The Essence Of Belief Is The Establishment

For Example, There Are Numbers Of Chemists Who Occupy Themselves Exclusively With The Study Of Dyestuffs. They Discover Facts That Are Useful To Scientific Chemistry; But They Do Not Rank As Genuine Scientific Men. The Genuine Scientific Chemist Cares Just As Much To Learn About Erbium-the Extreme Rarity Of Which Renders It Commercially Unimportant-as He Does About Iron. He Is More Eager To Learn About Erbium If The Knowledge Of It Would Do More To Complete His Conception Of The Periodic Law, Which Expresses The Mutual Relations Of The Elements.

Upon This First, And In One Sense This Sole, Rule Of Reason, That In Order To Learn You Must Desire To Learn, And In So Desiring Not Be Satisfied With What You Already Incline To Think, There Follows One Corollary Which Itself Deserves To Be Inscribed Upon Every Wall Of The City Of Philosophy: Do Not Block The Way Of Inquiry.

When An Image Is Said To Be Singular, It Is Meant That It Is Absolutely Determinate In All Respects. Every Possible Character, Or The Negative Thereof, Must Be True Of Such An Image.

Another Characteristic Of Mathematical Thought Is That It Can Have No Success Where It Cannot Generalize.

The One [the Logician] Studies The Science Of Drawing Conclusions, The Other [the Mathematician] The Science Which Draws Necessary Conclusions.