George Boole Quotes

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.

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.

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.

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.'

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.

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?

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.