As there are certain temperaments of the body that difpofe a man more to one clafs of difeafes than to another; and, on the other hand, difeafes of that kind, when they happen by accident, are apt to induce the tempera- ment that is fuited to them; there is fome- thing analogous to this in the difeafes of the underftanding.
A certain complexion of underftanding may difpofe a man to one fyflem of opinions more than to another; and, on the other hand, a fyftem of opinions, fixed in the mind by edu- cation or otherwife, gives that complexion to the underftanding which is fuited to them.
It were to be wifhed, that the different fyf- tems that have prevailed could be claffed ac- cording to their fpirit, as well as named from their founders. Lord Bacon has diftinsuifhed falfe philofophy into the fophiftical, the empi- rical, and the fuperftitious, and has made ju- B b 2 dicious ESSAY VI.
^ vm ^' ^'^^^^^^ obfervations upon each of thefe kinds. ^^^ryr■:^^ S"t I apprehend this fubjed deferves to be treated more fully by fuch a hand, if fuch a hand can be found.
ESSAY ESSAY VII.
Of Reafoning in general, and of Demonfiration» 'T"^HE power of reafoning Is very nearly I allied to that of judging; and it is of little confequence in the common affairs of life to diftinguilh them nicely. On this account, the fame name is often given to both. We include both under the name of reafon. The .aifent we give to a propofition is called judg- ment, whether the propofition be felf-evident, or derive its evidence by reafoning from other propofitions.
Yet there is a diflinction between reafoning and judging. Reafoning is the procefs by which we pafs from one judgment to another which is the confequence of it. Accordingly our judgments are diftinguiflied into intuitive, which are not grounded upon any preceding judgment, and difcurfive, v/hich are deduced fromfome preceding judgment by reafoning.
In all reafoning, therefore, there muft be a propofition inferred, and one or more from which it is inferred. And this power of in- ferring, or drawing a conclufion, is only another name I.
ESSAY VII.
CHAP, name for reafoning; the propofitlon inferred hting c2i\\ed the conchijton^ and the propofition, or propofitions from which it is inferred, the preniifcs.
Reafoning may confift of many fteps; the firft conclufion being a premife to a fecond, that to a third, and fo on, till we come to the laft conclufion, A procefs confiding of many fteps of this kind, is fo eafily dillinguiflied from judgment, that it is never called by that name. But when there is only a fingle Itep to the conclufion, the diftindion is lefs obvious, and the procefs is fometimes called judgment, fometimes reafoning.
It is not ftrange, that, in common difcourfe, judgment and reafoning fhould not be very nicely diftinguiflied, fince they are in fome cafes confounded even by Logicians. We are taught in logic, that judgment is exprefled by one propofition, but that reafoning requires two or three. But fo various are the modes of fpeech, that what in one mode is exprefled by two or three propofitions, may in another mode be exprefled by one. Thus I may fay, God is good; therefore good men JJjall be happy. This is reafoning, of that kind which Logici- ans call an enthymeme, confifl:ing of an ante- cedent propofition, and a conclufion drawn from it. But this reafoning may be exprefled by one propofition, thus: Becaiife God is goody good men Jhall be happy. This is what they call a caufal propofition, and therefore exprefles judgment; yet the enthymeme which is rea- foning, expreiles no more.
Reafoning, as well as judgment, mufl: be true or falfej both are grounded upon evi- dence Of Reafoning, and of Demonjlraikn. $7$ dence which may be probable or demonfcrative, ^ ^^ ^'• and both are accompanied with affent or be- lief.
The power of reafoning is juftly accounted one of the prerogatives of human nature; becaufe by it many important truths have been, and may be difcovered, which without it would be beyond our reach; yet it feems to be only a kind of crutch to a limited underftandino-.
o We can conceive an underftanding, fuperior to human, to which that truth appears intui- tively, which we can only difcover by reafon- ing. For this caufe, though we mud afcribe judgment to the Almighty, we do not afcribe reafoning to him, becaufe it implies fome de- fe6t or limitation of underftanding. Even among men, to ufe reafoning in things that are felf-evident, is trifling; like a man going Aipon crvitches when he can walk upon his legs.
