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George Boole

Data de nascimento: 2. Novembro 1815
Data de falecimento: 8. Dezembro 1864

George Boole foi um matemático, filósofo britânico, criador da álgebra booleana, fundamental para o desenvolvimento da computação moderna.

Citações George Boole

„That logic, as a science, is susceptible of very wide applications is admitted; but it is equally certain that its ultimate forms and processes are mathematical.“

—  George Boole

Fonte: 1850s, An Investigation of the Laws of Thought (1854), p. 12; Cited in: William Stanley Jevons (1887) The Principles of Science: : A Treatise on Logic and Scientific Method. p. 155

„It is upon the foundation of this general principle, that I purpose to establish the Calculus of Logic, and that I claim for it a place among the acknowledged forms of Mathematical Analysis,“

—  George Boole

Fonte: 1840s, The Mathematical Analysis of Logic, 1847, p. iii
Contexto: That to the existing forms of Analysis a quantitative interpretation is assigned, is the result of the circumstances by which those forms were determined, and is not to be construed into a universal condition of Analysis. It is upon the foundation of this general principle, that I purpose to establish the Calculus of Logic, and that I claim for it a place among the acknowledged forms of Mathematical Analysis, regardless that in its object and in its instruments it must at present stand alone.

„I am now about to set seriously to work upon preparing for the press an account of my theory of Logic and Probabilities“

—  George Boole

Letter to William Thomson (2 January 1851), indicating his early work on what has since become known as Boolean logic.
1850s
Contexto: I am now about to set seriously to work upon preparing for the press an account of my theory of Logic and Probabilities which in its present state I look upon as the most valuable if not the only valuable contribution that I have made or am likely to make to Science and the thing by which I would desire if at all to be remembered hereafter.

„It appeared to me that, although Logic might be viewed with reference to the idea of quantity, it had also another and a deeper system of relations. If it was lawful to regard it from without, as connecting itself through the medium of Number with the intuitions of Space and Time, it was lawful also to regard it from within, as based upon facts of another order which have their abode in the constitution of the Mind.“

—  George Boole

Fonte: 1840s, The Mathematical Analysis of Logic, 1847, p. i: Lead paragraph of the Preface; cited in: R. H. Hutton, " Professor Boole http://books.google.com/books?id=pfMEAAAAQAAJ&pg=PA157," (1866), p. 157
Contexto: In presenting this Work to public notice, I deem it not irrelevant to observe, that speculations similar to those which it records have, at different periods, occupied my thoughts. In the spring of the present year my attention was directed to the question then moved between Sir W. Hamilton and Professor De Morgan; and I was induced by the interest which it inspired, to resume the almost-forgotten thread of former inquiries. It appeared to me that, although Logic might be viewed with reference to the idea of quantity, it had also another and a deeper system of relations. If it was lawful to regard it from without, as connecting itself through the medium of Number with the intuitions of Space and Time, it was lawful also to regard it from within, as based upon facts of another order which have their abode in the constitution of the Mind. The results of this view, and of the inquiries which it suggested, are embodied in the following Treatise.

„I firmly believe, for the accomplishment of a purpose of the Divine mind…“

—  George Boole

George Boole (1854), "Address at Cork" as cited in: R. H. Hutton, " Professor Boole http://books.google.com/books?id=pfMEAAAAQAAJ&pg=PA165," (1866), p. 165; Also cited in: Boole, George. Studies in Logic and Probability. 2002. Courier Dover Publications. p. 451
1850s
Contexto: Perhaps it is in the thought that there does exist an Intelligence and Will superior to our own,—that the evolution of the destinies of our species is not solely the product either of human waywardness or of human wisdom; perhaps, I say, it is in this thought, that the conception of humanity attains its truest dignity. When, therefore, I use this term, I would be understood to mean by it the human race, viewed in that mutual connexion and dependence which has been established, as I firmly believe, for the accomplishment of a purpose of the Divine mind... One eminent instance of that connexion and dependence to which I have referred is to be seen in the progression of the arts and sciences. Each generation as it passes away bequeaths to its successor not only its material works in stone and marble, in brass and iron, but also the truths which it has won, and the ideas which it has learned to conceive; its art, literature, science, and, to some extent, its spirit and morality. This perpetual transmission of the light of knowledge and civilisation has been compared to those torch-races of antiquity in which a lighted brand was transmitted from one runner to another until it reached the final goal. Thus, it has been said, do generations succeed each other, borrowing and conveying light, receiving the principles of knowledge, testing their truth, enlarging their application, adding to their number, and then transmitting them forward to coming generations

„They are in all cases, and in the strictest sense of the term, probable conclusions“

—  George Boole

Fonte: 1850s, An Investigation of the Laws of Thought (1854), p. 4; Ch. 1. Nature And Design Of This Work
Contexto: The general laws of Nature are not, for the most part, immediate objects of perception. They are either inductive inferences from a large body of facts, the common truth in which they express, or, in their origin at least, physical hypotheses of a causal nature serving to explain phenomena with undeviating precision, and to enable us to predict new combinations of them. They are in all cases, and in the strictest sense of the term, probable conclusions, approaching, indeed, ever and ever nearer to certainty, as they receive more and more of the confirmation of experience. But of the character of probability, in the strict and proper sense of that term, they are never wholly divested. On the other hand, the knowledge of the laws of the mind does not require as its basis any extensive collection of observations. The general truth is seen in the particular instance, and it is not confirmed by the repetition of instances.

