E .584 i39s D MORGAN STATEMENT IN ANSWER TO AN ASSERTION MADE BY SIR WILLIAM HAMILTON THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES J.n STATEMENT IN ANSWER TO AN ASSERTION MADE BY SIR WILLIAM HAMILTON, Bart., Professor of Logic in the University of Edinburgh ; By AUGUSTUS DE MORGAN, Sec. R.A.S., F.C.P.S., Of Trinity College, Cambridge, Professor of Mathematics in University College, London. If any one should be surprised at my printing this statement, on account of the smallness of the pretext for the things alleged against me, I have only to tell him that I am as well aware of the insignificance of that pretext as he is, and that the cogent necessity, as I believe it to be, for taking immediate notice of it, arises from the unquestioned literary celebrity and private worth of a gentleman who was rash enough to tax me with conduct which, could his words be made good, ought to drive me from the society of honest men. The learning and character of the accuser, while they force this publication, make me desirous that it should contain the least possible amount of counter- charge, and cause the least possible annoyance. This statement arises out of an assertion made by Sir William Hamilton*, Professor of Logic in the University of Edinburgh. He charges me with wilfully and knowingly (for so I interpret the words breach of confidence and false dealing) attempting to appropriate as my own certain ideas on the subject of logic, which he avers he communicated to me privately. It is true that he has desired to withdraw the letter in which these imputations were made. But this, as will be pointed out, was done in a manner which amounts only to a proposal of suspension followed by private inquiry, and that after a month's persistence in the charge. I prefer a public inquiry. To the assertion I reply, first, that the substance of all which I have claimed was deposited at Cambridge, and out of my hands, before I ever saw his handwriting ; secondly, that no intelligible communication was ever made by him to me ; thirdly,' that so soon as I received anything which induced me to suppose that we must have had something in common, I gave him full information of what I then had by return of post, even to the means of identifying the papers on which all that * To prevent all mistake, I must desire the reader to avoid a confusion which frequently occurs between the eminent professor of logic in the University of Edinburgh, and my friend Sir William Rowan Hamilton of Dublin, Astronomer Royal for Ireland, and so widely known as one of the first of our mathematicians. development was written which was not already at Cambridge ; fourthly, that I have steong subsequent reason to suppose we really have nothing in common ; fifthly, that his mode of conducting his own case, subsequently to the pro- duction of his charge, is enough to satisfy any reasonable person that he never had any confidence in bis own power of proving it. I shall offer proof of the first, second, and third of the above points. The fourth I can so far establish as to throw upon Sir William Hamilton the onus of proving that he ever published in his lectures or otherwise any of the notions which I have advanced ; indeed, he must in any case furnish this proof. The fifth is matter of opinion, which I must leave to the reader. There is something to say which is not evidence, except to those who know me. I think I can show that I never had the opportunity of copying Sir William Hamilton's ideas ; but, be this how it may, I declare upon my honour that I never derived a single hint of any kind from his communications. I declare also, that I remember (and what is more to the purpose, that I re- membered in February, when I printed it,) that the papers which I gave the means of identifying in January, were written before 1 received any communi- cation from Sir William Hamilton, except a civil note, promising to answer certain questions on the history of logic when he returned to Edinburgh. In any question of mere priority which may arise, these papers of course can only date, at the earliest, from the time at which I announced their existence. ]3ut as regards my own integrity in this matter, the two declarations above made will, as I said, be enough with those who know me. I will now pro- ceed with my statement. Early in the last summer I began to collect matters, which had suggested themselves to me at different times, connected with the theory of the syllogism in logic. My intention was, and is, to enlarge a slight treatise on that sub- ject, which I published a few years ago, into a work on formal logic. In the course of my investigations I fell upon various matters which I thought worth communicating to the Cambridge Philosophical Society. I accordingly sent to that body a Memoir headed, ' On the Structure of the Syllogism, and on the Application of the Theory of Probabilities to questions of Argument and Authority.' That paper is now printed, and will appear in vol. viii. part 3 of the Cambridge Transactions. It is dated October 3, 184G. The Master of Trinity College (to whom I sent it in the first instance, and from whose hands it passed into those of the Secretary of the Society) testifies that he received it on the 6th. The manuscript, and the first proof taken from it, are in existence and can be produced ; neither has any corrections worth noting. By comparison of the dates of my communications from Sir William Hamilton (the first is dated October 7, and the first professing to speak of logic is of November 2), it will be seen that I have no occasion to say any more about the body of the paper. But when the printed proof came into my hands in February last, I made an addition at the end. This addition I assert to be a mere development of what is in the body of the paper ; and on the truth of this the question turns whether I can have borrowed, knowingly or unknowingly, from Sir William Hamilton. If there be any thing new in principle in the addition, then comes the question whether Sir William Hamilton's communication could have given me a hint of that new principle. To enable those who can and will to judge for themselves, I shall presently print 1 . The part of my paper which I assert to contain the principles developed in the addition. 