Academics From The United Kingdom

"Let x represent an act of the mind by which we fix our regard upon that portion of time for which the proposition X is true ; and let this meaning be understood when it is asserted that x denote the time for which the proposition X is true. (. . .) We shall term x the representative symbol of the proposition X."

"Let us conceive, then, of an algebra in which the symbols x, y z etc. admit indifferently of the values 0 and 1, and of these values alone The laws, the axioms, and the processes, of such an Algebra will be identical in their whole extend with the laws, the axioms, and the processes of an Algebra of Logic. Difference of interpretation will alone divide them. Upon this principle the method of the following work is established."

"It is not possible, I think, to rise from the perusal of the arguments of Clark and Spinoza without a deep conviction of the futility of all endeavors to establish, entirely à priori, the existence of an Infinite Being, His attributes, and His relation to the universe. The fundamental principle of all such speculations, viz. that whatever we can clearly conceive, must exist, fails to accomplish its end, even when its truth is admitted. For how shall the finite comprehend the infinite? Yet must the possibility of such conception be granted, and in something more than the sense of a mere withdrawal of the limits of phænomal existence, before any solid ground can be established for the knowledge, à priori, of things infinite and eternal."

"To deduce the laws of the symbols of Logic from a consideration of those operations of the mind which are implied in the strict use of language as an instrument of reasoning."

"That axiom of Metaphysicians which is termed the principle of contradiction and which affirms that it is impossible for anything to possess a quality, and in the same time not to possess it, is a consequence of the fundamental law of thought, whose expression is x²=x."

"The above interpretation has been introduced, not on account of its immediate value in the present system, but as an illustration of a significant fact in the philosophy of the intellectual powers, viz., that what has commonly been regarded as the fundamental axiom of metaphysics is but the consequence of a law of thought, mathematical in its form."

"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; - 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."

"That language is an instrument of human reason, and not merely a medium for the expression of thought, is a truth generally admitted."

"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."

"[Boole's apparent goal was to] unfold the secret laws and relations of those high faculties of thought by which all beyond the merely perceptive knowledge of the world and of ourselves is attained or matured, is a object which does not stand in need of commendation to a rational mind."

"There is not only a close analogy between the operations of the mind in general reasoning and its operations in the particular science of Algebra, but there is to a considerable extent an exact agreement in the laws by which the two classes of operations are conducted."

"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 product, 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 subvert the 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 human trust and hope... Now to this, as to a former development of the sceptical spirit, Science stands in implied but real antagonism."

"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"

"It is not of the essence of mathematics to be conversant with the ideas of number and quantity."

"I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form."

"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."

"THEY who are acquainted with the present state of the theory of Symbolical Algebra, are aware, that the validity of the processes of analysis does not depend upon the interpretation of the symbols which are employed, but solely upon the laws of their combination. Every system of interpretation which does not affect the truth of the relations supposed, is equally admissible, and it is thus that the same process may, under one scheme of interpretation, represent the solution of a question on the properties of numbers, under another, that of a geometrical problem, and under a third, that of a problem of dynamics or optics. This principle is indeed of fundamental importance ; and it may with safety be affirmed, that the recent advances of pure analysis have been much assisted by the influence which it has exerted in directing the current of investigation."

"A successful attempt to express logical propositions by symbols, the laws of whose combinations should be founded upon the laws of the mental processes which they represent, would, so far, be a step towards a philosophical language."

"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."

"The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation to establish the science of Logic and construct its method ; to make that method itself the basis of a general method for the application of the mathematical doctrine of Probabilities ; and, finally, to collect from the various elements of truth brought to view in the course of these inquiries some probable intimations concerning the nature and constitution of the human mind."

"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."

"A studious person may neglect his business for the sake of books; but if he does this, it is not his books that are to blame, but his want of principle of firmness."

"The following work is not a republication of a former treatise by the Author, entitled, "The Mathematical Analysis of Logic." Its earlier portion is indeed devoted to the same object, and it begins by establishing the same system of fundamental laws, but its methods are more general, and its range of applications far wider. It exhibits the results, matured by some years of study and reflection, of a principle of investigation relating to the intellectual operations, the previous exposition of which was written within a few weeks after its idea had been conceived."

"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."

"Some months ago I took the liberty of troubling you for a reference to Laplace. In your reply for which it still remains to me to thank you, you were pleased to express an interest in the subject of investigation alluded to in my letter. I have now drawn up a paper embodying the principal results of the inquiry which I have had some thoughts of laying before the Royal Society. Before taking a step of this nature I am however anxious to have the opinion of a more competent judge as to its propriety. Knowing that you have written much on kindred subjects, shall I presume too far on your courtesy in applying to you a second time?"

"Mr. Gregory: Late Fellow of Trinity College, Cambridge, and author of the -well-known Examples. Few in so short a life have done so much for science. The high sense which I entertain of his merits as a mathematician, is mingled with feelings of gratitude for much valuable assistance rendered to me in my earlier essays."

"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.'"

"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."

"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."

"Most probably some law hitherto undiscovered exists."

"There is no theology so desperate that you can’t find it."

"“Destiny’s bunk,” said the book. “That’s why this lot aren’t the Propheseers anymore.” “From here on in,” said Mortar, “we’re the Order of Suggesters.”"

"He tried to grin but it did not go well."

"There are no cats in UnLondon, for example, because they’re not magic and mysterious at all, they’re idiots."

"It had some allies. Believe me, there’s nothing so terrible that someone won’t support it."

"It is more foolish and childish to assume there is a conspiracy, or that there is not?"

"Ori supposed there were as many unspeakable stories as there were men come back from war."

"“History...” Jacobs spoke with terse authority. Brought Ori to a hush. “Is all full. And dripping. With the corpses. Of them who trusted the incorruptible.”"

"“We’re all racing,” he said. “Yeah, but some of us in the wrong direction.”"

"When the rich grow afraid, they get nasty. We say: A government for need not greed!"

"“I’m asking you all to have faith. Don’t be afraid. ‘How could it have gone?’ people have asked me. ‘Why aren’t the gods doing anything?’ Remember two things. The gods don’t owe us anything. That’s not why we worship. We worship because they’re gods. This is their universe, not ours. What they choose they choose and it’s not ours to know why.” Christ, thought Billy, what a grim theology. It was a wonder they could keep anyone in the room, without the emotional quid pro quo of hope."

"The chief was a thuggish man: nervous, Cutter saw, because he knew he was a mediocrity become by kink of history a ruler."

"Judah knows the trow will be eradicated and their homes lost to history, but he will not be party to it, and he has tried to stand in its way."

"“My dad hates umbrellas,” said Deeba, swinging her own. “When it rains he always says the same thing. ‘I do not believe the presence of moisture in the air is sufficient reason to overturn society’s usual sensible taboo against wielding spiked clubs at eye level.’”"

"I want to know everything, he says."

"Neither dust nor light stirred. It was as if time had been bled dry and given up."

"For every action, there’s an infinity of outcomes. Countless trillions are possible, many milliards are likely, millions might be considered probable, several occur as possibilities to us as observers—and one comes true."

"“She probably used proxies and a cleaner-upper online too, because there was bugger-all of interest in her cache.” “You have no idea what you’re saying, do you, boss?” “None at all. I had the techies write it all out phonetically for me.”"

"We say what happens now. We’re taking control. We’re turning around; we’re heading home. Your orders to proceed...are in-fucking-validated."

"She felt so alien, bowed under culture shock as crippling as migraine."