Non Fiction Authors From England

"The new and wonderful results of the late Dr. Boole's mathematical system of Logic appear to develop themselves as most plain and evident consequences of the self-same process of substitution, when applied to the Primary Laws of Thought. Should my notion be true, a vast mass of technicalities may be swept from our logical text-books, and yet the small remaining part of logical doctrine will prove far more useful than all the learning of the Schoolmen."

"All acts of reasoning seem to me to be different cases of one uniform process which may perhaps be best described as the substitution of similars. ..The chief difficulty consists in showing that all the forms of the old logic, as well as the fundamental rules of mathematical reasoning, may be explained upon the same principle; and it is to this difficult task I have devoted the most attention."

"The alternatives before us are simple. Our empire and race already comprise one-fifth of the world's population, and by our plantation of new states, by our guardianship of the seas, by our penetrating commerce, by the example of our just laws and firm constitution, and above all by the dissemination of our new arts, we stimulate the progress of mankind in a degree not to be measured. If we lavishly and boldly push forward in the creation and distribution of our riches, it is hard to over-estimate the pitch of beneficial influence to which we may attain in the present. But the maintenance of such a position is physically impossible. We have to make the momentous choice between brief greatness and longer continued mediocrity."

"Have we not hereditary possessions in our just laws, our free and nobly developed constitution, our rich literature and philosophy, incomparably above material wealth, and which we are beyond all things bound to maintain, improve, and hand down in safety? And do we accomplish this duty in encouraging a growth of industry which must prove unstable, and perhaps involve all things in its fall?"

"Commerce is but a means to an end, the diffusion of civilization and wealth. To allow commerce to proceed until the source of civilization is weakened and overturned is like killing the goose to get the golden egg. Is the immediate creation of material wealth to be our only object?"

"It is very commonly urged, that the failing supply of coal will be met by new modes of using it efficiently and economically. ...It is wholly a confusion of ideas to suppose that the economical use of fuel is equivalent to a diminished consumption. The very contrary is the truth."

"Coal in truth stands not beside, but entirely above, all other commodities. It is the material source of the energy of the country—the universal aid—the factor in everything we do. With coal almost any feat is possible or easy; without it we are thrown back into the laborious poverty of earlier times."

"I need hardly stay to demonstrate that facts are valueless unless connected and explained by a correct theory; that analogies are very dangerous grounds of inference, unless carefully founded on similar conditions; and that experience misleads if it be misinterpreted."

"Pray accept my best thanks for your kindness in sending me a copy of your Memoir, and for the very courteous letter in which you draw my attention to it. When your letter came I had, indeed, already noticed in the Journal des Economistes your very remarkable theory. I felt the greater interest in the subject because my own speculations have led me in the same direction, now for the last twelve years or more. It is satisfactory to me to find that my theory of exchange, which, when published in England, was either neglected or criticised, is practically confirmed by your researches. I do not know whether you are acquainted with my writings on the subject. All the chief points of my mathematical theory were clear to my own mind by the year 1862, when I drew up a brief account of it, which was read at the meeting of the British Association at Cambridge... A very brief abstract was then alone inserted in the report, but the original paper was printed in the journal of the London Statistical Society in 1866... Finally, in 1871, I caused to be published... the Theory of Political Economy, in which is given a full explanation of the theory, with the aid of mathematical symbols. [...] You will find, I think, that your theory substantially coincides with and confirms mine, although the symbols are differently chosen, and there are incidental variations. You will see that the whole theory rests on the notion... that the utility of a commodity is not proportional to its quantity; what you call the rarity of a commodity appears to be exactly what I called the coefficient of utility at first, and afterwards the degree of utility, which... was really the differential coefficient of the utility considered as the function of the quantity of commodity. The theory of exchange is given... and may be considered to be contained in one sentence. An equation may thus be established on either side between the utility gained and sacrificed at the ratio of exchange of the whole commodities, upon the last increments exchanged. Now in my book of 1871, I show fully how this theory may be expressed in symbols. [...] Indeed, when the meaning of the terms is explained, your proposition 'Les prix courants ou prix d'equilibre sont égaux aux rapports des raretés' is seen to coincide precisely with my theory, except that you do not point out how many equations are requisite, or how many unknown quantities there are. The publication of your paper... tends to confirm my belief in the correctness of the theory, but it might lead to misapprehensions as to the originality and priority... I shall therefore take it as a favour if you will kindly inform me whether you are sufficiently acquainted with my writings, or whether you would desire me to forward a copy of my Theory of Political Economy."

"I cannot consent with the Radical party to obliterate a glorious past, nor can I consent with the Conservatives to prolong abuses into the present. I wish with all my heart to aid in securing all that is good for the masses, yet to give them all they wish and are striving for is to endanger much that is good beyond their comprehension. I cannot pretend to underestimate the good that the English monarchy and aristocracy, with all the liberal policy actuating it, does for the human race, and yet I cannot but fear the pretensions of democracy against it are strong, and in some respects properly strong. This antithesis and struggle, perhaps, after all, is no more than has always more or less existed, but is now becoming more marked. Compromise, perhaps, is the only resource. Those who rightly possess the power in virtue of their superior knowledge must yield up some, that they may carry with them the honest but uncertain wills of those less educated but more numerous and physically powerful."