2. The only communication which Sir William Hamilton can make a pretext for his charge, as will distinctly appear in my statement s of our correspondence. 3. All* the addition to my paper which was in any way mentioned in those letters of mine to Sir William Hamilton on which he wrote his charge. But as those who are not inclined to go into such matters will judge by the manner in which the imputation was made and met, I begin by a statement of all that has taken place between us. Sir William Hamilton of Edinburgh stands very high among the culti- vators of mental philosophy in these kingdoms, and is well known to have paid profound attention to the history of that science in all ages. Of his character as a man I never heard anything but the highest praise ; and I most distinctly say, that I am perfectly satisfied he believed the charge when he made it, and that, more or less doubtfully, he believes it up to this moment. At the end of September I wrote to him, without previous acquaintance, to gain some information on existing sources as to the history of technical logic. I think I mentioned my own investigations in general terms. The answer, dated Oct. 7 (received by me four days after my paper had been sent to Cam- bridge), contains the following : " I have for many years taught in my class, what, I think, affords a full extension and, thereby, a complete simplification, of the syllogistic theory ; and through the Notes and Essays of my students, this development of the doctrine has obtained considerable publicity, though I have not yet given it to the world through the press. Should you feel any curiosity on this matter ; or should you wish for a list of the professed Histories of Logic, I will do what I can to satisfy you, on my return home, in about a fortnight hence, . . . ." In my reply, I accepted Sir William Hamilton's offer as to his system of syllogism. The next communication I received was dated Nov. 2 ; it is (why will presently appear) the pretext for the charge made against me, and is printed in the sequel entire, between the two extracts from my paper. I shall reserve my comment on it, and shall point out the reason why it was as unintelligible to me as I predict it will be to the reader. I replied to this letter, with some remarks on parts of the requisites for the prize essay. The next communication is dated Dec. 28, and consisted of 1. A letter. 2. A printed prospectus of Sir William Hamilton's intended work on logic. Nothing turns on this, for the simple reason that my answer contained the most express and formal proof that, come by it how I might, I was then in the most com- plete written possession of all I have since published. The following is an extract from the letter : " I send you what I promised a more articulate statement of my syllogistic theory. I should have made it however less summary, had the prize Essays (for which I sent you the Requisites) been given in ; but the day of delivery is not till the 1st of January. I have ap- pended this statement to my edition of Reid's Works, which has just appeared, and should have sent it to you sooner, but waited for an answer to my application to Mr. , which ought to have come some ten days earlier. That gentleman was a pupil of mine six years ago, and obtained one of the highest honours of the class; he was therefore fully competent to afford you information, which I begged f him to do, in regard to my logical doctrines * To the best of my knowledge and belief: for I kept no copies of my letters previous to March 13. I have no doubt Sir William Hamilton would have supplied them ; but I did not think it necessary to ask, as it is on his communications that the charge was made. f Since that time, Mr. , who wis once my own pupil, called on me one evening after a lecture at University College, and left with me his notes of Sir William Hamilton's lectures. My knowledge of these notes has nothing to do with the present question, since it dates from some weeks after the 1st of January. I shall allude to them again presently. Not to omit mention of any communication which has passed, I should state that Sir William Hamilton, about the time I received these notes, sent me part of his supplement to Reid, con- taining notes into which an enormous amount of digested learning is thrown, but not having B 2 as they were taught so far back When he attended me, besides the twofold wholes in which the syllogism proceeds, the quantification of the predicate, and the effect of that on the doctrine of conversion, on the doctrine of syllogistic moods, on the special syllogistic rules, &c, were topics discussed, and partly given out for exercises. They were, in fact, then mere com- mon-place." The prospectus which accompanied this letter is very full on the results which Sir William Hamilton can produce from his principles ; but gives nothing, I think, certainly nothing intelligible to me, on those principles themselves. There is a curious circumstance about this prospectus. Of the two communications to me, it is avowedly the fuller, the more developed, the " more articulate statement." It begins, moreover, with a profession, that it was drawn up to secure the rights of authorship. And yet Sir William Hamilton could not wait till after January 1 (when the prize essays would have been sent in), but must publish it in December, though thereby obliged, as he says, to make it summary, and, as he implies, so summary, that those who had been and were his own pupils might not get help from it for their prize essays. Why this haste 1 I take it to have been because Sir William Hamilton was prepared to imagine that I, or any one who ventured into his science, might possibly appropriate his ideas. But be this as it may, I hold it rather a strong fact, that the more developed of his two communications was meant to be such as would recal no information for a prize essay to those who had heard the system discussed at many hours' length. As soon as I saw these results, I instantly saw that many of them agreed with my own. I had then no doubt that we possessed something in common; and I said so very distinctly in my reply. As the reader will presently see, this first impression has not been confirmed. Feeling it now time to secure whatever of independent discovery might belong to me, I answered Sir William Hamilton in two letters, dated December 31 and January 1 . In these letters 1. I returned the printed prospectus with the results underlined which my system would produce. 