„The general laws of Nature are not, for the most part, immediate objects of perception.“

—  George Boole

Fonte: 1850s, An Investigation of the Laws of Thought (1854), p. 4; Ch. 1. Nature And Design Of This Work
Contexto: The general laws of Nature are not, for the most part, immediate objects of perception. They are either inductive inferences from a large body of facts, the common truth in which they express, or, in their origin at least, physical hypotheses of a causal nature serving to explain phenomena with undeviating precision, and to enable us to predict new combinations of them. They are in all cases, and in the strictest sense of the term, probable conclusions, approaching, indeed, ever and ever nearer to certainty, as they receive more and more of the confirmation of experience. But of the character of probability, in the strict and proper sense of that term, they are never wholly divested. On the other hand, the knowledge of the laws of the mind does not require as its basis any extensive collection of observations. The general truth is seen in the particular instance, and it is not confirmed by the repetition of instances.

„Perhaps it is in the thought that there does exist an Intelligence and Will superior to our own,—that the evolution of the destinies of our species is not solely the product either of human waywardness or of human wisdom; perhaps, I say, it is in this thought, that the conception of humanity attains its truest dignity.“

—  George Boole

George Boole (1854), "Address at Cork" as cited in: R. H. Hutton, " Professor Boole http://books.google.com/books?id=pfMEAAAAQAAJ&pg=PA165," (1866), p. 165; Also cited in: Boole, George. Studies in Logic and Probability. 2002. Courier Dover Publications. p. 451
1850s
Contexto: Perhaps it is in the thought that there does exist an Intelligence and Will superior to our own,—that the evolution of the destinies of our species is not solely the product either of human waywardness or of human wisdom; perhaps, I say, it is in this thought, that the conception of humanity attains its truest dignity. When, therefore, I use this term, I would be understood to mean by it the human race, viewed in that mutual connexion and dependence which has been established, as I firmly believe, for the accomplishment of a purpose of the Divine mind... One eminent instance of that connexion and dependence to which I have referred is to be seen in the progression of the arts and sciences. Each generation as it passes away bequeaths to its successor not only its material works in stone and marble, in brass and iron, but also the truths which it has won, and the ideas which it has learned to conceive; its art, literature, science, and, to some extent, its spirit and morality. This perpetual transmission of the light of knowledge and civilisation has been compared to those torch-races of antiquity in which a lighted brand was transmitted from one runner to another until it reached the final goal. Thus, it has been said, do generations succeed each other, borrowing and conveying light, receiving the principles of knowledge, testing their truth, enlarging their application, adding to their number, and then transmitting them forward to coming generations

„For I cannot but regard it as the same spirit which, with whatever profession of zeal, and for whatever ends of supposed piety or obedience, strives to subvertthe natural evidences of morals, - the existence of a Supreme Intelligent Cause. There is a scepticism which repudiates all belief; there is also a scepticism which seeks to escape from itself by a total abnegation of the understanding, and which, in the pride of its new-found security, would recklessly destroy every internal ground of humant trust and hope… Now to this, as to a former development of the sceptical spirit, Science stands in implied but real antagonism.“

—  George Boole

George Boole (1851), "The Claims of Science, especially as founded in its relation to Human Nature". Published in Boole, GeorgeStudies in Logic and Probability. 2002. p. 201-202
1850s
Contexto: The scepticism of the ancient world left no department of human belief unassailed. It took its chief stand upon the conflicting nature of the impressions of the senses, but threw the dark shade of uncertainty over the most settled convictions of the mind; over men's belief in an external world, over their consciousness of their own existence. But this form of doubt was not destined to endure. Science, in removing the contradictions of sense, and establishing the consistent uniformity of natural law, took away the main pillars of its support. The spirit, however, and the mental habits of which it was the roduct, still survive; but not among the votaries of science. For I cannot but regard it as the same spirit which, with whatever profession of zeal, and for whatever ends of supposed piety or obedience, strives to subvertthe natural evidences of morals, - the existence of a Supreme Intelligent Cause. There is a scepticism which repudiates all belief; there is also a scepticism which seeks to escape from itself by a total abnegation of the understanding, and which, in the pride of its new-found security, would recklessly destroy every internal ground of humant trust and hope... Now to this, as to a former development of the sceptical spirit, Science stands in implied but real antagonism.

