C' v.ni i' y i - ■•,:yji:.:w--ii!..!:- 1: Cornell University Library B1609.N5S3 M6 Miscellanies, cliiefiy addresses academi olin 3 1924 029 046 121 The original of tiiis book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/cletails/cu31924029046121 -rilMill! MISCELLANIES; CHIEFLY ADDRESSES, ACADEMICAL AND HISTORICAL. FRANCIS WILLIAM NEWMAN Emeritus Professor of University College, London. LONDON : TRUBNER & CO., 60 PATERNOSTER ROW. 1869. fAU rights reserved.) t President White, Library PREFACE Eequests from time to time have been made for a selec- tion from my anonjonous writings : in consequence, a volimie was planned and arranged. But my Publisher, on learning how much material, hitherto imprinted, lay in my drawers, requested me to furnish it to him in preference. Nov is it all yet exhausted. On the reception given to this volume it must depend, whether others shall foUow. Although the Lectures have received recent correction, I have carefully avoided to alter any allusions which indicate the year or place of original delivery. The last article appeared in the National JRmmo, an unfortunately short-lived quarterly. The Lecture on Elocution was delivered at a Ladies' College. F. W. N . Jwme, 1869. CONTENTS. PAGES. Fragments on Logic - . . i — 64 Lectures on Poetry, — 1. — Topics and Essence of Poetry - - 65 — 81 2.— Forms of Poetry -, - - 82—102 3.— Poetical Description - - 103—122 4. — Poetical Ornament - - 123 — 145 Lectures on the Chief Forms of Ancient Nations. — 1.— The Prehistorical State 146—165 2. — Priestly Kingdoms, especially Egypt 166 — 181 3. — Commercial States, especially Phoenician - - - 182—199 4. — Equestrian Empires — (Scythian — Mesopotamian — Persian) - - 200 — 218 5. — Eepublics, especially Athens 219 — 238 6.— The Eoman Eepublic 239—258 7.— The Eoman Empire - 259—277 A Defence of Carthage - - 278 — 304 Fragment on Liberal Instruction in Mathe- matics - 305 — 315 Elocution as a part of Education - 316 — 333 Essay on National Loans - - - 334 — 356 MISCELLANIES. LOGICAL FEAGMENTS. Notice. — Thirty-four years ago I delivered a short course of lectures on Logic to a class of young pupils. I was induced to publish them. On reading them with fresh eyes I was annoyed at their many blemishes, which nevertheless did not hinder the whole edition from selling in a few years. Various applications were (and are still from time to time) made to me for a new edition of my very unpretending little book; but I was quite indisposed to reprint it without large correction. Correction became an entire new writing; and I at length elaborated it into a treatise called " Ancient and Modern Logic," which had so much pretension to completeness, that I was distressed at my inability to satisfy myseK in one part of what I was then essaying. Before I could complete the part alluded to, Mr. J. Stuaet Mill's Logic came out. It did not supersede mine in my own estimate ; for I was sorry to find myseK at variance with him on some fundamental points. Nevertheless his great powers, learning, and high reputation made it difficult for another book of Logic to enter the market: and if otherwise, to pass him by in silence might seem arro- gant, to enter controversy would have been vexatious. In short I had other studies than Logic to attend to ; and my MS. has in consequence lain in my drawer to this day. Fragments of it nevertheless admit of being separated from the rest, and after final revision laid before the public. Such is the origin of those which follow. (1.) Absteaction. It has often been said that the geometrical conception of a Triangle is devoid of colour and material. It is an abstract Triangle. This is true, only if it mean that the colour and the material are never adverted to in the argument. The same may be said of the thickness of lines, and of absolute magnitude. Practically I accept every geometrical figure as of the same hue as the paper on which it is drawn. If any one remark to me that my triangle is white, or its side an inch long, I reply : " True ; but that is nothing to me geo- metrically." It may immensely help me in conducting si geometrical argument, to have before me a figure which I know to be extremely inaccurate. Crooked and thick lines are to my eye symbols of lines straight and wliolly without thickness. I do not let their crookedness and thickness enter my argument, yet I can ill dispense with the aid which the figure (however rude) gives to argumentation. The same cube the sight of which aids me in Geometry, where its weight is wholly disregarded, may aid me also in Mechanics, where its weight enters my argument, and possibly its form is dis- regarded. Yet iu neither case do I reaUy suppose (or conceive or imagine) it to be really without colour, weight or form. This is just as in a lawsuit about property the stature or weight of the suitors does not enter the argument, yet we do not conceive or imagine suitors without weight or height. It is no peculiarity of abstract Science ; but it belongs to aU argument, as such, to disregard, as irrelevant, munberless particulars of an object. If " conceiving " mean a pictorial setting before the mind, our power of conceiving is very limited : yet that does not affect our power of understanding, and of accurate reasoning. I understand a million as easily as a score, but I cannot (pictorially) conceive a million. I can reason as accurately •concerning a polygon with a , billion sides, as concerning a triangle. I cannot conceive the former, but I can conceive of