"The requisites for the axioms are various. They should be simple, in the sense that each axiom should enumerate one and only one statement. The total number of axioms should be few. A set of axioms must be consistent, that is to say, it must not be possible to deduce the contradictory of any axiom from the other axioms. According to the logical 'Law of Contradiction,' a set of entities cannot satisfy inconsistent axioms. Thus the existence theorem for a set of axioms proves their consistency. Seemingly this is the only possible method of proof of consistency. "Alfred N Whitehead, "The axioms of projective geometry, 1906)
"A symbol which has not been properly defined is not a symbol at all. It is merely a blot of ink on paper which has an easily recognized shape. Nothing can be proved by a succession of blot, except the existence of a bad pen or a careless writer." (Alfred N Whitehead, "An Introduction to Mathematics", 1911)
"The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish. It is in a way the most civilized of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought.” (Alfred N Whitehead, “An Introduction to Mathematics”, 1911)
"[…] algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world." (Alfred N Whitehead, “The Organization of Thought”, 1916)
"Mathematics is merely an apparatus for analyzing the deductions which can be drawn from any particular premises, supplied by common sense, or by more refined scientific observation, so far as these deductions depend on the forms of the propositions." (Alfred N Whitehead, "The Organization of Thought", Science N.S Vol. 44 1134, 1916)
“Through and through the world is infected with quantity: To talk sense is to talk quantities. It is not use saying the nation is large - How large? It is no use saying the radium is scarce - How scarce? You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves.” (Alfred N Whitehead, “The Aims of Education and Other Essays”, 1917)
“To come very near to a true theory, and to grasp its precise application, are two very different things, as the history of a science teaches us. Everything of importance has been said before by somebody who did not discover it.” (Alfred N Whitehead, “The Organization of Thought”, 1917)
“The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, ‘Seek simplicity and distrust it.’” (Alfred N Whitehead, “The Concept of Nature”, 1919)
“Even now there is a very wavering grasp of the true position of mathematics as an element in the history of thought. I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him.” (Alfred N Whitehead, “Science and the Modern World”, 1925)
”It requires a very unusual mind to undertake the analysis of the obvious.” (Alfred N Whitehead, “Science in the Modern World”, 1925)
"Nature is probably quite indifferent to the aesthetic preferences of mathematicians.” (Alfred N Whitehead, “Science and the Modern World”, 1925)
"Progress in truth - truth of science and truth of religion - is mainly a progress in the framing of concepts, in discarding artificial abstractions or partial metaphors, and in evolving notions which strike more deeply into the root of reality." (Alfred N Whitehead, "Religion in the Making", 1926)
"A precise language awaits a completed metaphysics." (Alfred N Whitehead, "Process and Reality: An Essay in Cosmology", 1929)
“Through and through the world is infected with quantity: To talk sense is to talk quantities. It is not use saying the nation is large - How large? It is no use saying the radium is scarce - How scarce? You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves.” (Alfred N Whitehead, “The Aims of Education and Other Essays”, 1917)
“To come very near to a true theory, and to grasp its precise application, are two very different things, as the history of a science teaches us. Everything of importance has been said before by somebody who did not discover it.” (Alfred N Whitehead, “The Organization of Thought”, 1917)
“The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, ‘Seek simplicity and distrust it.’” (Alfred N Whitehead, “The Concept of Nature”, 1919)
“Even now there is a very wavering grasp of the true position of mathematics as an element in the history of thought. I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him.” (Alfred N Whitehead, “Science and the Modern World”, 1925)
”It requires a very unusual mind to undertake the analysis of the obvious.” (Alfred N Whitehead, “Science in the Modern World”, 1925)
"Nature is probably quite indifferent to the aesthetic preferences of mathematicians.” (Alfred N Whitehead, “Science and the Modern World”, 1925)
"Progress in truth - truth of science and truth of religion - is mainly a progress in the framing of concepts, in discarding artificial abstractions or partial metaphors, and in evolving notions which strike more deeply into the root of reality." (Alfred N Whitehead, "Religion in the Making", 1926)
"A precise language awaits a completed metaphysics." (Alfred N Whitehead, "Process and Reality: An Essay in Cosmology", 1929)
"There is a tradition of opposition between adherents of induction and of deduction. In my view it would be just as sensible for the two ends of a worm to quarrel." (Alfred N Whitehead, "The Aims of Education & Other Essays", 1929)
"Apart from blunt truth, our lives sink decadently amid the perfume of hints and suggestions.” (Alfred N Whitehead, “Adventures of Ideas”, 1933)
"Apart from blunt truth, our lives sink decadently amid the perfume of hints and suggestions.” (Alfred N Whitehead, “Adventures of Ideas”, 1933)
"Our reasonings grasp at straws for premises and float on gossamers for deductions." (Alfred N Whitehead, "Adventures of Ideas", 1933)
"Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghost-like character of the real variable.” (Alfred N Whitehead, “Essays in Science and Philosophy”, 1948)
"There are no whole truths; all truths are half-truths. It is trying to treat them as whole truths that plays the devil.” (Alfred North Whitehead, “Dialogues”, 1954)
"Our minds are finite, and yet even in those circumstances of finitude, we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of that infinitude." (Alfred N Whitehead)
"There is no getting out of it. Through and through the world is infected with quantity. To talk sense is to talk in quantities. […] You cannot evade quantity. You may fly to poetry and to music, and quantity and number will face you in your rhythms and your octaves. Elegant intellects which despise the theory of quantity are but half developed. They are more to be pitied than blamed." (Alfred N Whitehead)
"You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves.” (Alfred N Whitehead)
"Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghost-like character of the real variable.” (Alfred N Whitehead, “Essays in Science and Philosophy”, 1948)
"There are no whole truths; all truths are half-truths. It is trying to treat them as whole truths that plays the devil.” (Alfred North Whitehead, “Dialogues”, 1954)
"Our minds are finite, and yet even in those circumstances of finitude, we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of that infinitude." (Alfred N Whitehead)
"There is no getting out of it. Through and through the world is infected with quantity. To talk sense is to talk in quantities. […] You cannot evade quantity. You may fly to poetry and to music, and quantity and number will face you in your rhythms and your octaves. Elegant intellects which despise the theory of quantity are but half developed. They are more to be pitied than blamed." (Alfred N Whitehead)
"You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves.” (Alfred N Whitehead)
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