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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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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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It is not of the essence of mathematics to be conversant with the ideas of number and quantity.
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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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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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.
George Boole
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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.
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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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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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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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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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.
George Boole
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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 of firmness.
George Boole
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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.
George Boole
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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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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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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?
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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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.
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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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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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.
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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The principles of the theory of probabilities [cannot] serve to guide us in the election of... [scientific] hypotheses.
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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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:
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science
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logic
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mind
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principle
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time
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method
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operations
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analysis
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forms
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thought
,
fundamental
,
probabilities
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