"It was during the year 1851, while living almost unhappily among thoughtless, if not bad companions, in Gower Street a gloomy house on which I now look with dread it was then, and when I had got a quiet hour in my small bedroom at the top of the house, that I began to think that I could and ought to do more than others. A vague desire and determination grew upon me. I was then in the habit of saying my prayers like any good church person, and it was when so engaged that I thought most eagerly of the future, and hoped for the unknown. My reserve was so perfect that I suppose no one had the slightest comprehension of my motives or ends. My father probably knew me but little. I never had any confidential conversation with him. At school and college the success in the classes was the only indication of my powers. All else that I intended or did was within or carefully hidden. The reserved character, as I have often thought, is not pleasant nor lovely. But is it not necessary to one such as I? Would it have been sensible or even possible for a boy of fifteen or sixteen to say what he was going to do before he was fifty? For my own part I felt it to be almost presumptuous to pronounce to myself the hopes I held and the schemes I formed. Time alone could reveal whether they were empty or real; only when proved real could they be known to others."

"I used to think I should like to be a bookbinder or bookseller it seemed to me a most delightful trade and I wished or thought of nothing better. More lately I thought I should be a minister, it seemed so serious and useful a profession, and I entered but little into the merits of religion and the duties of a minister. Every one dissuaded me from the notion, and before I arrived at any age to require a real decision, science had claimed me."

"When quite young I can remember I had no thought or wish of surpassing others. I was rather taken with a liking of little arts and bits of learning. My mother carefully fostered a liking for botany, giving me a small microscope and many books, which I yet have. Strange as it may seem, I now believe that botany and the natural system, by exercising discrimination of kinds, is the best of logical exercises. What I may do in logic is perhaps derived from that early attention to botany."

"One of the most important axioms is, that as the quantity of any commodity, for instance, plain food, which a man has to consume, increases, so the utility or benefit derived from the last portion used decreases in degree. The decrease in enjoyment between the beginning and the end of a meal may be taken as an example. And I assume that on an average, the ratio of utility is some continuous mathematical function of the quantity of commodity. This law of utility has, in fact, always been assumed by political economists under the more complex form and name of the Law of Supply and Demand. But once fairly stated in its simple form, it opens up the whole of the subject."

"You will perceive that economy, scientifically speaking, is a very contracted science; it is in fact a sort of vague mathematics which calculates the causes and effects of man's industry, and shows how it may be best applied. There are a multitude of allied branches of knowledge connected with mans condition; the relation of these to political economy is analogous to the connexion of mechanics, astronomy, optics, sound, heat, and every other branch more or less of physical science, with pure mathematics."

"But, when tales of the cosmos are told, this period of ours may always be recalled as that in which men first came to realise what a violent universe we inhabit."

"That we shall probably never know the whole "truth" about the universe does not really matter very much; the fun comes in trying to find out. The natural pattern of current astronomy … is provided by the cryptic unity of nature itself (belief in which is the chief act of faith of the scientist) and by questions astronomers ask today, as their predecessors have done for centuries:"

"The big discoveries raise questions that make astronomers work feverishly and argue with an agitation that verges on rudeness."

"One of my complaints is that you've got far more scientists than ever before but the pace of discovery has not increased. Why? Because they're all busy just filling in the details of what they think is the standard story. And the youngsters, the people with different ideas have just as big a fight as ever and normally it takes decades for science to correct itself. But science does correct itself and that's the reason why science is such a glorious thing for our species."

"In a sense, human flesh is made of stardust. Every atom in the human body, excluding only the primordial hydrogen atoms, was fashioned in stars that formed, grew old and exploded most violently before the Sun and the Earth came into being. The explosions scattered the heavy elements as a fine dust through space. By the time it made the Sun, the primordial gas of the Milky Way was sufficiently enriched with heavier elements for rocky planets like the Earth to form. And from the rocks atoms escaped for eventual incorporation in living things: carbon, nitrogen, oxygen, phosphorus and sulphur for all living tissue; calcium for bones and teeth; sodium and potassium for the workings of nerves and brains; the iron colouring blood red… and so on. No other conclusion of modern research testifies more clearly to mankind’s intimate connections with the universe at large and with the cosmic forces at work among the stars."

"All relations are either qualitative or quantitative. Qualitative relations can be considered by themselves without regard to quantity. The algebra of such enquiries may be called logical algebra, of which a fine example is given by Boole. Quantitative relations may also be considered by themselves without regard to quality. They belong to arithmetic, and the corresponding algebra is the common or arithmetical algebra. In all other algebras both relations must be combined, and the algebra must conform to the character of the relations."

"Frege's development began with... "an epoch-making little book" called ', translated as Concept Script or Conceptual Notation... Just as Aristotle's ' is the foundation of traditional or syllogistic logic—the logic of the categorical three-term syllogism, Frege's Begriffsschrift is the keystone of modern or mathematical logic."