it, and in reasoning concerning it I may urgently need a rude and obviously inaccurate drawing of it. All this applies to Theology. We cannot conceive Gon, but we can conceive 0/ Him, and reason about Him. Symbols of Him, metaphors concerning Him, notoriously inaccurate, may often, not only not damage, but help our severest reasoning. (2.) Abstract Tekms. To distinguish the Abstract from the Concrete belongs in some sense more to Grammar than to Logic. Adjectives are •often said to be Concrete, as Just, Good, White, and substan- tives derived from them to be Abstract, as Justice, Goodness, Whiteness. Be it so in Grammar ; yet this \s accidental. A language is possible which may have no Adjectives, and not miss them. In some barbaric languages they are rare ; nay, and in the most highly cultivated tongues we see a tendency to discard them. We say : A man of quality, A man of celebrity. Latia says : Moris erat, for, it was customary. In Arabic and Hebrew this superseding of the adjective is noto- rious. On the contrary, Thucydides wonderfully supersedes the abstract noun by the neuter adjective. It is evident that we mean the same thing, neither more nor less, whether we say : " There was a redness on the snow," or, " The snow was some- what red :" they differ as to 'dm form of the expression, which •concerns Grammar ; not in the substance, which alone Logic regards. If we see three red objects, we mentally abstract the colour which they have in comm6n, which we regard as a quality possessed by the objects : but whether we denote that quality by adjective or by substantive, it remains equally an abstraction. Colour, being presented to the eye, so possesses the pic- torial imagination that we seem ahle to conceive it in isolation; but of course our conception is of something with form, though we are not thinking of the form. But when the abstract idea is more purely mental, a pictorial idea may be impossible. We have not in this sense " conceptions" commensurate with ova abstract terms. If I try to think of Beauty, I can but summon to my mind a series of beautiful objects, as, a statue, a prospect, a noble animal, a building. It is not the adjective " beautiful" which is concrete, but the comiined adjective and substantive " beautiful object," which the word concrete was invented to denote. It seems impossible for us to conceive " The Long" in the abstract, (adjective without substantive,) any more than Length. We have to pass rapidly over a mimber of long objects ; a long road, a long stick, a long dis- course, a long illness. Tlius we can answer the old question: Is Justice, Is Virtue, a real existence ? and if so, where is it ? Justice exists, wherever relations exist, which admit of just or unjust actions. The question has no greater mystery or difficulty, than. Does Superiority exist, and if so, where ? Every adjective or abstract noun is the index to a special classifica- tion of objects, external or mental. (Mental phenomena, when obsei-ved and named, are objects to the observing mind, as much as external objects to the perceiving sense.) The indefinite article A An often denotes that a word becomes concrete : as in the difference of Pain and A Pain Belief and A Belief, Action and An Action. This olves sometimes to our language greater perspicuity than has Greek or Latin. The neglect to distinguish Nature from A Nature, Existence or Being from An Existence, A Being, would involve grave error. (3.) Logical Lessons of the Old G-EoiffiTRY. Geometry had the following valuable results. 1. It silenced objection and iacreduHty as to the adaptation of the human mind to Truth. With the barbarian intellect, there is no worse enemy to truth than scepticism as to power of learn- ing, from which must follow listlessness and laziaess. To have established that certain knowledge is attainable ia at least one branch of thought, gave hope that the same must be true in others. 2. It showed one principal condition of success, — coherent and continuous thought in a succession of minds. As in material efforts civilization is characterized by the co-operation of hands, so ia intellectual inquiry must minds co-operate if science is to be attained. 3. In this science peculiar care is taken to distinguish lohat we prove from what ; and how mioch in that which we make our basis is necessary to our superstructure. For instance ; if a square be presented to the eye, every body understands, * that its sides are equal, * that its opposite sides are equidistant or .parallel, ' that its angles are all equal, * that its angles are all right. Which of these is known from which, and how much suffices as hypothesis to secure the rest, it does not concern the vulgar to discuss : but the habit of such inquiry is of great importance. (4.) Pernicious Effects of Geometry on other Science. Geometry, for reasons which need not here be stated, begins from Definitions : hence arose the notion, that to begin from Definition is the very law of Science. Cicero lays this down concerning Duties ; yet in fact he does not do it : his nnnri Hpnsp Tvas too stroticr foT his crfip.d, Pt.ATO desiTed tn st,a.rf; with a general definition of Virtue, from which all the proper- ties and relations of Virtue should be deduced. In the opening of the Menon, he represents Sockatbs as saying : " I am so far from knowing whether virtue is communicable by- instruction, that I do not know even what Virtue is : and when I do not know the essence of a thing, how can I know its qualities ?" According to the modems, we know qualities and properties first, and if we ever learn the essence, it is only at the last. — So Plato would begin a proof of the immortality of the soul by definitions of life and death made offhand. — So Aeistotle eagerly and rapidly (though not without efforts at analysis of fact) sets up definitions of Happiness, of Virtue, of Pleasure. Facts were not neglected, but they were unduly subordinate ; and, it may seem, were rather used to illustrate and confirm opinions formed by independent thought, than treated as the material out of which each Science and its special form was to be evolved. Por the evil may be stated more widely. Prom geometry, as above noticed, they learned the powers of the human mind. True : but they learned to overrate its powers. They imagined that in the highest and most complicated questions, they could (to use a popular phrase) take the bull by the horns ; and rushed by a few bold arguments to a commanding generalization, (comparable to our Laws of Mechanics,) from which they attempted to reason downward to all truth.- — This I find to be Thiklwall's judg- ment in his History of Greece ; and so far as I know any thing of the facts, they lie decidedly in that direction. Pro- fessor Baden Povstell's remarks on even Aeistotle, are to the same effect. (5.) Essence and Chaeactekistics. If there be any set of properties wMdi belong to every individual of a class, and to tlwm, alone, they are called Characteristics. Thus, if it be admitted, that every human being, and no other animal, is competent to laugh or to cook, power of laughter or of cookery becomes a Characteristic of man, and the word Man becomes commensurate with Laughing animal, or Cooking animal: that is, each phrase embraces precisely the same gTOup of individuals. Yet the phrases are not admitted to be identical : for (it is said) the essence of man does not consist in either power; and for this reason neither phrase is a fit definition of man : for the definition ought to tell what is the essence of a thing : — (rather, it should be, what is the essential meaning of a word). But all this does but show more forcibly, that Definition (except provisionally) must come at the end, not at the be- ginning. We classify, and give names, with reference to leading and obvious properties. Whether they are, or are not, possessed exclusively by this class, is matter of outward research and iniinite detail. Definition thus made is apt to be overthrown suddenly by some new discovery. It is easier to know what is n^t the essential meaning of a word, than what is. If we admit the hypothesis for argument's sake, that an animal, of form and other instincts quite unJiuman, were found to practise cookery, no one would on that account allow it to be a man : that is why we decisively reject the power of cookery as an appropriate definition of Man. The fact is clear, that we start from some central point, such as, our own nation, and say : " We are men." How many besides are to be taken in to the family, is long uncertain. While we are wholly ignorant of a foreign language, we may mistake baTbarians for anes. But. little bv little, we enlarge the basis of humanity. Ere long we lay down : " Whoever are in body and mind like enough to TJS to enter into practical relations of life and intermarriage, they are men." The word us forbids this to be logic or science ; but it is a practical test, and quite decisive. Meanwhile we do but grope our way towards the collection of properties, which is to be admitted as the essential meaning of the word Man. (6.) Approximate Definitions. If Definition is the goal at which we drive, it is to be expected that we shall have at first only imperfect and provi- sional definitions. Even in Geometry this has happened ; but in general it ought not to happen there. Euclid's definitions of similar figures, of parallelism, of tangents, of diameters, of centres, are all needlessly limited, and have to be enlarged in the stage beyond. But consider the popular word Level, which seems to belong to elementary Physics. It is at first regarded as a horizontal plane ; that is, a plane perpendicular to the plumb line. But on observing the bulge of the sea, we modify the definition, and perhaps say, that a Level is a spherical surface concentric with the earth. When further research judges the earth to be spheroidal, a Level is said to be a spheroidal surface, similar to and concentric with the earth. Wlien the spheroid equally is found to be inaccurate, the Level is defined as " the surface which at every point is perpendicular to its own plumb hne." Even this may be exchanged in Hydrostatics to " a surface of equal pressure" (below the surface) or " of tw pressure" (at the surface). We cannot wonder that in more recondite sciences, as chemistry and physiology, successive approximation towards a just definition is the only mode of proceeding. (7.) Innate Ideas. Is a man's beard innate ? 