George Boole

“ It will be seen from the above that the forms under which the four categorical propositions A, E, I, O are exhibited in the notation of elective symbols are analogous with those of pure language, i.e. with the forms which human speech would assume, were its rules entirely constructed upon a scientific basis. In a vast majority of the propositions which can be conceived by the mind, the laws of expression have not been modified by usage, and the analogy becomes more apparent, e.g. the interpretation of the equation
is, the class consists of all s which are not-s and of all s which are not-Xs. ”

“ We have now arrived at this step,—that we are in possession of a class of symbols , , , &c. satisfying certain laws, and applicable to the rigorous expression of any categorical proposition whatever. It will be our next business to exhibit a few of the general theorems of the calculus which rest upon the basis of those laws, and these theorems we shall afterwards apply to the discussion of particular examples.
Of the general theorems I shall only exhibit two sets: those which relate to the development of functions, and those which relate to the solution of equations. ”

“ There may be but one individual in a class, or there may be a thousand. There may be individuals common to different classes, or the classes may be mutually exclusive. All elective symbols are distributive, and commutative, and all elective symbols satisfy the law expressed by (3) . ”

“ With these laws there is connected a general axiom. We have seen that algebraic operations performed with elective symbols represent mental processes. Thus the connexion of two symbols by the sign + represents the aggregation of two classes into a single class, the connexion of two symbols as in multiplication, represents the mental operation of selecting from a class those members which belong also to another class , and so on. By such operations the conception of a class is modified. But beside this the mind has the power of perceiving relations of equality among classes. ”

“ When propositions are said to be affected with quantity and quality, the quality is really that of the predicate, which expresses the nature of the assertion, and the quantity that of the subject, which shews its extent.
[9] Partial, because they have reference only to the quantity of the X, even when the proposition relates to the not-X. It would be possible to construct an exact counterpart to the Aristotelian rules of syllogism, by quantifying only the not-X. The system in the text is symmetrical because it is complete. ”

“ This belongs to Case 2, and satisfies the second condition. The extreme Some s becomes All not-s,
∴ All not-s are s.
The other extreme treated in the same way would give
All not-s are s,
which is an equivalent result.
If we confine ourselves to the Aristotelian premises A, E, I, O, the second condition of inference in Case 2 is not needed. The conclusion will not necessarily be confined to the Aristotelian system. ”

“ The personal character of Boole inspired all his friends with the deepest esteem. He was marked by the modesty of true genius, and his life was given to the single-minded pursuit of truth. Though he received a medal from the Royal Society for his memoir of 1844, and the honorary degree of LL.D. from the university of Dublin, he neither sought nor received the ordinary rewards to which his discoveries would entitle him. ”

“ Functions of three symbols,
in which (111) , (110) , &c. are the moduli, and , (1 - ) , &c. the constituents.
From these examples the general law of development is obvious. And I desire it to be noted that this law is a mere consequence of the primary laws which have been expressed in (1) , (2) , (3) .
THEOREM. If we have any equation (..) = 0, and fully expand the first member, then every constituent whose modulus does not vanish may be equated to 0.
This enables us to interpret any equation by a general rule. ”

“ Elizabeth and Frances were both probably still “the girls,” and living with their mother, when Robert Boyle, in 1669, left Oxford for good. Their uncle Robyn, the “deare Squire”—was long ago turned philosopher; something of a valetudinary; a virtuoso of an European fame. Philosophers of all nations flocked to see Mr. Boyle’s experiments. The Royal Society—all intellectual London—was waiting for his coming. ”

“ In 1612, after another visit to London and an audience of King James, he found himself Privy Councillor of State for the Kingdom of Ireland. He was created Lord Boyle, Baron of Youghal, in 1616, and Viscount of Dungarvan and Earl of Cork in 1620. His home life had run parallel with his public services. “My Howses,” “My deare Wife,” “the Children,” “my Famullye,” fill an important place in the Earl’s life and diary and letters; while the wife’s few little epistolary efforts to her husband have only one beginning: he was to her always “My owne goode Selfe.” ”