2. I stated that I had a system * written on certain sheets of paper, which I described as to number, size, &c, adding the head words of each page. I felt inclined to get the signature of some good witness put upon these papers ; but at the same time I felt reluctant that Sir William Hamilton should see, if it ever became necessary to produce these papers, that I had been taking precautions against him. I therefore determined to make himself my witness. 3. I stated distinctly the first principles of both my systems, and the syllo- gistic formulae to which they lead. I heard no more, till by note of March 3, Sir William Hamilton informed me that he had been ill for two months, and asked, as I thought, for a sight of the requirements for the prize essay which had been forwarded on Nov. 2. I therefore sent them, and received another note, dated the 8th, correcting my mistake, returning them, and asking for his own letter of Nov. 2. This I sent; and it was returned with another letter (the cause of this statement), dated Edinburgh, March 1 3 ; as follows : " Dear Sir, Your note of the 10th, with its enclosure of my letter, I received this morning. Having again read over the whole correspondence and being now sufficiently recovered, I reference to any system of formal logic, except in the prospectus already mentioned, which is attached to them, and of which I then received a second copy. * This is my second system, described, I assert, in all its essentials, in my paper then at Cambridge, but more developed from these very sheets, in the Addition. I had then quite forgotten how nearly the papers safe at Cambridge contained the matters which I was proving to be in my possession by thus describing them. JB. 5 1$W D Ms proceed briefly to answer your communications of the 31st Dec. and 1st Jan. ult., which reached me after I was laid up by a tedious inflammatory attack. From these (if I am not mistaken) it appears that you claim for yourself the independent re-discovery of the funda- mental doctrine of syllogism, which I privately communicated to you, and of many of its most important consequences more fully developed in the printed prospectus. This claim, though it be only to secondary originality, I am altogether unable to admit. To me, it is manifest, that for the principle of the doctrine you are wholly indebted to my information; and I cannot but think that if you (though recognising always my priority) give forth that doctrine as a speculation of your own, you will be guilty, pardon the plain speaking, both of an injurious breach of confidence towards me and of false dealing towards the public. Am I therefore correct in my understanding of your letters ? I shall be glad to find that I am wrong. " I remain, dear Sir, your most obedient Servant, " VV. Hamilton." There is nothing so pardonable as plain speaking ; in the present instance I owe to it the opportunity of strangling this imputation in its cradle. I replied by return of post, that I saw the propriety of abstaining from fur- ther private correspondence upon the subject in question ; that, when my paper was published, he should have some copies ; and that the hasty manner in which he had expressed his suspicions of an odious charge did not di- minish the respect in which I held him. In a few days I received copies of my paper in the Cambridge Transactions, of which I forwarded a few copies to Edinburgh in a bookseller's parcel. On the 25th of March, judging they had been received, I addressed Sir William Hamilton again, still in terms of respect (indeed, I never have used any others), informing him that I intended to bring his charge to a speedy, and if necessary, a public issue ; and giving him till the 1 Oth of April (or any not unreasonably later date which he should propose) either to retract, or to announce the time and manner in which he would maintain his assertions by public proof: failing his acceptance of either alternative, I informed him that I should draw up a statement myself. The answer, dated the 2 7th, informed me that my paper had not been received, but that the expressions bore exclusive reference to my letters, and that there was no occasion to wait. That (I quote descriptively, in the third person) it would afford him sincere pleasure to be enabled to retract what was written both painfully and unwillingly, but which he could not but write under the con- viction of its truth (if he had said, under the conviction of his ability to prove it, it had been more to the purpose) . That there were only two ways in which this retractation would be for him possible : he must be satisfied either that the meaning of my letters was not what he supposed them unambiguously to express; or that I had been acting under the influence of some intellectual error (that he himself should be in such a predicament is virtually declared impossible, except only by misunderstanding my letters) . That it would truly gratify him to be allowed, on either alternative, to cancel all derogatory expres- sions and sentiments towards one whom otherwise, on many accounts, he was so much inclined to respect. That he cordially sympathised with my feelings on the occasion (I wonder how ; being sure that he believed his own charge, I should have thought he would have taken me to be putting a false front of in- tegrity over a consciousness of wilful theft) : and