21 quotes
The general laws of Nature are not, for the most part, immediate objects of perception.
An Investigation of the Laws of Thought (1854)
For how shall the finite comprehend the infinite?
An Investigation of the Laws of Thought (1854)
It is not of the essence of mathematics to be conversant with the ideas of number and quantity.
An Investigation of the Laws of Thought (1854)
I firmly believe, for the accomplishment of a purpose of the Divine mind...
George Boole (1854)
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.
An Investigation of the Laws of Thought (1854)
That logic, as a science, is susceptible of very wide applications is admitted; but it is equally certain that its ultimate forms and processes are mathematical.
An Investigation of the Laws of Thought (1854)
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.
A treatise on differential equations (1859)
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.
An Investigation of the Laws of Thought (1854)
The principles of the theory of probabilities [cannot] serve to guide us in the election of... [scientific] hypotheses.
An Investigation of the Laws of Thought (1854)
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.
An Investigation of the Laws of Thought (1854)
A distinguished writer (Siméon Denis Poisson) has thus stated the fundamental definitions of the science
An Investigation of the Laws of Thought (1854)
Spinoza's use of the term finite tends to make space the only form of substance, and all existing things but affections of space, and this, I think, is really one of the ultimate foundations of his system.
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.
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.
An Investigation of the Laws of Thought (1854)
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 treatise on differential equations (1859)
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.
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.
An Investigation of the Laws of Thought (1854)
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.
That language is an instrument of human reason, and not merely a medium for the expression of thought, is a truth generally admitted.
Attributed
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.
Attributed to George Boole in: Des MacHale (1993)