What reafoning is, can be underftood only by a man v/ho has reafoned, and who is capa- ble of receding upon this operation of his own mind. We can define it only by fynonimous words or phrafes, fuch as inferring, drawing a conclufion, and the like. The very notion of reafoning, therefore, can enter into the mind by uo other channel than that of reflect- ing upon the operation of reafoning in our own minds; and the notions of premifes and con- clufion, of a fyllogifm, and all its conftituent parts, of an entbymeme, forites, demonflra- tion, paralogifm, and many others, have the fame origin.
It is Nature undoubtedly that gives us the capacity of reafoning. When this is wanting, ^o art nor education can fupply it. But this capacity CHAP, capacity may be dormant through life, like the ^- feed of a plant, which, for want of heat and ' 'moifture, never vegetates. This is probably the cafe of fome favages.
Although the capacity be purely the gift of Nature, and probably given in very different degrees to different perfons; yet the power of reafoning feems to be got by habit, as much as the power of walking or running. Its firffc ex- ertions vve are not able to recollect in ourfelves, or clearly to difcern in others. They are ve- ry feeble, and need to be led by example, and fupported by authority. By degrees it acquires flrength, chiefly by means of imitati- on and exercife.
The exercife of reafoning on various fub- je£ts not only ftrengthens the faculty, but fur- nilhes the mind with a flore of materials. Eve- ry train of reafoning, which is familiar, be- comes a beaten track in the way to many others. It removes many obftacles which lay in our w^ay, and fmooths many roads which we may have occafion to travel in future dif- quifitions.
When men of equal natural parts apply their reafoning power to any fubjedt, the man who has reafoned much on the fame, or on fi- milar fubjeds, has a like advantage over him who has not, as the mechanic wdio has ftore of tools for his work, has of him who has his tools to make, or even to invent.
In a train of reafoning, the evidence of every flep, where nothing is left to be fup- plied by the reader or hearer, muft be imme- diately difcernible to every man of ripe under- (landing who hasadiflinctcomprehenfion of the premifes Of Reafoning, and of Demonjiration. 377 premifes and conclufion, and who compares them C H A P. together. To be able to comprehend, in one view, a combination of fteps of this kind, is more difficult, and feems to require a fuperior natural ability. In all, it may be much im- proved by habit.
But the higheft talent in reafoning is the in-, vention of proofs; by which, truths remote from the premifes are brought to light. In all works of underftanding, invention has the higheft pralfe; it requires an extenfive view of what relates to the fubjeft, and a qiiicknefs in difcerning thofe affipities and relations which may be fubfervient to the purpofe.
In all invention there mull be fome end in view: And fagacity in finding out the road that leads to this end, is, I think, what we call invention. In this chiefly, as I apprehend, and in clear and diftinfl conceptions, confifts that fuperiority of underilanding which v/e call genius.
In every chain of reafoning, the evidence of the laft conclufion can be no greater than that of the weakeft link of the chain, whatever may be the ftrength of the reft.
The moft remarkable diftinclion of reafonings is, that fome are probable, others demonilra- tive.
In every ftep of demonftrative reafoning, the inference is neceifary, and we perceive it to be impofiible that the conclufion fliould not follow from the premifes. In probable reafon- ing, the connection between the premifes, and the conclufion is not neceifary, nor do we per- ceive it to be impoffible that the firfl fliould be true while the laft is falfe.
Henqe CHAP, Hence demonftrative reafoning has no de- ,__ grees, nor can one demonftration be ftronger than another, though, in relation to our fa- culties, one may be more eafily comprehended than another. Every demonftration gives equal flrength to the conclufion, and leaves no poffibiiity of its being falfe.
It vi-as, 1 think, the opinion of all the anci- ents, that demonftrative reafoning can be ap- plied only to truths that are neceffary, and not to thofe that are contingent. In this, I be- lieve, they judged right. Of all created things, the exiftence, the attributes, and con- fequently the relations refulting from thofe at- tributes, are contingent. They depend upon the will and power of him who made them. Thefe are matters of fadt, and admit not of demonftration.
The field of demonftrative reafoning, there- fore, is the various relations of things abftra£l, that is, of things which we conceive, without regard to their exiftence. Of thefe, as they are conceived by the mind, and are nothing but what they are conceived to be, we may have a clear and adequate comprehenfion. Their relations and attributes are necefiary and immutable. They are the things to which the Pythagoreans and Platonifts gave the name of ideas. I would beg leave to borrow this meaning of the word idea from thofe ancient Philofophers, and then I muft agree with them, that ideas are the only objefts about which we can reafon demonftratively.