that assuredly his co-opera- tion should not be wanting to lay the whole relevant documents fairly and faith- fully before the public, on the supposition, always, that my book preferred the same claim as my correspondence. That I might depend on a statement from him, of the grounds on which he felt himself constrained to advance the obnoxious allegations ; and that if his health continued as it was, I should receive it (in manuscript, mind) before the time I specified. But, as his public statement was thus to be communicated to me, of course mine, in like manner, would be communicated to him, before their joint publication ; and 1993231 cither, each made independent of the other, and final; or, if I were allowed to answer him, he should equally be allowed to answer me. He would there- fore, he concluded, before writing, await my determination upon this point. If I had felt any anger at the hasty and utterly groundless imputation which has given me the trouble of making this statement, I think the preceding letter would have removed it. There is something racy about the idea of private declaration and answer before going into court, circumstanced as we were. In cases of amicable literary controversy it would be an excellent plan, and would save a good deal of printing. But the notion of the prosecutor and the accused thief quietly interchanging their notes of evidence, and settling its balance before trial, would, if carried into effect, have vastly tickled the public, never indisposed to find jokes in controversies of this sort. I replied, March 30, by totally declining the arrangement, and calling upon Sir William, as he valued his own honour, either forthwith to retract, or pub- licly to attempt the proof of his accusation. I begged him to understand distinctly, that when I proposed to him to retract, it was because such a mark of consideration Avas usual and proper : but that as far as I was concerned, I had much rather that he should attempt publicly to maintain his words. I added, that I should give no explanations except in print : that had they been asked for in the first instance I would have given them ; but certainly not to a person who had preferred to make facts of his surmises, and inferences of his suspicions. I now certainly thought I should draw him out. From that time to the limit fixed, the 10th of April, I heard no more di- rectly from Sir William Hamilton. But, in a circuitous way, I was offered a sort of retractation on terms. Sir William, I am certain, did not believe me when I said that I would rather he should attempt to maintain than retract. A friend of mine, to whom I had mentioned the whole matter, numbers among his friends one of Sir William Hamilton's, a gentleman of high consideration at Edinburgh. To this gentleman my friend wrote, ex- pressing his regret at the quarrel that was taking place. Some correspondence ensued, to which, as I was no party to it (though I heard extracts read), I should not have alluded, had it not been that Sir William Hamilton became a party to it. And in the course of it he suggested (with a full knowledge, I believe, that it would be conveyed to me), that if I could manage to remember that the papers I had described in one of my letters of Dec. 31 and Jan. 1 were not written till after! had seen his letter, &c. of November 2, he, on his part, could say that I forget the words, but the substance was that I was probably acting only under intellectual confusion, and not under intention to appropriate his ideas. This I simply refused, for two reasons ; I forget whether I gave them or not, but here they are. In the first place, I could not remem- ber what did not happen : though, as I will show presently, it has nothing to do with the matter, yet those papers were Avritten before the letter of No- vember arrived. And in the second place, nothing should ever induce me to buy the withdrawal of such a charge by any concession whatever. I could only meet it by every possible defiance, expressed in the most peremptory terms which would consist with the respect I wished (and wish) to preserve towards great learning, high character, and ill health. When the 10th of April had passed over, I thought it necessary to make one more effort. Accordingly, on the 12th, I wrote to Sir William Hamilton, asking first, whether he was prepared to give me his assurance that he would immediately proceed to the public proof of his charge of March 1 3 ; and secondly, when I might expect his publication. I added, that on failure of an immediate and explicit answer to both questions, I should consider him as linking from the attempt to show cause for his assertions, and should pro- lim him as so shrinking in the public statement which I should immediately shrii claim draw up. On the loth of April I received, dated the 13th, what at first I thought (the course of post making it possible) was the answer: and what Sir William Hamilton allowed to stand in place of an answer for several days : " Dear Sir, As I find that ray letter of the 13th March ult. prevents you from favouring me with an answer to the inquiries which I would beg leave to propose; and as I am anxious that there should be no possible misunderstanding in reference to your claim of being an original excogitator of the doctrine of syllogism founded on the expressed quantity of the predicate; I request your permission to withdraw that letter to hold it unconditionally pro non scripto ; expressing also my regret that the allegations it contains, though only hypo- thetical*, were stated before you had an opportunity of explanation. This being done on my part, I trust on yours, that you will not deny me the satisfaction of answering the ques- tions which I am desirous to put ; in the hope that the whole question may be solved by the detection of a mistake on the one side or the other. 