“ Boyle was still in Oxford in November, when the Duke of York and “many gallants” were going off to join the Fleet; and in December, when the “mighty vote” of £2,500,000 was passed, that Charles II might “be possessed of the dominion at sea, and the disposal of Trade.” [288] Everybody in London was feeling very rich and belligerent—the exact methods by which the money was to be raised not having been yet decided upon. That same November, Oldenburg was begging for Boyle’s communications to the Society on the History of Cold. ”

“ Where were the King and Queen, whose hands Frank and he had kissed? And the gay Court that had clustered about them? And his Father! There was no “Great Earl of Cork” any more; no “greatest family in all London,” living “extraordinarily high,” in the House of the Savoy; no child weddings in the royal chapel at Whitehall. What had become of Frank’s wedding shoes, that had been lent afterwards to poor Kynalmeaky?
There can have been little but troops, and talk of troops, on the dusty summer roads, as Robert Boyle [123] came towards London ”

“ Except for the loss of my father, and that of my own and only son, I have never suffered one more bitter than that inflicted by the death of my dear and noble and most beloved Boyle O'Reilly. He is a great rook torn out of the foundations of my life. Nothing will ever replace that powerful prop, that magnificent buttress. I wish we could make all the people in the world stand still and think and feel about this rare, great, exquisite-souled man until they should fully comprehend him.
Boyle was the greatest man, the finest heart and soul I knew in Boston, and my most dear friend. ”

“ If these two men could be present at a meeting of the Royal Society in Burlington House to-day! Their two portraits are on its walls. Their two faces look down on modern experimental science. Their self-restraint has had its reward.
Already, in 1670, Boyle was at the height of his literary and scientific popularity, the acknowledged chief of the circle of New Philosophers in London. He had long been a valetudinary, saving his strength for his work, and holding himself aloof from uncongenial company. ”

“ Boyle could have lived with much satisfaction to himself.” [186]
His horse would carry him between Oxford and London at any time: each night, on the road, he might lie under some hospitable roof of friend or relative, in mansions set in shady parks, amid flower-gardens and fishponds. And once in London, his sister Ranelagh’s door in the Old Mall was always open to him. And Gresham College, and Mr. Hartlib, and Mr. Clodius, and the rest of the Invisibles would receive him with ecstasy. The Hartlib family had moved to Charing Cross ”

“ In the middle of Salisbury Plain they were surrounded by a party of horse, who would have searched them for “Malignant Letters” such as “use to be about the King’s Picture in a Yellow-Boy.” [134] But the [142] States-Messenger carried them safely through, and they rode on, past weary troops of foot, “poor pressed countrymen,” goaded on by the party of horse. “Amongst them,” wrote Robert Boyle, “I saw one poor rogue, lacqueyed by his wife, and carrying a child upon his shoulders.” Even then, as now, “new models” leave much to be desired. ”

“ Delicious Leeze, in Essex, where Charles and Mary lived, was not far from London. “You shall be absolute master of your own time,” Mary assured him—conscious, no doubt, that Charles did not know much about the New Philosophy. And at Marston Bigot, in Somersetshire, dear Broghill and Lady Pegg, when they were in England, were most excellent company. Marston was not far from Stalbridge, and though Boyle did not now often stay at his manor-house, he liked to keep it in perfect order, for Frank’s sake, who might have it after him. ”

“ After his wife’s death, Richard Boyle, now a landowner and a man of some importance in Munster, [8] had his time full fighting his personal enemies. There were powerful men among them, and by his own account they “all joined together, by their lies, complaining against me to Queen Elizabeth.” ”

“ Robert Boyle, the son of an Earl, and with all moneyed appliances to help him, was one of the early promoters and founders of the Royal Society I spoke of; a noticeable man every way in that epoch of the Ethereges and the Buckinghams and the Gwynnes—devoting his fortune to worthy works; estimable in private life; dignified and serene; tall in person and spare—wearing, like every other well-born Londoner, the curled, long-bottomed wig of France, and making sentences in exposition of his thought which were longer and stiffer than his wigs. ”