There are many even of our ideas about which we can carry on no confiderable train, of reafoning. Though they be ever fo well defined and perfedly comprehended, yet their agreements Of Reafoning, and of Dcmonjiration. 2>79 agreements and difagreements are few, and^HAP, thefe are difcerned at once. We may go a flep or two in forming a conclufion with re- gard to fuch objects, but can go no farther. There are others, about which we may, by a long train of demonftrative reafoning, arrive at conclufions very remote and unexpected.
The reafonings I have met with that can be called flridly demonftrative, may, I think, be reduced to two claiTes. They are either meta-r phyfical, or they are mathematical.
In metaphyseal reafoning, the procefs is always fhort. The conclufion is but a ftep or two, feldom more, from the firft principle or axiom on which it is grounded, and the dif- ferent conclufions depend not one upon ano- ther.
It is otherwife in mathematical reafoning. Here the field has no limits. One proportion leads on to another, that to a third, and fo on without end.
If it fliould be afked, why demonftriitive reafoning has fo wide a field in mathematics, while, in other abftract fubjecls, it is confined within very narrow limits? I conceive this is chiefly owing to the nature of quantity, the objeft of mathematics.
Every quantity, as it has magnitude, and is divifible into parts without end, fo, in ref- peft of its magnitude, it has a certain ratio to every quantity of the kind. The ratios of quantities are innumerable, fuch as, a half, a third, a tenth, double, triple. All the pow- ers of number are infufficient to exprefs the variety of ratios. For there are innumerable ratios which cannot be perfeftly expreffed by numbers, fuch as, the ratio of the fide to the diagonal 38o ESSAY Vir.
CHAP, diagonal of a fquare, of the circumference of J-_ a circle to the diameter. Of this infinite va- riety of ratios, every one may be clearly con- ceived, and diftindly exprefled, fo as to be in no danger of being miflaken for any other.
Extended quantities, fuch as lines, furfaces, folids, befides the variety of relations they have ' in refpe£t of magnitude, have no lefs variety in refpect of figure; and every mathe- matical figure may be accurately defined, fo as to diftinguifh it from all others.
There is nothing of this kind in other ob- jects of abftracl reafoning. Some of them have various degrees; but thefe are not capa- ble of meafure, nor can be faid to have an afiignable ratio to others of the kind. They are either fimple, or compounded of a few in- diviiible parts; and therefore, if we may be allowed the expreifion, can touch only in few points. But mathematical quantities being made up of parts without number, can touch in innumerable points, and be compared in innumerable different ways.
There have been attempts made to meafure the merit of adions by the ratios of the affec- tions and principles of adion from which they proceed. This may perhaps, in the way of analogy, ferve to illuilrate what was before known; but I do not think any truth can be difcovered in this way. There are, no doubt, degrees of benevolence, felf-love, and other affections; but, when we apply ratios to them, I apprehend we have no diftinft meaning.
Some demonflrations are called dired, others indireO;. The firfh kind leads direftly to the conclufion to be proved. Of the indi- red fome are called demonflrations ad abfurdunu Of Reafonini^ and of Demonfiration, 381 dum. In thefe the propofition contradictory CHAP, to that which is to be proved is demonftrated ^• to be falfe, or to lead to an abfurdity; whence ^""^''"""^ it follows, that its contradictory, that is, the propofition to be proved, is true. This infe- rence is grounded upon an axiom in logic. That of two contradictory propofitions, if one be falfe, the other muft be true.
Another kind of indirect demonfiration proceeds by enumerating all the fuppofitions that can polTibly be made concerning the pro- pofition to be proved, and then demonftrating, that all of them, excepting that which is to be proved, are falfe; whence it follows, that the excepted fuppofition is true. Thus one line is proved to be equal to another, by prov- ing firft that it cannot be greater, and then that it cannot be lefs: For it muft be either greater, or lefs, or equal; and two of thefe fuppofitions being demonftrated to be falfe, the third muft be true.