1 remain, dear Sir, " Your most obedient Servant, " W. Hamilton." I acknowledged the receipt of this letter, referring to my statement now before the reader for the further answer, which I proceed to give. In the first place, I never will have anything to do with the doctrine of scriptum pro non scripto. The only Latin I hold by on such a matter in Litera scripta manet. I understand a man when he says he has changed his opinion, or that he will not or cannot maintain what he formerly said he could maintain ; but I do not understand holding what was written as not having been written. If Sir William Hamilton had said in effect, "I have made a charge, which, though I thought it true at the time, I now do not believe," or " which, though I thought I could prove at the time, I do not find I can prove it now," he would have put me in a difficult position. I am not at all prepared to say that even in such a case, I should, looking at all that has passed, have judged it safe to withhold my present statement. But, with reference to the letter above given, I am firmly and clearly of opinion, that I owe this publication to myself, to the Cambridge Society, and to the college in which I teach. In the first place, the withdrawal is made, not because the accuser has found out his mistake, but because he finds the accused will not enter on the matter with him while it stands, except with the whole public to judge. Secondly, it is a suspension, and a suspension only : Sir William Hamilton, who now sees that he came to a decision too hastily, invites me into the court in which he proposes to hear the case. I am to defend myself upon interrogatories, and a hope is expressed that it will turn out to be all a mistake. But if that hope should be disappointed (as ten to one it would be), what must be supposed likely to follow 1 a renewal of the charge ; the suspension will be taken off. Thirdly, the acceptance of a withdrawal of the charge, accompanied by regret expressed for having made it before I could explain, would be an admission on my part, that there was some reasonable prima facie case against me. Now, if Sir William Hamilton should complain that I would not give him grounds for retracting his assertion, I ask him, what were his grounds for making it '! I say he had none but what were utterly futile : I say this before I absolutely know what they were ; a' id once * So far hypothetical that they depend on my " book preferring the same claim as my correspondence," and upon Sir William Hamilton's correctly understanding my letters. Now the book (that is, the Memoir) does prefer that claim ; and my correspondence does, as Sir William Hamilton correctly understands it, make a full declaration of my having indepen- dently arrived at everything new which I did arrive at. Besides, he afterwards informs me that he was constrained to write the derogatory expressions under a conviction of their truth. again I challenge him to produce them, and to let them undergo my public handling. My reader will see that I have been most anxious to be put on mv defence, or as Sir William says, to give explanations refutations I should call them. But not to my respected accuser himself: I have preferred to appeal to Csesar ; and Sir William would have done better if he had answered, Unto Caesar shalt thou go. [This statement was put into the printer's hands on the 1 9th of April, and on the 23rd I received the following note, dated the 20th, being the seventh day after the receipt of the letter in which I had asked for an immediate and explicit answer to the two questions above : "Sir William Hamilton presents his compliments to Professor De Morgan, whose note of the 12th he delayed answering, until he received the reply to his own of the 13th. Sir Wm. Hamilton is surprised, that Mr. De Morgan could think the intimation, he required, even pos- sible, so long as the conciliatory intervention of Mr. De Morgan's friend Dr. was not ended, and ended, in effect*, it was not, until Mr. De Morgan's last note terminated all hope of the difference being resolved into a mistake, on the one side or the other: Sir William Hamilton has now therefore no alternative f, but to state the evidence on which he disputes Mr. De Morgan's claim to an independent rediscovery! of the new principle of syllogism ; and is too confident of the strength of his position, to deny his opponent the advantage of seeing the one case, before publishing the other. Sir William will, therefore, proceed without delay ; and though he has at present much** else to do, hopes, if health permit him, to have his proof written during the present week, and printed in the course of next. There is how- ever a strike at present among the Edinburgh printers. What effect ff this may have in re- tarding the publication Sir William Hamilton is unable to say."] My reader must take notice, that I and my accuser are at issue on some important points of social ethics. He "could not but write," he was "con- strained" to write, under "the conviction of the truth" of his charge. In the day of swords, it was one of the objects of public policy to prevent people from sticking them into each other's bodies upon trivial grounds. We now wear pens : and it is just as great a point to hinder ourselves from sticking them into each other's characters without serious and well-considered reasons. To this end, I have always considered it as one of the first and most special rules, that conviction of the truth of a charge is no sufficient reason for its promulgation. I assert that no one is justified in accusing another until he has his proof ready : and that, in the interval, if indeed it be right that there should be any interval, between the charge and the attempt at substantiation, all the leisure and energies of the accuser are the property of the accused. Such being my mind, I cannot now accept Sir William Hamilton, whose theory and practice are so much at variance with mine, either as an opponent in private controversy, or a judge of the result of mutual explanations. More than this, there has been throughout his correspondence, too much of the feeling that he could hold certain points as assumed, and upon those as- sumptions frame his own conditions, without any reference to whether I granted them or not : and too little of the feeling that when an accusation is * I was no party to that correspondence, as was avouched by the letters themselves. It was terminated before the 10th of April, with a definite announcement, on the part of my friend Dr. , that he saw the matter must become public. The distinction between ter- mination in fact, and termination in effect, is above my comprehension. f This regretful announcement is curious, as addressed to me. What have I been pressing for all along ? X This will not do. Breach of confidence and false dealing must be maintained, or Sir William Hamilton abandons his charge. ** So have I. ft I* need have none at all. Why not print at Glasgow ? 