The Pragmatist Knows That Doubt Is An

Truth Is That Concordance Of An Abstract Statement With The Ideal Limit Towards Which Endless Investigation Would Tend To Bring Scientific Belief, Which Concordance The Abstract Statement May Possess By Virtue Of The Confession Of Its Inaccuracy And One-sidedness, And This Confession Is An Essential Ingredient Of Truth.

Among The Minor, Yet Striking Characteristics Of Mathematics, May Be Mentioned The Fleshless And Skeletal Build Of Its Propositions; The Peculiar Difficulty, Complication, And Stress Of Its Reasonings; The Perfect Exactitude Of Its Results; Their Broad Universality; Their Practical Infallibility.

It Is A Common Observation That Those Who Dwell Continually Upon Their Expectations Are Apt To Become Oblivious To The Requirements Of Their Actual Situation.

This Branch Of Mathematics [probability] Is The Only One, I Believe, In Which Good Writers Frequently Get Results Which Are Entirely Erroneous.

Every Work Of Science Great Enough To Be Well Remembered For A Few Generations Affords Some Exemplification Of The Defective State Of The Art Of Reasoning Of The Time When It Was Written; And Each Chief Step In Science Has Been A Lesson In Logic.