'No one would think of using such a phrase. But if any one did use it^ no one would understand him to mean that the beard was connate with him. He could only mean, that it grew out from an inward nature, sooner or later. So if any one call the idea of Justice innate, he does not mean that we have it at birth, but that it grows up in the normal man sooner or later. Nor does it avail to object that experience is needed and a supply of facts from, without, in order that the idea may arise. Of course. So also food is needed from without, in order that the beard may grow from within. The faculty or organs within, the supplies from without, must ia each case co-operate for the result. It is senseless to contest whether experience or the Mind fur- nishes the ideas. Neither alone will suffice. Yet we could not rightly call any developement innate, unless it arose normally to our whole race under normal, nay, inevitable circumstances. Nor is it perhaps wise to use the word Innate without occasion, when it has been so strangely misinterpreted. (8.) Intuition. A man holds out to me the twig of a tree, with green leaves and red cherries, and asks me to name the colours. I reply, — Green and red. — How do you know that ? says he. — Because I see them. No-v? a metaphysician has plenty to say in proof that " sight " is a very compound process ; that the faculty is gradually earned, slowly (perhaps) perfected, and withal very faUible. All true. But that does not make my reply less just : " I know it because I see it." How we earned the faculty of seeing, few (if any of us) can trace. That the 10 faculty is, beyond certain limits, or in unfavourable circum- stances, liable to en'or, we all are aware. But no sound- minded man wiU permit himself to doubt Ms sight without special and powerful reasons. So, when we say, that we know a Truth by Intuition, we do not claim infallibility ; nor do we imply that Intuition is a special primary faculty irresolvible by analysis. Intuition (as any Latin dictionary will show) means simply a gazing upon, and though practi- cally it is confined to the discernment of mental truth, this is but as in other cases we take words of our own language either literally or metaphorically, but reserve for metaphorical use words borrowed from the foreigner. The analogy never- theless of Sight and Intuition, as to their trustworthiness and fallaciousness is easy to understand. Two thousand years passed after Akistotlb, before Berkeley discovered his theory of Vision. Before him neither common men nor philosophers had been aware that we gradually learn to see distance ; but aU had known, that the power of the eye to judge of distance is highly trustworthy within certain limits and very uncertain beyond them. The theory is of interest ; yet it has not given us practical power to see better or more surely, nor has it had the slightest tendency to make us distrust the organ within iihe limits within which we formerly trusted it. Much of this applies to the Mind, — ^to Intuition. If different men's eyes, ostensibly equal and equally favoured by circumstances, report different objects, the accu- racy of sight in one or all is doubted. The same is true when the intuitions of different minds are at variance. But if in any matters our intuitions either agree, or converge towards agreement in proportion to cultivation, we have in so far a basis for truth, just as in the tlpings attested by outward sense. See farther below concerning Specific Infoemants. 11 (9.) Veebai Teuth. Every Dictionary is a storehouse of Verbal Truth. Such are the assertions, that vingt (in French) means twenty (in English) : that roi means king : that a score means twenty, and a myriad ten thousand. Such Verbal truths are also matter of fact, to be attested by external inquiry. But, the meaning of words once settled and agreed upon, many sentences made by their combination are such as no one seeks to verify by external inquiry ; but solely by asking what the separate words mean, and what is the force of grammatical forms. The proposition is then possibly either verified or refuted without looking beyond the words. As extreme examples consider the sentences : " A thing cannot be its opposite. Uneven ground is not even. The crooked is not straight. ISTo taU man is short." He must be a fanatical devotee of Experience, who should confess that he knew these propositions to be - true by Experience alone ; that he had therefore no absolute conviction of them ; only, since (in his own limited Experience) he had never yet found a tall man who was short, (and other observers, even experienced tailors, reported the same thing,) he was disposed not to expect it in the future. — But is it at all less absurd to appeal to Experience in proof that a man six feet high is taUer than a man five feet eight inches ? Surely it is to the words, and the words only, that we look for our ground of conviction. The same must be said of the propositions, A hundred is greater than a score : and : The whole is greater than its part. All Arithmetical truths appear to me to be Verbal ; because the definitions are verbal, and the truths flow out of, and were from the beginning implicated in, the definitions. Some of these truths are extremely obvious, and others very obscure : yet phraseology alone may make the difference. 