9 made, the bringer of it puts himself into the balance as well as the party whom he accuses. He is not, I am well aware from his writings, apt to think much of the mathematician out of mathematics : but he must bear with me while I quote, without meaning to apply its point offensively, something for his in- struction from the mouth of a mathematician. The late Professor Vince was once arguing at Cambridge against duelling, and some one said, "Well, but, Professor, what could you do if any one called you a liar." " Sir," said the fine old fellow, in his peculiar brogue, " I should tell him to pruv it : and if he did pruv it, I should be ashamed of myself: and if he didn't pruv it, he ought to be ashamed of himself." I will not permit myself to suppose that Sir William Hamilton is either ignorant of, or unconsenting to, the infamy which would attach to any one who had deserved the terms he used for the conduct he described. But I doubt if he be aware of the serious character of his own position, if he persist in declining to attempt the establishment of what he has said more than once he believed in his right to assert, and what, up to this moment, he has only suspended the assertion of, with no other avowed purpose except that of inducing me to put myself on my justification for his private satisfaction, instead of proceeding to a public discussion. [And now my doubt is changed into certainty. For in the letter introduced in [ ], Sir William Hamilton grants me permission to see, if I please, the evidence on which I am accused before I publish my answer. Not because it is my right ; not because it is due to his own character ; but because he feels himself so strong that he can afford it. It is rather a better presumption for my case, that I feel I can afford to do without it. I will not wait for his tardy publi- cation : but, if it ever do appear, I will try the "strength of his position" at once, and the reader shall soon see how I set about it.] I know how it would be if I allowed the matter to end thus. Sir William Hamilton has by this time no doubt put it out of his own power to silence whispers, those whispers which sometimes circulate for a quarter of a century, and are then published in recollections and memoirs, perhaps at a time when neither party can correct them. Of course /have widely announced the pur- port of the letter of March 13: I receive no confidences of that kind. Ac- cordingly I am now determined to prevent all risk as to this matter : and further, to show any one who, having the character which will give weight to his words, may be disposed to attack mine, that he will have to look to his own retreat ; that his bridge shall neither be of gold, nor of my providing. I will now proceed to the extracts already promised. To make the extracts from my paper intelligible, I premise that I consider every proposition as limited, if so mentioned, to a given range of objects of thought ; the whole collection of which I call its universe. If no limitation be intended, then the universe of the proposition is the universe. Contrary names are those one of which must belong to every object of thought, but never both : and they are denoted by large and small letters. Thus x means not-X, and everything is either X or x. And X and Y being two names, and with reference to this order, the following notation is used : (A) or X) Y means < Every X is Y' (E) or X.Y 'NoXis Y' (a) or x) y ' Every x is y ' (e) or x.y 'No x is y' (0) or X : Y means ' Some Xs are n ot Ys ' (1) or XY . . . . ' Some Xs are Ys' (o) or x : y .... ' Some xs are not ys' (i) or xy . . . . ' Some a;s are ys' When Z is introduced instead of X, the same vowels are used. 10 Extract I. From the paper assent to Cambridge before I had any communica- tion what soever from. Sir William Hamilton {without any corrections). Section III. On the quantity of propositions. "The logical use of the word some, as merely ' more than none,' needs no further expla- nation. Exact knowledge of the extent of a proposition would consist in knowing, for in- stance in ' some Xs are not Ys,' both what proportion of the Xs are spoken of, and what pro- portion exists between the whole number of Xs and ofYs. The want of this information compels us to divide the exponents of our proportions into 0, more than not necessarily 1, and 1. An algebraist learns to consider the distinction between and quantity as identical, for many purposes, with that between one quantity and another: the logician must (all writers imply) keep the distinction between and a. however small a may be, as sacred as that between and 1 a : there being but the same form for the two cases. We shall now see that this matter has not been fully examined. "Inference must consist in bringing each two things which are to be compared into com- parison with a third. Many comparisons may be made at once, but there must be this process in every one. When the comparison is that of identity, of is or is not, it can only be in its ultimate or individual case, one of the two following: 'This X is a Y, this Z is the very same Y, therefore this X is this Z ; or else ' This X is a Y, this Z is not the very same Y, therefore this X is not this Z.' And collectively, it must be either ' Each of these Xs is a Y ; each of these Ys is a Z ; therefore each of these Xs is