Best Reasoning Quotes | Short & Famous Sayings Page 9

Source: The Evanston Colloquium: Lectures on Mathematics Delivered from Aug. 28 to Sept. 9, 1893 Before Members of the Congress of Mathematics Held in Connection with the World's Fair in Chicago at Northwestern University, Evanston, Ill

“ALGEBRA is a general Method of Computation by certain Signs and Symbols which have been contrived for this Purpose, and found convenient.”

Has Beens Purpose Certain Found Logic Method Symbols Certainty Uncertainty Reasoning Convenient Algebra Ontology Computation Signs And Symbols

Book:A Treatise of Algebra, in Three Parts: Containing I. The Fundamental Rules and Operations; II. The Composition and Resolution of Equations of All Degrees, and the Different Affections of Their Roots; III. The Application of Algebra and Geometry to Each Other. To which is Added an Appendix Concerning the General Properties of Geometrical Lines

Source: A Treatise of Algebra, in Three Parts: Containing I. The Fundamental Rules and Operations; II. The Composition and Resolution of Equations of All Degrees, and the Different Affections of Their Roots; III. The Application of Algebra and Geometry to Each Other. To which is Added an Appendix Concerning the General Properties of Geometrical Lines

“A good proof is one that makes us wiser.”

Logic Proof Certainty Uncertainty Reasoning Wiser Ontology

Author:IU?. I. Manin

“Thought that accepts reality as given is no thought at all.”

Reality Given Accepting Logic Certainty Uncertainty Reasoning Ontology

Author:Herbert Marcuse

“Infinity is a dark illimitable ocean, without bound.”

Dark Ocean Logic Bounds Certainty Uncertainty Reasoning Infinity Ontology

Author:John Milton

“Heaven is angered by my arrogance; my proof [of the four-color theorem] is also defective.”

Heaven Four Color Logic Proof Certainty Uncertainty Arrogance Reasoning Ontology Theorems Defective

Author:Hermann Minkowski

“If we base our belief systems on the humble assumption that the complexities of the world are ontologically beyond our understanding, then maybe our belief systems will make more sense and end up causing less suffering.”

Ifs World Ends Suffering Belief Understanding Logic Humble Certainty Uncertainty Complexity Assumption Reasoning Belief Systems Ontology

Author:Moby

“The world is too big and too intricate to conform to our ideas of what it should be like... Just because we invent myths and theories to explain away the chaos we're still going to live in a world that's older and more complicated than we'll ever understand.”

World Should Stills Ideas Bigs Theory Logic Chaos Complicated Myth Certainty Uncertainty Reasoning Conform Intricate Ontology

Author:Moby

“How many pizzas are consumed each year in the United States? How many words have you spoken in your life? How many different peoples names appear in the New York Times each year? How many watermelons would fit inside the U.S. Capital building? What is the volume of all the human blood in the world?”

“Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.”

“Mathematics is purely hypothetical: it produces nothing but conditional propositions.”

Produce Logic Mathematics Certainty Uncertainty Reasoning Propositions Ontology Hypothetical Conditional

Book:Collected papers of Charles Sanders Peirce

Source: Collected papers of Charles Sanders Peirce

“But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was not more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.”

World Way Years Fall Found Logic Twenties Conclusion Secure Certainty Mathematical Uncertainty Reasoning Elephants Toil Constructs Fables Ontology Tortoises Great Math

Book:Autobiography

Source: Autobiography

“Do you think it's possible that things that seem to be discrete in three dimensions might all be part of the same bigger object in four dimensions? ...What if humanity- that collective noun we so often employ- really is, at a higher level, a singular noun? What it what we perceive in three dimensions as seven billion individual human beings are really all just aspects of one giant being?”

“We admit, in geometry, not only infinite magnitudes, that is to say, magnitudes greater than any assignable magnitude, but infinite magnitudes infinitely greater, the one than the other. This astonishes our dimension of brains, which is only about six inches long, five broad, and six in depth, in the largest heads.”

Long Brain Five Greater Six Logic Infinite Depth Certainty Uncertainty Reasoning Dimensions Broads Inches Geometry Magnitude Ontology

Book:Voltaire – The Philosophical Works: Treatise On Tolerance, Philosophical Dictionary, Candide, Letters on England, Plato’s Dream, Dialogues, The Study of Nature, Ancient Faith and Fable, Zadig…: From the French writer, historian and philosopher, famous for his wit, his attacks on the established Catholic Church, and his advocacy of freedom of religion and freedom of expression

Source: Voltaire – The Philosophical Works: Treatise On Tolerance, Philosophical Dictionary, Candide, Letters on England, Plato’s Dream, Dialogues, The Study of Nature, Ancient Faith and Fable, Zadig…: From the French writer, historian and philosopher, famous for his wit, his attacks on the established Catholic Church, and his advocacy of freedom of religion and freedom of expression

“We think of the number "five" as applying to appropriate groups of any entities whatsoever - to five fishes, five children, five apples, five days... We are merely thinking of those relationships between those two groups which are entirely independent of the individual essences of any of the members of either group. This is a very remarkable feat of abstraction; and it must have taken ages for the human race to rise to it”