12 The truth which in one language is obscure, in another might he obvious ; and conversely. Etymology generally warns us what are the definitions of numbers : else it would often be uncertain whether a nume- rical proposition be a definition, or a truth inferred from definition. In Unglish, to say that eighty is eight tens, is a definition ; and that eighty is four score, is a proposition deduced from the definitions of the words. But in French the latter, (if we translate eighty by guatrevingt and score by vingtaine) is an unveUed identical proposition. All arith^ metical truths are nothing but identical propositions veiled ; veiled by mere phraseology ; and are to be proved by substi- tuting one phrase for another which is equivalent. Languages in general agree very nearly in their organiza- tion of numbers. This is referred to our having five fingers on each hand. A six-fingered family, it is thoTight, would have counted by twelves : twenty would have been caUed twelve-eight, and twenty-four twelftwy, (or, a lot,) thirty-six ihirtwy : a hundred and forty-four would have iDeen called by some single short word, like a heap ; which would have been written duodecimaUy 100 : while a hundred and forty^- six would be called " a heap and two," and written 102. It was equally possible to count by nines; then 20 would mean twice nine or eighteen, and 100 would mean eighty-one, while 121 would mean eighty-one -|- eighteen -|- one, that is, a hundred. Manifestly a proposition which with us is aU but a truism, such as " eighteen hundreds make a thousand eight hundred," might be any thing but obvious in the phraseology of a nume- rical system differently organized. In the duodecimal system it would be expressed (symbolically) by 84 x 16 = 1060; in the nonal system by 121 x 20=2420, which here happens to be easier. Take instances however complicated, however lofty, and the propositions (if true) are always reducible to identity by mere substitution of equivalent words. In this consists their proof, and this makes the truth Verbal. A language is possible, in which the numbers might be 13 organized irregularly, vacillating from decimal to nonal or duodecimal or tredeoimal : or again, it might have no organisa- tion at all, but every number, from one to ten thousand, might have a new name, as whoUy unconnected in etymology, one with another, as one two three. In any such language, the proposition " A hundred and one added to two hundred and two makes three hundred and three " (which . with us is obvious) would need elaborate proof. Nevertheless, the nature of the proof would be precisely that, by which we prove that " two and three make &v^." It stands thus : 5=4+l=(3-|-l)-|-l=3 + l-|-l=3 + (l + l)=3+2; by that substitution of equivalents which the definitions permit. Suppose a language with its numerical system- wholly unorganized. A man who taught the people a new artificial way of counting (which he might call the Science of Arith- metic) would instantly facilitate to them problems previously unmanageable. Notation is the new power which he imparts. Our higher Arithmetic, which we call Algebra and Calculus, does the same thing by a more comprehensive notation and proportionably comprehensive results ; and the short cuts to truth thus obtained disguise to. us the fact that in principle these Sciences are on the same plan as our popular Decimal organization of language. As, in order to multiply by ten, we do but add a zero, and think this the easiest of processesy though it would be a stupendous mystery to a people who had no decimal organization of numbers ; so are the compact and powerful processes of algebra to a person wholly untaught in them. A few words may be fitly added concerning its elementary rules. Suppose that in a case similar in kind to the proof that 5=34-2, but more complicated, we brought the equation which is to he proved into the form 7-|-9 + a=7-f9+b, where a and b represent certain combinations of numbers. %^ Inspec- tion shows that we shall have proved identity if we can prove that a=b. Since then this alone remains,^^we strike out 7-1-9 from each side. Out of this comes the eule, that it 14 is permitted to expunge any quantity from both sides of an equation at once. So ; if we had reduced it to the form a + a=b + b, or twice a = twice b, we should see it sufficed to prove that a = b. Hence the eule, that you may divide, each side by 2 (or by 3, or by 4, &c.). These rules, per- fectly simple and obvious as they are, enormously assist the processes ; but certainly ought not to blind us to the fact that i% principle we are arguing just in the same way^ as in the proof that 5=3+2. Of Geometrical truths, beyond the chief Axioms, which are not exclusively Geometrical, few (if any) are verbal. They cannot be inferred from the definitions by a mere sub- stitution of equivalent words. Geometry, like the doctrine of Statics, needs some appeals to Experience, (whether by laws of movement or by other experiment,) before it can get even the ideas of a Straight Line and Plane ; nor can the celebrated difficulty of Parallels long be evaded. Its truths are there- fore, I think, comparable to those of Mechanics, as truths of the outer world, based on Experimental laws ; which is not true of the doctrine of pure Niraiber. Only withia very narrow limits, by a play of useless ingenuity, we may construct some Geometrical propositions which are purely Verbal, re- solvible by a comparison of Definitions. Such is the following : " An equilateral rectangle is a rightangled rhombus." This is not logically comparable to ordinary Geometrical truth, but with such verbal truths as, " The antiquity of the world was the youth of mankind." (10.) Axioms. Axiom in Greek is nothing but the Latin Postulate, viz. a thing claimed. Owing to the celebrity of Euclid, it has passed to mean a sure truth, carrying conviction without proof. All of Euclid's irreprovable Axioms are mere verbal truths. Thus, that Things equal to the same are equal to one 15 another, is verified by the meaning of tlie word Equal. But tlie 12th Axiom, the great scandal of Elementary Geometry, is widely different from the rest. Neither is it a mere verbal truth, nor can it be verified by trials