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It is not of the essence of mathematics to be conversant with the ideas of number and quantity.
George Boole
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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
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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.
George Boole
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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.
George Boole
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[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.
George Boole
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The general laws of Nature are not, for the most part, immediate objects of perception.
George Boole
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So to apprehend in all particular instances the relation of cause and effect, as to connect the two extremes in thought according to the order in which they are connected in nature (for the modus operandi is, and must ever be, unknown to us), is the final object of science.
George Boole
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Logic is conversant with two kinds of relations, relations among things, and relations among facts.
George Boole
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Each new scientific conception gives occasion to new applications of deductive reasoning; but those applications may be only possible through the methods and the processes which belong to an earlier stage.
George Boole
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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
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It is the ability inherent in our nature to appreciate Order, and the concurrent presumption, however founded, that the phenomena of Nature are connected by a principle of Order. Without these, the general truths of physical science could never have been ascertained.
George Boole
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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.
George Boole
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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.
George Boole
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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.
George Boole
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That language is an instrument of human reason, and not merely a medium for the expression of thought, is a truth generally admitted.
George Boole
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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.
George Boole
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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.
George Boole
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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.
George Boole
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The most accomplished in the use of symbols must sometimes throw aside his abstractions and resort to homelier methods for trial and verification - not doubting, in so doing, the truth which lies at the bottom of his symbolism, but distrusting his own powers.
George Boole
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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 v advanced information. These distinct, but not inconsistent - aims determined the plan of composition.
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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.
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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.
George Boole
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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.
George Boole
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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.
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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
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I always turn to the sports pages first, which records people's accomplishments. The front page has nothing but man's failures.
Earl Warren
George Boole
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Born:
November 2, 1815
Died:
December 8, 1864
(aged 49)
Bio:
George Boole was an English mathematician, educator, philosopher and logician. He worked in the fields of differential equations and algebraic logic, and is best known as the author of The Laws of Thought which contains Boolean algebra.
Known for:
The Laws of Thought (1854)
The mathematical analysis of logic (1847)
Studies in logic and probability
Treatise on differential equations (1859)
Most used words:
laws
mathematical
science
logic
mind
principle
time
method
operations
knowledge
analysis
forms
thought
fundamental
probabilities
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