George Boole Quotes

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.

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.

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.

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.

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.

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.

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.

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.

[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.

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.'

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.

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.

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.

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.

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.