a Z ;' or else ' Each of these Xs is a Y, no one of these Ys is a Z, therefore no one of these Xs is a Z.' " All that is essential then to a syllogism is that its premises shall mention a number of Ys, of each of which they shall affirm either that it is both X and Z, or that it is one and is not the other. The premises may mention more : but it is enough that this much can be picked out ; and it is in this last process that inference consists. "Aristotle noticed but one way of being sure that the same Ys are spoken of in both pre- mises: namely, by speaking of all of them in one at least. But this is only a case of the rule: for all that is necessary is that more Ys in number than there exist separate Ys shall be spoken of in both premises together. Having to make m-\-n greater than unity, when neither m nor n is so, he admitted only that case in which one of the two m or n, is unity and the other is anything except 0. Here then are two syllogisms which ought to have appeared, but do not, Most of the Ys are Xs Most of the Ys are Xs Most of the Ys are Zs Most of the Ys are not Zs .. Some Xs are Zs .'. Some of the Xs are not Zs. And instead of most, or \-\-a, of the Ys, may be substituted any two fractions which have a sum greater than unity. If these fractions be m and n, then the middle term is at least the frac- tion m-\-n 1 of the Ys. It is not really even necessary that all the Ys should enter in one pre- miss or the other: for more than the fraction m-\-n 1 of the whole may be repeated twice. " And in truth it is this mode of syllogising that we are frequently obliged to have recourse to ; perhaps more often than not in our universal syllogisms. ' All men are capable of some instruction ; all who are capable of any instruction can learn to distinguish their right and left hands by name ; therefore all men can learn to do so.' Let the word all in these two cases mean only all but one, and the books on logic tell us with one voice that the syllogism has particular premises, and no conclusion can be drawn. But in fact idiots are capable of no in- struction, many are deaf and dumb, some are without hands: and yet a conclusion is admis- sible. Here m and n are each very near to unity, and m-\-n 1 is therefore near to unity. Some will say that this is a probable conclusion : that in the case of any one person it means there is the chance m that he can receive instruction, and n that one so gifted can be made to name his right and left hand : therefore mXn (very near unity) is the chance that this man can learn so much. " But I cannot see how in this instance the probability is anything but another sort of in- ference from the demonstrable conclusion of the syllogism, which must exist under the pre- mises given. Besides which, even if we admit the syllogism as only probable with regard to any one man, it is absolute and demonstrative in regard to the proposition with which it concludes. " But this is not the only case in which the middle term need not enter universally : this however is matter for the next Section. I now go on to another point." Extract II. " I now take the two cases in which particular premises may give a conclusion : namely \ n XY-f-XY = XZ XY + Y:Z = X:Z /s less or greater. Designation. Syllogism. Condition of its existence. I /r YX + YZ = XZ Yj + Y 2 greater than 1 Jo YX+Y:Z=XZ ij Y:X-fY:Z= xz O oi X:Y+ yz = X:Z Yj+Y,, less than 1 'a yx + yz = xz 0i X:Y+ yz =X:Z 1 ?0 X:Y+Z:Y=XZ " Communication received on the 4th or 5th of November from Sir William Hamilton, being the pretext for his charge that I have, with injurious breach of confidence towards himself , and false dealing towards the public, appropriated his " Fundamental Doctrine of Syllogism" privately commu- nicated to me. " 16 Great King Street, November 2nd, 1846. " Dear Sir, I have been longer than I anticipated in answering your last letter. I now send you a copy of the requisites for the prize Essay, which I gave out to my students at the close of last session. It will show you the nature of my doctrine of syllogism, in one of its halves. The other, which is not there touched on, regards the two wholes, or quantities in which a syllogism is cast. I had intended sending you a copy of a more articulate statement which I meant, at any rate, to have drawn up; but I have not as yet been able to write this. I will send it when it is done. From what you state of your system having ' little in com- mon with the old one,' and from the contents of your First Notions, we shall not, I find, at all interfere, for my doctrine is simply that of Aristotle, fully developed. It will give me great pleasure if I can be of any use, in your investigations concerning the history of Logical doctrines. I have paid great attention to this subject, on which I found, that I could obtain little or no information from the professed historians of Logic ; and my collection of Logical books is probably the most complete in this country. But, as I men- tioned to you in my former letter, it is only in subordinate matters that in abstract Logic there has been any progress. " I remain, dear Sir, very truly yours, " W. Hamilton." Essay on the new Analytic of Logical Forms. Without wishing to prescribe any definite order, it is required that there should be stated in the Essay, 1. What Logic postulates as a condition of its applicability. 2. The reasons why common language makes an ellipsis of the expressed quantity fre- quently of the subject, and more frequently of the predicate, though both have always their quantities in thought. 3. Conversion of propositions on the common doctrine. 4. Defects of this. 5. Figure and Mood of Categorical syllogism, and Reduction, on common doctrine (General statement). 6. Defects of this (General statement). 7. The one supreme Canon of Categorical Syllogisms. 8. The evolution, from this canon, of all the species of Syllogism. 9. The evolution, from this canon, of all the general laivs of categorical Syllogisms. 10. The error of the special laws for the several Figures of Categorical Syllogism. 