or any direct experience; while to discern its truth by Intuition is too high a demand on the intellect untrained hitherto in Geometry. The moderns in general regard this Axiom as injudicious, and several sub- stitutes are proposed ; of which the honestest* may be : " If, in any plane, a series of points are equidistant from a straight line, their locus is a straight line." We may (with more or less plausibOity, more or less self-satisfaction) dispense with the Axiom by some doctrine of Infinites or of Homogeneity : yet the remarkable fact remains, that the ancients, who knew none of these theories, were as thoroughly convinced of the truth of this Axiom as any of us can be. Perhaps, if they had momentary mistrust of their Intuition, they verified it to themselves by the harmonious results of Geometry, and by the power which it gave them in practical calculations and prediction. Concerning the Straight Line also Euclid has an Axiom, (which might be superseded by a legitimate definition,) and he ought to have had one concerning the Plane. These also we must either discern to be true by gazing at a diagram, or must prove by outward experience. As to straighthess, Instinct suggests its identity with shortness of path. A young dog, making for a gate, runs in as straight a line as he can : yet, it may be replied. Light, moving to his eye in straight lines, probably guides him. To us, the experience of pulling a string tight suffices to demonstrate, that between any two given points there is one path shorter than every other path ; and this will amply suffice to establish the doctrine of the Straight line. So also, easy experiment convinces us, * (Note) I say the honestest ; tecaiise some that have heen proposed are made plausible only by a juggle concerning the -word Parallel, which Euclid has defined in an arbitrary unp9pular sense. Popularly, it means equidistant ; as we see in Parallel Circles on a sphere. 16 that if a polygon have given rigid sides, but moveable joints at their ends, the angles may vary ; that this is true, even when there are four sides ; but if there be only three, then the angles are rigidly fixed : in other words, " If the lengths of the sides of a triangle be given, the angles are determined:" and out of this the doctrine of the Plane may be proved. Yet, resort as we may to these or other improved methods, it is not the less true that men have believed for ages, intensely, absolutely, rightfully, witlmd our methods, which are mere after-thought. Here are three clear instances of the force of Intuition, concerning things not verbal, as the basis of Geometry itself, which , is the historical type of certain, perfect, infallible truth. (11.) Confusion of Verbal with Eeal Tkuth. Verbal Truths are often of great value in argument. For instance, they give warning of a change of nomenclature, which, unless carefully conducted, may involve fallacy. Or again, they bring unreasonableness and injustice into strong light : as, to say, in rebuking religious bigotry : " A heretic is a man. To murder a heretic is to murder a man." Each of these is a purely verbal truth ; yet certainly not superfluous or impotent. Yet if there be any uncertainty whether a statement is meant to be verbal or real (owing to some ambiguity in a word), confusion or juggling may follow. It is an old joke : " Treason never prospers : where 's the reason? Why, when it prospers, none dare call it Treason." The first statement, that " Treason never prospers," sounds like a his- torical proposition, attested by the experience of nations. But the words that follow turn it into a verbal truth, or even truism, from which the whole supposed meaning has evapo- rated. This is a type of a numerous class of statements, — 17 sometimea highly important. Examples may be useful to elucidate the topic. Equal and opposite forces neutralize each other. This is a truism, if we have no criterion of the equality of forces, except the fact that they neutralize each other when directly opposed. But if any independent estimate is attainable, the proposition expresses real truth. Motion always takes place in the direction in which an unimpeded force acts. If we have no means of testing the direction of a force (or perhaps even its existence) except by the motion and its initial direction, this is of course a verbal truth. But it becomes a real truth, if the force be a pressure cognizable prior to motion. The rate of acceleration is proportional to the accelerating force. This might be a verbal truth ; but in the experiments on Attwood's machine it becomes real; for the forces are there weights measurable without any estimate of velocities. A man on every occasion acts according to the strongest motive which at the time urges him. If we have some mode of measuring a priori the strength of motives, this (if true) is a real truth. But if we have no test of their strength but by observing whether (on that occasion) they prevailed, the pro- position merely asserts that on every occasion a man acts as as he does act, and we call those motives (momentarily) strongest which, prevail. He always thinks his own opinion to he right. To the letter this is a verbal truth, fitly called a truism. But people mean to say by it, that the man is too confident that his opinion, based on his present knowledge, may not need to be modified by fuller knowledge and sounder faculties. The will of God is holy, just, and good. If the epithets have an independent measure, this is a real proposition