George Boole: Quotes about laws

“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

Source: 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
Context: 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.

Law , Idea , Appearance , Time

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

George Boole

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 4; Ch. 1. Nature And Design Of This Work
Context: 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.

Law , Nature , Parting

“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.”

George Boole

Source: 1840s, The Mathematical Analysis of Logic, 1847, p. ii: Lead paragraph of the Introduction

Truth , Law , Question , Problem

“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

George Boole, " Solution of a Question in the Theory of Probabilities http://books.google.nl/books?id=9xtDAQAAIAAJ&pg=PA32" (30 November 1853) published in The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science‬‎ (January 1854), p. 32
1850s

Law , Mathematics , Question , Universe

“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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 6; As cited in: Leandro N. De Castro, Fernando J. Von Zuben, Recent Developments in Biologically Inspired Computing, Idea Group Inc (IGI), 2005 p. 236

Law , Science

“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.”

George Boole

Source: 1840s, The Mathematical Analysis of Logic, 1847, p. 5

Law , Success

“[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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 3: as cited in: John Cohen (1966) A new introduction to psychology. p. 121

Secret , World , Law , Knowledge

“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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 37; Cited in: William Torrey Harris (1879) The Journal of Speculative Philosophy, p. 109

Law , Indifference

“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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 49: as cited in: " Professor Boole's Mathematical theory http://books.google.com/books?id=tBNLAAAAYAAJ&pg=PA62" in: Henry Longueville Manse, Philosophical pamphlets, (1853), p. 6

Law , Time

“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

Truth , World , Law , Freedom

“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.”

George Boole

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 1; Ch. 1. Nature And Design Of This Work, lead paragraph

Truth , Law , Mathematics , Nature

“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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. i; Preface, lead paragraph

Law , Mathematics , Idea , Study

“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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 42