George Boole Quotes
The general laws of Nature are not, for the most part, immediate objects of perception.
It is not of the essence of mathematics to be conversant with the ideas of number and quantity.
The object of science, properly so called, is the knowledge of laws and relations.
Life in all its forms may thus be contrasted with the passive fixity of inorganic nature.
The particular question of the constitution of the intellect has, it is almost needless to say, attracted the efforts of speculative ingenuity in every age.
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 nether room nor demand for a theory of probabilities.
In a word, what is the nature of scientific truth, and what are the grounds of that confidence with which it claims to be received?
That to such questions as the above, no single and general answer can be given, must be evident.
It may be that the progress of natural knowledge tends towards the recognition of some central Unity in Nature.
The application of scientific methods to the study of the intellectual phaenomena, conducted in an impartial spirit of inquiry, and without overlooking those elements of error and disturbance which must be accepted as facts, though they cannot be regarded as laws, in the constitution of our nature, seems to furnish the materials of a juster analogy.
We cannot separate any portion of nature laws from the rest, and pronounce them alone worthy of obedience, alone charged with the fulfilment of her highest purpose. On the contrary, all her laws seem to co-ordinate, and the larger our acquaintance with them, the more necessary does their united action seem to the harmony and, so far as we can comprehend it, to the general design of the system.
No general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise, 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.
The truth that the ultimate laws of thought are mathematical in their form, viewed in connexion with the fact of the possibility of error, establishes a ground for some remarkable conclusions. If we directed our attention to the scientific truth alone, we might be led to infer an almost exact parallelism between the intellectual operations and the movements of external nature.
The mathematical laws of reasoning are, properly speaking, the laws of right reasoning only, and their actual transgressions is a perpetually recurring phaenomenon. Error, which has no place in the material system, occupies a large one here. We must accept this as one of the ultimate facts, the origin of which it lies beyond the province of science to determine. We must admit that there exist laws which even the rigour of their mathematical forms does not preserve from violation.
Perhaps it is in the thought that there does exist an Intelligence and Will superior to our own,—that the evolution of the destinies of our species is not solely the product either of human waywardness or of human wisdom; perhaps, I say, it is in this thought, that the conception of humanity attains its truest dignity. When, therefore, I use this term, I would be understood to mean by it the human race, viewed in that mutual connexion and dependence which has been established, as I firmly believe, for the accomplishment of a purpose of the Divine mind...
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. And these are the causes that operate in perfect harmony. 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.
Hence, perhaps, it is that we sometimes find juster conceptions of the unity, the vital connexion, and the subordination to a moral purpose, of the different parts of Truth, among those who acknowledge nothing higher than the changing aspect of collective humanity, than among those who profess an intellectual allegiance to the Father of Lights. But these are questions which cannot further be pursued here. To some they will appear foreign to the professed design of this work. But the consideration of the has arisen naturally, either out of the speculations which that design involved, or in the course of reading and reflection which seemed necessary to its accomplishment.