of infinite importance. If we have no measure of their sense, except by an appeal to the "will of God," the proposition evaporates into a truism, which the votaries of every Pagan deity may hold. c 18 Many verbal truths depend in part on Grammar for their verification. They remind us perhaps of the sense implied in a graminatical form. Such are the following. He who is dead, must have died at some time. He who was born, must have been born at s'ome time. If he was murdered, some one must have murdered him. Every son must have had a parent. Every effect must have had a cause. Every cause produces an effect. Design implies a designer. But fallacy arises, when a verbal proposition is confounded with a real proposition, such as the following : He who was born, was previously non-existent. Every child must have had parents. Every phenomenon must have had a cause. Every state of things must have had a cause. Like causes always produce like results. Fitnesses imply design. On the other hand, apparent verbal truths are sometimes made false by the high colour which a word has received : as : A man whose creed is amiss is a mis-creant. Yet such are pftener jokes than fallacies. (12.) Scholastic Definition. Logicians are accustomed to prescribe, that the definition of a term shall recount its genus and its specific difference. Thus to say that Man is a talking animal, or, is a cookino animal, or, is a religious animal, — whether true or false, are aU (in form) logical definitions, because they assign, 1, the genus. Animal ; 2, the specific difference,— to talk, to cook, to be religious. But a definition may be quite unexceptionable, without marking out which part is Genus. Thus, if a Square be defined as " a four-sided figure whose sides are all equal '& 19 and angles all equal," it admits the comments, 1, that the Genus is Rhomhus, and specific difference equal angles : or 2, that the Genus is Kectangle and specific difference equal sides: or 3, that the Genus is Parallelogram and the specific dif- ference equal sides and angles ; or 4, that the Genus is Equi- angular and Equilateral Polygon, and the specific difference the having four sides and angles : or 5, that the Genus is Pour-sided Figure, and the specific difference all the other par- ticulars of the definition. In short, we may divide the definition any how, and always make out one part to he Genus and the other Specific Difference. I take from Johnson's Dictionary the definition of Brothers, " males born of the same parents." Here we may either say, that "those born of the same parents " are Genus, and " to be of male sex " is the Specific Difference. But again, we may say, that " Males " are the Genus ; and that to be born of the same parents is the Specific Difference. Of what imaginable use is such logical doctrine ? In fact, when we pass beyond mathematics, the chief use of definition is to secure ourselves against the anibiguities of words half popular, half scientific. Thus it is with regard to such terms as Material, Spiritual, Natural, Preternatural, Miraculous, Inspired. "Matter" with some means, "that which gravitates;" with others, "that which affects the human senses;" with others, "that which possesses extension and resists pressure ;" with others, " that which exists in space ;" with others perhaps, "that which is subject to geometrical laws;" with others, "that which is incapable of thought or spontaneous action." Nay, the same person may unawares shift from one of these meanings to another in even a short argument. But provided the definition given be self-con- sistent and fixes the meajiing ; be not opposed to popular use, nor so subtle as to embarrass ; we need no scholastic rules concerning it. The common sense of the dictionary-maker is the best guide. g2 20 (13.) Necbssaky Tkuth. There are Ihose who, in telling us that Truth is of two sorts,— Truth that is, and Truth that must be ; — add that the latter is knmon by our "inability to conceive"* the contrary. Yet an ignorant person is perfectly ahle to conceive that the three angles of a triangle are together greater (or together less) than two right angles. He can conceive that the ratio of a sphere to its circumscrihing rectangle is 3J to 4|, as easily as that it is 2 to 3. Were it otherwise, we might, without study or reasoning, reject by a sort of instinct every false mathematical statement, from our mere inability to " conceive" it. "What proof could ever establish this doctrine, I avow myself " unable to conceive." Will this avowal be accepted, in proof that the doctrine is " necessary falsehood." If the ignorant man may fancy that he does conceive what he cannot, or fancy that a thing must be, which only is ; no test of necessary truth can be based on the assumption that the educated man is proof against a like delusion. But though " conceiving " has nothing to do with the question, this is not to say that no truth is justly called Necessary. Verbal truth, such as most of the Axioms of Euclid, is obviously necessary and irreversible. (As said the Greek comedian : To make undone what has been done, is the one thing which even God cannot do.) To say that two and three make four, or that the part is equal to the whole, is not merely contrary to truth, but is a seZ/-contradiction. But though Geometrical Axioms be necessary truth. Geometrical Propositions are not obviously so ; nay, nor are those of Arith- metic, for we may be difi&dent of our processes of proof. Boys, when they have proved an algebraic formula, delight in * (Note.) Hence the recent ungrammatical jargon, " unthinkable." To think is not an active verb. To say, " I think a horse," is neither true nor false, but simple nonsense. The same is true of, " A horse is unthink- able," or, " An assumption is unthinkable." 