Mathematics Is Purely Hypothetical: It

By An Object, I Mean Anything That We Can Think, I.e. Anything We Can Talk About.

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.

If Man Were Immortal He Could Be Perfectly Sure Of Seeing The Day When Everything In Which He Had Trusted Should Betray His Trust.

Consider What Effects That Might Conceivably Have Practical Bearings You Conceive The Objects Of Your Conception To Have. Then, Your Conception Of Those Effects Is The Whole Of Your Conception Of The Object.

The Opinion Which Is Fated To Be Ultimately Agreed To By All Who Investigate, Is What We Mean By The Truth, And The Object Represented In This Opinion Is The Real. That Is The Way I Would Explain Reality.