1 1. How many Figures are there. 12. What are the Canons of the several Figures. 13. How many moods are there in all the Figures : showing in concrete examples, through all the Moods, the unessential variation which Figure makes in a syllogism. (14 was missing, or those which follow 13 were wrong numbered.) 15. What relation do the Figures hold to extension and comprehension. 16. Why have the second and third Figures no determinate major and minor premi-es and two indifferent conclusions ; while the first Figure has a determinate major and minor pre- mise, and a single proximate conclusion. 12 17. What relation do the Figures hold to Deduction and Induction. N.B. This Essay open for competition to all students of the class of Logic and Metaphysics during the last or during the ensuing session. April 15th, 1846. Extract from the Addition to my Paper, taken, as can be shoion, from the papers which I gave the means of identifying in January last, and ivhich papers {though I hold it immaterial) I assert to have been written before I received any logical communication from Sir William Hamilton. (To be compared with the extracts given above.) " Since thi.; paper was written, I found that the whole theory of the syllogism might be deduced from the consideration of propositions in a form in which definite quantity of assertion is given both to the subject and the predicate of a proposition. I had committed this view to paper, when I learned from Sir William Hamilton of Edinburgh, that he had. for some time past publicly taught a theory of the syllogism differing in detail and extent from that of Aristotle. From the prospectus of an intended work on logic, which Sir William Hamilton has recently issued, at the end of his edition of Iteid, as well as from information conveyed to me by himself in general terms, I should suppose it will be found that I have been more or less anticipated in the view just alluded to. To what extent this has been the case, I cannot now ascertain ; but the book of which the prospectus just named is an announcement, will settle that question. From the extraordinary extent of its author's learning in the history of philosophy, and the acuteness of his written articles on the subject, all who are interested in logic will look for its appearance with more than common interest. " The footing upon which we should be glad to put propositions, if our knowledge were minute enough, is the following. We should state how many individuals there are under the names which are the subject and predicate, and of how many of each we mean to speak. Thus, instead of ' Some Xs are Ys,' it would be, ' Every one of a specified Xs is one or other of b specified Ys.' And the negative form would be as in ' No one of a specified Xs is any one of b specified Ys.' If propositions be stated in this way, the conditions of inference are as follows. Let the effective number of a proposition be the number of mentioned cases of the subject: if it be an affirmative proposition, or of the middle term, if it be a negative pro- position. Thus, in ' Each one of 50 Xs is one or other of 70 Ys,' is a proposition, the effect- ive number of which is always 50. But ' No one of 50 Xs is any one of 70 Ys ' is a propo- sition, the effective number of which is 50 or 70, according as X or Y is the middle term of the syllogism in which it is to be used. Then two propositions, each of two terms, and having one term in common, admit an inference when 1. They are not both negative. 2. The sum of the effective numbers of the two premises is greater than the whole number of existing cases of the middle term. And the excess of that sum above the number of cases of the middle term is the number of the cases in the affirmative premiss which are the subjects of inference. Thus, if there be 100 Ys, and we can say that each of 50 Xs is one or other of 80 Ys, and that no one of 20 Zs is any one of 60 Ys ; the effective numbers are 50 and 60. And 50 + 60 exceeding 100 by 10, there are 10 Xs, of which we may affirm that no one of them is any one of 20 Zs mentioned. "The following brief summary will enable the reader to observe the complete deduction of all the Aristotelian forms, and the various modes of inference from specific particulars, of which a short account has already been given. " Let Q, be the whole number of Xs ; and t the number specified in the premiss. Let c be the whole number of Zs ; and w the number specified in the premiss. Let b be the whole number of Ys ; and u and v the numbers specified in the premises of a; and z. Let XT u de- note that each of tXs is affirmed to be one out of u Ys : and X^: Y u that each of tXs, is denied to be any one out of u Ys. Let X signify m Xs taken out of a larger specified number n ; and so on. Then the five possible syllogisms, on the condition that no contraries are to enter either premises or conclusion, are as follows : 1. XT + Z Y t U ' W V 2. XT +YZ t U ' V w 3. Y X,+ Y Z U t V w 4. XT + Z : Y t U W I 5. Y X,+ Z i Y _ w t w v u + v- b, t w " The condition of inference expresses itself; in the X t of the conclusion, m must neither be nor negative. The fhst case gives no Aristotelian syllogism; the middle term never V t+w-b, t Z Z , X . w t + w b, w t Y t + v-b, t Z =Z.^ . X.. IV t + V- 0, w t = X u + v b, t Z = Z a. A X /' w u + vb, w t = X t + v-b, t : Z . w = x ,. , : z . 13 entering universally (of necessity) into any of its forms, under any degree of specification which the usual modes of speaking allow. The other cases divide the old syllogisms among them- selves in the following manner: they are written so as to show that there is sometimes a little difference of amount of specification between the results of different figures, which changes in the reduction from one figure to another. The Roman numerals mark the figures. 2. t = a, t> = 6 Y)Z w +X)Y k =X)Z MjW Barbara I. t a, v = b X)Y u +Y)Z=Z. >t X Bramanlip IV t^.a, v = b *)Vr-X* Y = X , Z , Darii I. /<, v = b X t Y+Y)Z w =Z^X t . Dimaris IV. 3. u = b, v = b Y)X t + ^)Z w =Z bw X bt Darapti III. w