All thefe kinds of demonftration are ufed in mathematics, and perhaps fome others. They have all equal ftrength. The dired de- monftration is preferred where it can be had, for this reafon only, as I apprehend, becaufe it is the ftiorteft road to the conclufion. The nature of the evidence and its ftrength is the fame in all: Only we are conducted to it by different roads.
CHAP.
Whether Morality be capable of Demon/iration* WHAT has been faid of demonftrative reafoning may help us to judge of an opinion of Mr. Loc ke, advanced in feve- rai places of his ElTay; to wit, " That morahty " is capable of demonftration as well as ma- " thematics."
In book 3. chap. 1 1. having obferved, that mixed modes, c£pecially thofe belonging to morality, being fuch combinations of ideas as the mind puts together of its own choice, the fignification of their names may be perfecily and exactly defined, he adds, Se6t. 16. " Upon this ground it is that I am " bold to think, that morality is capable of " demonftration as well as mathematics: Since *' the precife real elTence of the things moral " words {land for may be perfectly known, " and fo the congruity or incongruity of the " things themfeives be jcertainly difcovered, in " which confifts perfect knowledge. Nor let *' any one object, That the names of fubllan- " ces are often to be made uie of in morality, " as well as ihofe of modes, from which will " arife obfcurity: For, as to fubftances, when " concerned in moral difcourfes, their divers " natures are not fo much enquired into as " fuppofed: v. g. When we fay that man is *' fubject to law, we mean nothing by man but " a corporeal rational creature: What the real " effence or other quahties of that creature are, *' in this cafe, is no way confidered."
Again, Of Reafonin^, and of Defnonflration. S^^f Again, in book 4. ch. 3. § 18. " The idea^ HAP. " of a Supreme Being, whofe workmanfliip '^ *' we are, and the idea of ourfelves, being " fuch as are clear in us, would, I fuppofe, if '^ duly confidered and purfued, afford fuch " foundation of our duty and rules of action, " as might place morality among the fciences " capable of demonftration. The relation of " other modes may certainly be perceived, as " well as thofe of number and extenfion; and " I cannot fee why they lliould not be capable " of demonftration, if due methods were " thought on to examine or purfue their agree- " ment or difagreement.'* He afterwards gives as inftances two propo- rtions, as moral propofitions of which we may be as certain as of any in mathematics; and confiders at large what may have given the ad- vantage to the ideas of quantity, and made them be thought more capable of certainty and demonftration.
Again, in the 12th chapter of the fame book, § 7, 8. " This I think I may fay, that " if other ideas that are the real as well as no- " minal elTences of their feveral fpecies, were *' purfued in the way familiar to Mathematici- " ans, they would carry our thoughts farther, " and with greater evidence and clearnefs, " than poffibly v/e are apt to imagine. This " gave me the confidence to advance that con- " jefl:ure which I fuggeft, chap. 3. 'viz. That " morality is capable of demonftration as well " as mathematics."
From thefe paffages it appears, that this opi- nion was not a tranfient thought, but what he had revolved in his mind on different occafions. He offers liis reafons for it, illuftrates it by ex- amples.
CHAP, amples, and confiders at length the caufes that have led men to think mathematics more capa- '^'^^ble of demonflration than the principles of morals.
Some of his learned correfpondents, parti- cularly his friend Mr. Molyneux, urged and importuned him to compofe a fyflem of morals according to the idea he had advanced in his Eifay; and, in his anfwer to thefe folicitations, he only pleads other occupations, without fug- gelling any change of his opinion, or any great dilficulty in the execution of what was defired.
The reafon he gives for this opinion is inge- nious; and his regard for virtue, the higheft prerogative of the human fpecies, made him fond of an opinion which feemed to be favoura- ble to virtue, and to have a jufl foundation in reafon.
We need not, however, be afraid, that the intereft of virtue may fuffer by a free and can- did examination of this queflion, or indeed of any queftion whatever. For the interefls of truth and of virtue can never be found in oppo- fition. Darknefs and error may befriend vice, but can never be favourable to virtue.
Thofe Philofophers who think that our de- terminations in morals are not real judgments, that right and wrong in human conduft are only certain feelings or fenfations in the per- fon who contemplates the aftion, mull rejeft Mr. Locke's opinion without examination. For if the principles of morals be not a matter of judgment, but of feeling only, there can be no demonflration of them; nor can any other reafon be given for them, but that men are fo conflituted by the Author of their being, as to con-J Whether Morality be Demonstrable. 385 contemplate with plcafure the aclions we call; virtuous, and with difgucl thofe we call vi- cious.