"Boole literally transformed logic into a type of algebra (which came to be known as ') and extended the analysis of logic even to probabilistic reasoning. ...Boole managed to mathematically tame the logical connectives and, or, if...then, and not, which are currently at the very core of computer operations and various switching circuits. Consequently, he is regarded by many as one of the "prophets" who brought about the digital age. Still, due to its pioneering nature, Boole's algebra was not perfect. First, Boole made his writings somewhat ambiguous and difficult to comprehend by using a notation that was too close to that of ordinary algebra. Second, Boole confused the distinction between s (e.g., "Aristotle is mortal"), s or predicates (e.g., "x is mortal"), and quantified statements (e.g., for all x, x is mortal"). Finally, Frege and Russell were later to claim that algebra stems from logic. One could argue, therefore, that it made more sense to construct algebra on the basis of logic rather than the other way around."

"Dr. George Boole, author of The Laws of Thought had introduced himself in the year 1842 to Mr. De Morgan by a letter on the Differential and Integral Calculus then recently published. His character and pursuits were in many points like those of the author who found great pleasure in his correspondence and friendship. ...In 1847, his attention having been drawn to the subject by the publication of Mr. De Morgan's Formal Logic, he published the Mathematical Analysis of Logic and in the following year communicated... a paper on the Calculus of Logic. His great work, An Investigation into the Laws of Thought... was a development of the principle laid down in the Calculus..."

"We believe that to the great body of the reading public the name of George Boole first became known, if indeed it has yet become known, through the announcement of his death; the announcement being accompanied in a few of the papers by a brief sketch of his life and works. Boole's researches were not of a nature to be appreciated by the multitude, and he never condescended to those arts by which less gifted men have won for themselves while living a more splendid reputation. When a great politician dies, or any man who has filled a large space in the public mind, and made a noise in the world, the newspapers long ring with the event. But it is otherwise with the great thinker, the mathematician or the philosopher, who has laboured silently and in comparative seclusion, to extend the boundaries of human knowledge. When such a man is removed by death there are public journals, even among those professedly devoted to literature and science, which can dismiss the event with a few faint and cold remarks.* But time rectifies all that. It is found sooner or later that no reputation, however brilliant, is permanent or durable which does not rest on useful discoveries and real contributions to our knowledge."

"‘European science could never have reached its present height had it not been fertilised by successive wafts from the […] knowledge stored up in the East.’ ‘Think what must have been the effect of the intense Hinduizing of three such men as Babbage, De Morgan and George Boole on the mathematical atmosphere of 1830–1865.’ ‘I do as George Boole and De Morgan did: I bow my head inreverent thankfulness to that mysterious East, whence come to us wafts of some transcendent power the nature of which we ourselves can hardly state in words.’"

"George afterwards learned, to his great joy, that the same conception of the basis of Logic was held by Leibnitz, the contemporary of Newton. De Morgan, of course, understood the formula in its true sense; he was Boole's collaborator all along. Herbert Spencer, Jowett, and understood, I feel sure; and a few others, but nearly all the logicians and mathematicians ignored the statement that the book was meant to throw light on the nature of the human mind; and treated the formula entirely as a wonderful new method of reducing to logical order masses of evidence about external fact."

"My husband told me that when he was a lad of seventeen a thought struck him suddenly, which became the foundation of all his future discoveries. It was a flash of psychological insight into the conditions under which a mind most readily accumulates knowledge."

"Mathematics had never had more than a secondary interest for him ; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to rest had no tendency to prove them. But he had been endeavouring to give a more active and positive help than this to the cause of what he deemed pure religion. That he was doing nothing in this way was a sore distress to him."

"George Boole took up Leibniz's idea, and wrote a book he called '. The laws he formulated are now called ... Boole seems to have had a grandiose vision about the applicability of his algebraic methods to practical problems—his book makes it clear that he hoped these laws would be used to settle practical questions. William Stanley Jevons heard of Boole's work, and undertook to build a machine to make calculations in Boolean algebra. He successfully designed and built... the Logical Piano... the first machine to do mechanical inference."

"No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it gives the impression of also being beautiful."

"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."

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

"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."

"I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary -- being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived."

"I have endeavoured, in the following treatise, to convey as complete an account of the present state of knowledge on the subject of Differential Equations, as was consistent with the idea of a work intended, primarily, for elementary instruction. It was my object, first of all, to meet the wants of those who had no previous acquaintance with the subject, but I also desired not quite to disappoint others who might seek for more advanced information. These distinct, but not inconsistent - aims determined the plan of composition."

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

"It has been said, that the principle involved in the above and in similar applications is that of the equal distribution of our knowledge, or rather of our ignorance the assigning to different states of things of which we know nothing, and upon the very ground that we know nothing, equal degrees of probability. I apprehend, however, that this is an arbitrary method of procedure. Instances may occur, and one such has been adduced, in which different hypotheses lead to the same final conclusion."

"Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities."

"A distinguished writer (Siméon Denis Poisson) has thus stated the fundamental definitions of the science:"

"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."

"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."

"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."

"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."

"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."

"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 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."

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

"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."