“ And again: “We find him to be a man fit to be employed by ourselves.”
Boyle was received at Court, and when he was sent back to Ireland it was as Clerk to the Council of Munster, the very post that Spenser had held. He bought Sir Walter Raleigh’s ship, the Pilgrim, freighted her with victuals and ammunition, sailed in her, “by long seas” to Carrickfoyle, and took up his new work under the splendid Presidentship of Sir George Carew. ”

“ Boyle lived, indeed, much among his books and manuscripts, and in his laboratory. With the help of an amanuensis, he carried on a large correspondence among the new philosophers of the Old World, and the Christian missionaries in the New. The New Englanders wrote to him as their fount of charity: “Right Honourable, charitable, indefatiguable, nursing father.” He had tried to spread the knowledge of the Bible in the East, in Turkish and Arabic, and in the Malayan tongue; and the publication of the Irish Bible was one of the great interests of his later years. ”

“ I pensiori stretti, was the advice he handed on in his charming letter to Milton,—ed il viso sciolto; while to all young Etonians travelling [67] in diplomacy he used to say, Always tell the truth; for you will never be believed.
It is hard to say how much Robert Boyle may have owed to the guidance and talk of Sir Henry Wotton. Boyle remembered him as a fine gentleman who possessed the art of making others so; and it was John Harrison’s methods of teaching that had impressed the boy. ”

“ Page— 119, line— 6, the letter imperfect, like .
Page— 000,„ line— 10, for read .
Page— 120, line— 1, last term, for read .
Page— 128, line— 4 from bottom, for read .
Page— 000,„ line— 6 from bottom, for read .
Page— 000,„ line— 8 from bottom, the letter imperfect, like .
Page— 129, line— 2, for read .
Page— 221, line— 18, for read .
Page— 231, line— 10 from bottom, for read .
Page— 261, line— 2 from bottom, for , read .
Page— 262, line— 22, for and read and .
Page— 270, line— 6 from bottom, for read .
Page— 274, line— 11, for read .
Page— 282, line— 10, dele (1) gives. ”

“ Boyle was unconscious, as he had been from the moment he fell. They stretched him on the doctor’s cot. With the blankets spread underfoot to keep down the dust, the early sun shining in through the lifted flap, Slavens put aside whatever animosity he held against the man and went to work earnestly in an endeavor to save his life. 313
Ten-Gallon showed a nervous anxiety to get away. He wanted to go after his horse; he wanted to go to Boyle’s tent and get breakfast for himself; and then he pressed the necessity of his presence in Comanche to keep and preserve the peace. ”

“ Bishop Burnet, in Mr. Boyle’s funeral sermon, has given an eloquent account of this great philosopher and scholar.
Charles, fourth Earl of Orrery, grand-nephew to Mr. Boyle, was born at Little Chelsea in 1676. He was author of a comedy, entitled, “As you Find it,” and of some verses which discover his wit and poetical genius. Queen Anne created him a peer of Great Britain in 1711, by the title of Lord Boyle, of Marston, in the county of Somerset. His lordship died in 1737. He was the improver of that noble instrument the Orrery, which, in honour of him, was called after his name. ”

“ Boyle had “entertained himself” with a pretty child in her nurse’s arms; and when Sir Geoffrey at last appeared and apologised for having kept his visitor waiting, the young man “pleasantly told him he had been courting a young lady for his wife.” ”

“ The Queen and Prince and the Royalist Court at St. Germains were on tip-toe of expectation; while the young Duke of York had escaped from London abroad, disguised in girl’s clothes. [157] Ormonde was with the Court in France, and Inchiquin in Ireland had declared himself a Royalist. There had been also successive Royalist risings in Wales and in the English counties. Of the Parliamentary Party, Lambert was in the north, Cromwell in Wales; and Fairfax and Ireton—the Kentish rising crushed—were now besieging Colchester.
And what was Robert Boyle doing during this London visit? ”

“ Boyle's was a resort for politicians, journalists, artists, actors, musicians, merchants, gamblers, professional men generally, and sporting men specially. Boyle himself has always been a lover of the horse and a patron of the turf ”