It is not therefore to be expecled, that the Philofophers of this clafs fliould think this opi- nion of Mr. Locke worthy of examination, fince it is founded upon what they think afalfe hypothefis. But if our determinations in mo- rality be real judgments, and, like all other judgments, be either true or falfe, it is not un- important to underftand upon what kind of evidence thofe judgments reft.
The arguments offered by Mr. Locke, to jfliow that morality is capable of dcmonftration, is, " That the precife real effence of the things *' moral words ftand for, may be perfectly " known, and fo the congruity or incongruity " of the things themfelves be perfectly difco- " vered, in which confifts perfe£t knowledge.'* It is true, that the field of dcmonftration is the various relations of things conceived ab- ftracliy, of which we may have perfect and adequate conceptions. And Mr. Locke, taking all the things which moral words ftand for to be of this kind, concluded that morahty is as capable of dcmonftration as mathematics.
I acknowledge, that the names of the vir- tues and vices, of right and obligation, of liberty and property, ftand for things abftracl, which may be accurately defined, or, at leaft, conceived as diftindly and adequately as ma- thematical quantities. And thence indeed it follows, that their mutual relations may be per- ceived as clearly and certainly as mathematical truths.
Of this Mr. Locke gives two pertinent ex- amples: The firft, " where there is no pro- J 86 ESSAY VIL CHAP." perty, there is no injudice, is, fays he, 2: ^ • '' propofition as certain as any demonftration " in Euclid."
When injuftice is defined to be a violation of property, it is as neceffary a truth, that there can be no injuflice where there is no pro- perty, as that you cannot take from a man that which he has not.
The fecond example is, " That no govern- " ment allows abfolute liberty.'* This is a truth no lefs certain and necefiarv.
Such abilraci: truths I would call metaphyfical rather than moral. We give the name of ma- thematical, to truths that exprefs the relations of quantifies confidered abflractly; all other abilracl truths may be called metaphyfical. But if thofe mentioned by Mr. Locke are to be called moral truths, I agree with him that there are many fuch that are necelfarily true, and that have all the evidence that mathematical truths can have.
It- ought however to be remembered, that, as was before obferved, the relations of things abftracl, perceivable by us, excepting thofc of mathematical quantities, are fev/, and for the m.oit part immediately difcerned, fo as not to require that train of reafoning which we call demonftration. Their evidence refembles more that of mathematical axioms than mathematical propofitions.
This appears in the two propofitions given as examples by Mr. Locke. The firft follows immediately from the definition of injulHce; the fecond from the definition of govern- ment. Their evidence may more properly be called intuitive than demonflrativc: And this I apprehend to be the cafe, or nearly the cafe of of Whether Morality he Demonstrable. 387 of all abftraft truths that are not mathematical, ^ ^ ^^- TT for the reafon given in the laft chapter. v,-v-^ The propofitions which I think are properly called moral, are thofe that affirm fome moral obligation to be, or not to be incumbent on one or more individual perfons. To fuch pro- portions Mr. Locke's reafoning does not ap- ply, becaufe the fubjecls of the propofition are not things whofe real eflfence may be perfectly known. They are the creatures of God; their obligation refults from the conflitution which God hath given them, and the circumftances in which he hath placed them. That an in- dividual hath fuch a conflitution, and is placed in fuch circumftances, is not an abftracl and neceflary, but a contingent truth. It is a mat- ter of fad, and therefore not capable of demon- ftrative evidence, which belongs only to ne- ceflary truths.
The evidence which every man hath of his own exiftence, though it be irrefiftible, is not demonflrative. And the fame thing may be faid of the evidence which every man hath, that he is a moral agent, and under certain moral obligations. In like manner, the evi- dence we have of the exiftence of other men is not demonftrative; nor is the evidence we have of their being endowed with thofe faculties which make them moral and accountable agents.
If man had not the faculty given him by God of perceiving certain things in condudtto be right, and others to be wrong, and of per- ceiving his obligation to do what is right, and not to do what is wrong, he would not be a moral and accountable being.