21 verifying it in detail, and, by actual trials with numbers taken at random, earn a faith in the validity of general reasonings. It must have been the same with the earliest students of Geometry. Confidence in the generalizing power of the human mind, confidence in the validity of certain processes of proof, grows up gradually ; but when it is attained, the truth thus established appears as necessary as its foundations. Then all geometry and algebra appear necessary, because the axioms are necessary. It is alleged that the law of gravity might be other than it is. No doubt we find nothing contradictory or obscure in the hypothesis that it is as the inverse cube of the distance. But when we observe that emanations, as light and heat, neces- sarily vary as the inverse square of the distance, I (for one) cannot doubt that the time will come, when the laws of celestial mechanics, now known, wiU be recognised as equally necessary with the propositions of geometry. But it is asked ; — Are you not improperly assumiag that Space is a something external to our minds, and not a mere mode of apprehension invented by the mind ? So to put the question as to be intelligible to myself, and not run the risk of being said to misrepresent a celebrated speculative doc- triae, is probably beyond my power. Yet the topic is here virtually obtruded on us. Notoriously our interpretation of our sensible experience is often delusive. When we feel a mass of lead to be " heavy," we suppose this quality to inhere in the lead, and are slow to believe that the weight might change, without any change at all in the substance, by a mere change in the globe of the earth or by carrying the lead higher or lower. To reveal to us that we have misinterpreted our senses does not involve us in universal distrust, but only inculcates caution and . wise scepticism : for it does not impugn the sense itself as fundamentally unveracious. But, inasmuch as the earliest revelation, on which aU knowledge whatsoever is built, is the revelation of Matter, of Self And of Space, as things contrasted; I cannot believe that Matter, nor yet that Space, is an illusion of my Mind, without 22 total distrust of every thing. To say that Space has no existence external to my mind, is to say that it is an illusion. Change of phraseology may he good, had, or pedantically ahsurd ; as to say A congeries of forces, instead of a particle of matter ; hut this does not impugn the truthfulness of sense nor the trustworthiness of perception : on the other hand, to deny that Matter is an ohject external to the mind, would be fatal. So too, a change of mere phraseology about empty Space, cannot concern logic ; but fundamentally to deny the existence of Space is to me a proclamation of universal disbelief (14.) Infinity. Infinite is merely the Latin for Boundless, and it is hard to understand by what right any one ever uses the word to mean any thing else. Some metaphysicians appear to go astray from a very superficial understanding of the higher mathematics. When a mathematician tallcs (for instance) of an infinite circle, they have evidently no idea that this means a varying circle, of uncertain magnitude, not merely indefinite, but liable to increase, at Ms mere will, beyond any limits which you may assign. The metaphysician who talks of the Deity as infinite, will often imagine that he employs the term as the mathematician does. This would amount to saying that the Deity is a varying magnitude ; nay, that I can make him vary beyond any limits which you assign.. Alike in mathematics and in metaphysics Infinite means Boundless : so far they agree. In both it is obviously a negative term. To say that Space is infinite, is merely to say,, that it has no^ bounds, — or that we cannot conceive bounds to it : and that is aU that can be meant in applying the word Infinite to- Time or to Deity. He co-exists with Space and Time. Of course, the above does not touch the question, whether it be a delusion in us to suppose Space or Time or Deity to exist at all ; but simply what we mean by calling them Infinite. 23 (15.) Transcendental Truth. Whetlier Coleridge's Literary Eemains, picked up often from his pencillings, represent his deliberate convictions, others may inquire. I find them to reason on the most arduous questions with unshrinking confidence, and when contradictory results are elicited, to put forward as excuse the transcendental nature of the subject, instead of confessing that some mistake has somewhere been made. But who is to draw the limits of Transcendental Truth, — that Elysian field within which a speculator may self-compla- eently indulge in contradictiug himseK, without reproof, as often as he likes ? To imagine our notions to be clear, and the transcendentalist's dim, might seem a gratuitous insult. If his ideas are clearer or juster than ours, his business is to help us to precision and truth, to lessen confusion,^to separate the known from the unknown; not, to teach us to rest com- placently on avowed contradictions. It avails not to plead in excuse, that his words (suppose. Angel, God) inadequately "express the things" intended. Neither do Man and Horse express "things" adequately. It is enough if words express