Ontology Quotes - Page 2

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

  Charles Sanders Peirce

  Logic, Mathematics, Produce

  Charles Sanders Peirce (1931). “Collected Papers of Charles Sanders Peirce”

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• The Fates are here because of supernal anger, celestial imbalance, and arrogance of men and gods that must be curbed.

  Janet Morris

  God, Fate, Destiny

  Janet Morris, Chris Morris (2010). “The Sacred Band”, p.179, Paradise Publishing

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• The new painters do not propose, any more than did their predecessors, to be geometers. But it may be said that geometry is to the plastic arts what grammar is to the art of the writer. Today, scholars no longer limit themselves to the three dimensions of Euclid. The painters have been lead quite naturally, one might say by intuition, to preoccupy themselves with the new possibilities of spatial measurement which, in the language of the modern studios, are designated by the term fourth dimension.

  Guillaume Apollinaire

  Art, Intuition, Today

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• Calculus works by making visible the infinitesimally small.

  Keith Devlin

  Logic, Certainty, Calculus

  Keith Devlin (2003). “Sets, Functions, and Logic: An Introduction to Abstract Mathematics, Third Edition”, p.7, CRC Press

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• 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?

  Robert J. Sawyer

  Thinking, Humanity, What If

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• The world of learning is so broad, and the human soul is so limited in power! We reach forth and strain every nerve, but we seize only a bit of the curtain that hides the infinite from us.

  Maria Mitchell

  Soul, Nerves, World

  Maria Mitchell (1896). “Maria Mitchell: Life, Letters, and Journals”

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• Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

  Alan Turing

  Exercise, Two, Intuition

  "Systems of Logic Based on Ordinals". Proceedings of the London Mathematical Society, Series 2, Volume 45, 1939.

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• 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.

  Ivars Peterson

  Islands, May, Ingredients

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• How are we to adjudicate among rival ontologies? Certainly the answer is not provided by the semantical formula "To be is to be the value of a variable"; this formula serves rather, conversely, in testing the conformity of a given remark or doctrine to a prior ontological standard.

  Willard Van Orman Quine

  Doctrine, Answers, Variables

  Willard Van Orman Quine, Roger F. Gibson (2004). “Quintessence: Basic Readings from the Philosophy of W.V. Quine”, p.189, Harvard University Press

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• The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.

  Georg Cantor

  Independent, Order, Numbers

  "Mind Tools: The Five Levels of Mathematical Reality". Book by Rudy Rucker, 1987.

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• My opinion of mankind is founded upon the mournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in.

  Augustus De Morgan

  Believe, Mean, Facts

  Augustus De Morgan (1872). “A Budget of Paradoxes Reprinted, with the Author's Additions, from the Athenaeum Augustus De Morgan”, p.70

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• There are no solved problems; there are only problems that are more or less solved.

  Henri Poincare

  Knowledge, Math, Logic

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• And as for death - we get what we expect.

  Janet Morris

  Humility

  Lynn Abbey, C. J. Cherryh, Janet Morris (1986). “Soul of the city”, Ace Books

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• Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

  David Hilbert

  Vitality, Connections, Opinion

  "Mathematical Problems". Lecture delivered before the International Congress of Mathematicians at Paris, translated by Maby Winton Newson, mathcs.clarku.edu. 1900.

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• Generally speaking there is no irreducible taste or inclination. They all represent a certain appropriative choice of being. It is up to existential psychoanalysis to compare and classify
  them. Ontology abandons us here; it has merely enabled us to determine the ultimate ends of human reality, its fundamental possibilities, and the value which haunts it.

  Jean-Paul Sartre

  Reality, Choices, Fundamentals

  Jean-Paul Sartre (1985). “Existentialism and Human Emotions”, Citadel Press

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• The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it.

  Eugene Wigner

  Logic, Mysterious, Mathematics

  Eugene Paul Wigner, Jagdish Mehra, Arthur S. Wightman (1997). “Philosophical Reflections and Syntheses”, p.535, Springer Science & Business Media

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• Absence of evidence is not evidence of absence.

  Martin Rees

  Science, Vastness, Logic

  Quoted in Project Cyclops: A Design Study of a System for Detecting Extraterrestrial Intelligent Life, rev. ed., ed. B. M. Oliver and J. Billingham (1973). An earlier version by A. R. Burn appeared in a book review by Burn in The Classical Review, June 1969: "absence of evidence is not identical with evidence of absence."

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• The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

  Eugene Wigner

  Science, Law, Miracle

  Eugene Paul Wigner (2012). “Philosophical Reflections and Syntheses”, p.549, Springer Science & Business Media

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• Although my knowledge grows more and more, nevertheless I do not for that reason believe that it can ever be actually infinite, since it can never reach a point so high that it will be unable to attain any greater increase.

  Rene Descartes

  Believe, Logic, Infinite

  Rene Descartes, Elizabeth Sanderson Haldane, G. R. T. Ross (2003). “Discourse on Method and Meditations”, p.89, Courier Corporation

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• Our account does not rob the mathematicians of their science... In point of fact they do not need the infinite and do not use it.

  Aristotle

  Doe, Needs, Use

  Aristotle (2016). “Physics”, p.82, Aristotle

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• A good proof is one that makes us wiser.

  IU?. I. Manin

  Logic, Proof, Certainty

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• Utopia would seem to offer the spectacle of one of those rare phenomena whose concept is indistinguishable from its reality, whose ontology coincides with its representation.

  Fredric Jameson

  Reality, Utopia, Offers

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• When the boy begins to understand that the visible point is preceded by an invisible point, that the shortest distance between two points is conceived as a straight line before it is ever drawn with pencil and paper...the fountain of all thought has been opened to him...the philosopher can reveal him nothing new, as a geometrician he has discovered the basis of all thought.

  Johann Wolfgang von Goethe

  Distance, Boys, Two

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• Every man heals himself.

  Janet Morris

  Destiny, Men, Heal

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• One to a customer was the rule: one body; one mind; one swing through life. - Tempus

  Janet Morris

  Swings, Mind, Body

  Janet Morris (2011). “Tempus with His Right-Side Companion Niko”, p.56, Paradise Publishing

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