If man be endowed with fuch a faculty^ there mud be fome things, which, by this fa* cuUy, are immediately difcerned to be right, and others to be wrong; and therefore there muft be in morals, as in other faiences, firfl principles, which do not derive their evidence from any antecedent principles, but may be faid to be intuitively difcerned.
Moral truths, therefore, may be divided into two clafles, to wit, fuch as are felf-evident to every man whofe underftanding and moral faculty are ripe, and fuch as are deduced by reafoning from thofe that are felf evident. If the firft be not difcerned without reafoning, the lad never can be fo by any reafoning.
If any man could fay with fmcerity, that he is confcious of no obligation to confult his own prefent and future happinefs; to be faithful to his engagements; to obey his Maker; to in- jure no man; I know not what reafoning, ei- ther probable or demonftrative, I could ufe to convince him of any moral duty. As you cannot reafon in mathematics with a man who denies the axioms, as little can you reafon with a man in morals who denies the firft principles of morals. The man who does not, by the light of his own mind, perceive fome things in condu6t to be right, and others to be wrong, is as incapable of reafoning about morals as a blind man is about colours. Such a inan, if any fuch man ever was, would be no m^oral agent, nor capable of any moral obligation.
Some firfl principles of morals muft be im- mediately difcerned, otherwife we have no foundation on which others can reft, or from v;hich we can reafon.
Every Whether Morality be Demonstrable. 3^9 Every man knows certainly, that, what heC H Ai»- approves in other men he ought to do in Hke ^"^• circumftances, and that he ought not to do '-""^^""^ what he condemns in other men. Every man knows that he ought, with candour, to ufe the beft means of knowing his duty. To every man who has a confcience, thefe things are felf-evident. They are immediate dictates of our moral faculty, which is a part of the human conftitution; and every man condemns himfelf, whether he will or not, when he know- ingly ads contrary to them. The evidence of thefe fundamental principles of morals, and of others that might be named, appears therefore to me to be intuitive rather than demonflrative.
The man who ads according to the didates of his confcience, and takes due pains to be rightly informed of his duty, is a perfed man with regard to morals, and merits no blame, whatever may be the imperfedions or errors of his underflanding. He who knowingly ads contrary to them is confcious of guilt, and felf-condemned. Every particular adion that falls evidently within the fundamental rules of morals is evidently his duty; and it requires 310 reafoning to convince him that it is fo. , Thus I think it appears, that every man of Ixommon underflanding knows certainly, and without reafoning, the ultimate ends he ought to purfue, and that reafoning is neceffary only to difcover the mod proper means of attaining them; and in this, indeed, a good man may often be in doubt.
Thus, a Magiflrate knows that it is his duty to promote the good of the community which hath.entrufted him with authority; and to offer to prove this to him by reafoning would be to affront CHAP. afFront him. But whether fuch a fcheme of Jl'.^ condu6t in his office, or another, may befl ferve that end, he may in many cafes be doubt- ful. I beheve, in fuch cafes, he can very rarely have demonflrative evidence. His con- fcience determines the end he ought to purfue, and he has intuitive evidence that his end is good; but prudence muft determine the means of attaining that end; and prudence can very rarely ufe demonflrative reafoning, but muft reft in what appears moft probable.
I apprehend, that in every kind of duty we owe to God or man, the cafe is fimilar; that is, That the obligation of the moft general rules of duty is felf-evident; that the applica^ tion of thofe rules to particular adions is often no lefs evident; and that, when it is not evi- dent, but requires reafoning, that reafoning can very rarely be of the demonftrative, but m.uft be of the probable kind. Sometimes it depends upon the temper and talents and cir- cumftances of the man himfclf; fometimes up- on the character and circumftances of others fometimes upon both; and thefe are things which admit not of demonftratlon.
Every man is bound to employ the talents which God hath given him to the beft purpofe; but if, through accidents which he could nc forefee, or ignorance which was invinciblt they be lefs ufefullv employed than they mis;! have been, this will not be imputed to him b^ bis righteous Judge.
It is a common and a juft obfervation, ths the man of virtue plays a furer game in ordej to obtain his end than the man of the work It is not, however, becaufe he reaf^ns better concerning the means of attaining his end; for Whether Morality be Demonstrable. 391