that "by a widening of their experience men may by-and-by be enabled to conceive things before inconceivable to them," as Spencer says. That statement may be made even stronger and be within the truth, for this may not only be so "by-and-by," but it is so now, inasmuch as men with wide experience are able to conceive things inconceivable to others who have had little experience. Nevertheless, this is also true, — that when it comes to conceiving the possibility of an absurdity involving the mixing of incongruous ideas, such as that nothing can be changed into something, or something into nothing, ability to form this class of conceptions is measured, not by that strengthening of mentality which comes from a "widening of experience," but by that childish credulity which is the companion of ignorance. It is true that learned men have for ages accepted without question beliefs now inconceivable to learned men, — such as that matter is destructible, — can be changed to nothing, and its corollary, — that it might be made from nothing, which Fiske likens to "framing in thought an equation between something and nothing." Such vagaries are not to be dignified by the title of thoughts, or conceptions; they are mere assertions uttered by the mouth, and disregarded by the mind. There have been always people ready to take their beliefs second-hand, as children do, and to resent assault upon such fancied beliefs as heartily as if they were real. Fiske well says:

"The assent of philosophers in past ages, or of uneducated people in our own age, to sundryunthinkable propositions, is not to be cited as evidence that there are minds which can think what is unthinkable. The building up of enormous theories out of purely verbal propositions, which do not correspond to any thinkable concatenation of conceptions, has always been the besetting sin of human philosophizing. ' '

While I do not like the term "absolute" truth because it implies that there may be truth which is less than truth ; nor "relative" truth which suggests a sort of quasi truth that may be true from one stand-point and not from another ; nor " contingent" truth because it signifies that what may be false should be presumed innocent until its guilt is proven, I have no fault to find with the term "self-evident" truth, as it means a truth which proves itself, — fits into human consciousness without demonstration, — nor "demonstrated" or "demonstrable" truth, for these terms do not suggest any qualification of truth itself, they merely imply the process whereby we become conscious of it.

Mind, however, that I am not speaking of that truth which can only be discerned spiritually, or through what has been called revelation. I believe there are truths which can, in the present state of existence, be found by no other means than revelation. But the history of the human race, if it proves anything, proves more convincingly than anything else, the danger and unwisdom of giving credulous attention to those who claim to have found spiritual truth. The human race seems to have stood, from its infancy to the present time, in an attitude of reverent submission before the Spirit-world, with implicit faith that it contains the infinite store-house of Truth, where an answer to every question, whether mundane or spiritual, can be found. Man has always been afraid that some spiritual message should come to him unheeded or unrecognized. This mental attitude of the race toward the spiritual has furnished an excellent opportunity for all sorts of cranks, confidence-men, and insane seekers of notoriety, and they have never been slow to take advantage of it. Hence, we have always presented to us the spectacle of multitudes following such as these, and ready to believe that in heaven there are round triangles and square circles, if their "prophet" declares the fact so to be.

Let us not be so unwise as to think that there are two degrees of truth, one for heaven, and another for earth. What is truth anywhere is, of necessity, truth everywhere. John Stuart Mill, though he was a philosopher, in order to equip himself for attack upon one of Spencer's propositions, appears to have persuaded his own mind, in some inscrutable way, to conceive the possibility that there may be some distant planet where two added to two will make five. If that were so, then "twice two are five" would be truth in that planet and falsehood in our own ; and if this proposition, inconceivable to us now, may be true in some other part of space, it may become conceivable to mankind at some distant period of time. Truth is not of such fluctuating- character. Like the eternal God, to whose kingfdom it belongs, it is the same yesterday, to-day, and forever.

Chapter IV The Theoretical And The Possible

That which is theoretical, and at the same time irrefutably logical, may, nevertheless, lead to a result that is impossible. When this is the case we may be sure that some essential factor was omitted from the premises. Two very ancient and familiar attempts to prove the theoretical possibility of infinite division will illustrate this :

The first relates to the divisibility of numbers,— Divide i by 2, the quotient by 2, that quotient again by 2, and so continue to divide each successive quotient by 2. It is inconceivable that a time will come when you will have a quotient not thus divisible. It is inferred from this that a mathematical number is infinitely divisible, — nay, more, — it is asserted that the human mind cannot conceive of it as being otherwise. Neither the inference nor the assertion will stand the test of cross-examination. In the first place we know that infinite division requires infinite time, and that which requires infinite time can never be done. However long the division be kept up it must always remain a finite result. An infinite task can never be finished. Such a result as the infinite divisibility of a given number is merely impossible. In the second place, as to the assertion that the human mind can form no conception of a number as being less than infinitely divisible, the reverse is true, for the human mind cannot conceive of a number as infinitely divided : — a conception of such actual division being impossible, a conception of infinite divisibility is impossible. We can conceive of the process going on interminably, but we cannot conceive of it as being finished, either by finite or by infinite intelligence or power, inasmuch as an end to eternity is an impossible conception.

Our second illustration comes firom the realm of the material. Let us take Fiske's statement of the current idea as set forth in his "Cosmic Philosophy :"

" Yet we shall find that an absolutely indivisible atom is quite inconceivable by human intelligence. Every such atom, if it exists, must have an upper side and an under side, a right side and a left side, or if spherical, must have a periphery that is conceived as covering some assignable area. Now by no effort of our intelligence can we imagine sides so close together that no plane of cleavage can pass between them ; nor can we imagine a sphere so minute that it cannot be conceived as divisible into hemispheres ; nor can we imagine a cohesive tenacity so great that it might not be overcome by still greater disruptive force such as we can equally well imagine. ' '

This may look like irrefutable logic, and yet it can be easily proved that matter is not and cannot be thus infinitely divisible. In the first place the modes of possible subdivision of matter are all included in the three processes of disruption by pulling asunder, cleavage, and explosive energy. In the second place the postulate with which we must start out is that there exists such a thing as absolute cohesion of particles, and this we do not know, and are beginning to seriously doubt. Still, if we assume that such absolute cohesion exists in any form of matter larger than the corpuscle,^ — a minute subdivision of the atom, we may, for the purpose of the argument, concede that division, as distinguished from the wider separation of things that were never in absolute contact, has been accomplished, and proceed with the work of further division, from the corpuscle downward. In the first place in order to be sure that we are dividing something, and not merely causing two somethings, not in contact, to move farther away from each other by some repeUing force, — as by heat, for instance, — we must assume that all parts of our corpuscle absolutely cohere,— that there is no space between them.