„To infer the existence of an intelligent cause from the teeming evidences of surrounding design, to rise to the conception of a moral Governor of the world, from the study of the constitution and the moral provisions of our own nature;“

—  George Boole

these, though but the feeble steps of an understanding limited in its faculties and its materials of knowledge, are of more avail than the ambitious attempt to arrive at a certainty unattainable on the ground of natural religion. And as these were the most ancient, so are they still the most solid foundations, Revelation being set apart, of the belief that the course of this world is not abandoned to chance and inexorable fate.
Also found in Boole, George (1851). The claims of science, especially as founded in its relations to human nature; a lecture, Volume 15. p. 24
Fonte: 1850s, An Investigation of the Laws of Thought (1854), p. 217: Ch. 13. Clarke and Spinoza : Concluding remarks of the chapter

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„The last subject to which I am desirous to direct your attention as to a means of self-improvement, is that of philanthropic exertion for the good of others. I allude here more particularly to the efforts which you may be able to make for the benefit of those whose social position is inferior to your own. It is my deliberate conviction, founded on long and anxious consideration of the subject, that not only might great positive good be effected by an association of earnest young men, working together under judicious arrangements for this common end, but that its reflected advantages would overpay the toil of effort, and more than indemnify the cost of personal sacrifice. And how wide a field is now open before you! It would be unjust to pass over unnoticed the shining examples of virtues, that are found among tho poor and indigent There are dwellings so consecrated by patience, by self-denial, by filial piety, that it is not in the power of any physical deprivation to render them otherwise than happy. But sometimes in close contiguity with these, what a deep contrast of guilt and woe! On the darker features of the prospect we would not dwell, and that they are less prominent here than in larger cities we would with gratitude acknowledge; but we cannot shut our eyes to their existence. We cannot put out of sight that improvidence that never looks beyond the present hour; that insensibility that deadens the heart to the claims of duty and affection; or that recklessness which in the pursuit of some short-lived gratification, sets all regard for consequences aside. Evils such as these, although they may present themselves in any class of society, and under every variety of circumstances, are undoubtedly fostered by that ignorance to which the condition of poverty is most exposed; and of which it has been truly said, that it is the night of the spirit,—and a night without moon and without stars. It is to associated efforts for its removal, and for the raising of the physical condition of its subjects, that philanthropy must henceforth direct her regards. And is not such an object great 1 Are not such efforts personally elevating and ennobling? Would that some part of the youthful energy of this present assembly might thus expend itself in labours of benevolence! Would that we could all feel the deep weight and truth of the Divine sentiment that " No man liveth to himself, and no man dieth to himself.“

—  George Boole

George Boole, "Right Use of Leisure," cited in: James Hogg Titan Hogg's weekly instructor, (1847) p. 250; Also cited in: R. H. Hutton, " Professor Boole http://books.google.com/books?id=pfMEAAAAQAAJ&pg=PA153," (1866), p. 153
1840s

„I have spoken of the advantages of leisure and opportunity for improvement, as of a right to which you were entitled. I must now remind you that every right involves a responsibility. The greater our freedom from external restrictions, the more do we become the rightful subjects of the moral law within us. The less our accountability to man, the greater our accountability to a higher power. Such a thing as irresponsible right has no existence in this world. Even in the formation of opinion, which is of all things the freest from human control, and for which something like irresponsible right has been claimed, we are deeply answerable for the use we make of our reason, our means of information, and our various opportunities of arriving at a correct judgment. It is true, that so long as we observe the established rules of society, we are not to be called upon before any human court to answer for the application of our leisure; but so much the more are we bound by a higher than human law to redeem to the full our opportunities. Tho application of this general truth to the circumstances of your present position is obvious. A limited portion of leisure in the evening of each day is allotted to you, and it is incumbent upon you to consider how you may best employ it.“

—  George Boole

George Boole, "Right Use of Leisure," cited in: James Hogg Titan Hogg's weekly instructor, (1847) p. 250 : Address on the Right Use of Leisure to the members of tho Lincoln Early Closing Association.
1840s

„You will feel interested to know the fate of my mathematical speculations in Cambridge. One of the papers is already printed in the Mathematical Journal. Another, which I sent a short time ago, has been very favourably received, and will shortly be printed together with one I had previously sent.“

—  George Boole

George Boole in letter to a friend, 1840, cited in: R. H. Hutton, " Professor Boole http://books.google.com/books?id=pfMEAAAAQAAJ&pg=PA147," in: The British Quarterly Review. (1866), p. 147; Cited in Des MacHale. George Boole: his life and work, Boole Press, 1985. p. 52
1840s

„The principles of the theory of probabilities [cannot] serve to guide us in the election of… [scientific] hypotheses.“

—  George Boole

Fonte: 1850s, An Investigation of the Laws of Thought (1854), p. 375, as cited in: Lev D. Beklemishev (2000) Provability, Computability and Reflection, p. 432

„Of the many forms of false culture, a premature converse with abstractions is perhaps the most likely to prove fatal to the growth of a masculine vigour of intellect.“

—  George Boole

Fonte: 1850s, A treatise on differential equations (1859), p. vi; cited in: Quotations by George Boole http://www-history.mcs.st-and.ac.uk/Quotations/Boole.html, MacTutor History of Mathematics, August 2010.

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“

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