It Is... Easy To Be Certain. One

...mathematics Is Distinguished From All Other Sciences Except Only Ethics, In Standing In No Need Of Ethics. Every Other Science, Even Logic, Especially In Its Early Stages, Is In Danger Of Evaporating Into Airy Nothingness, Degenerating, As The Germans Say, Into An Arachnoid Film, Spun From The Stuff That Dreams Are Made Of. There Is No Such Danger For Pure Mathematics; For That Is Precisely What Mathematics Ought To Be.

We Shall Do Better To Abandon The Whole Attempt To Learn The Truthunless We Can Trust To The Human Mind's Having Such A Powerof Guessing Right That Before Very Many Hypotheses Shall Have Been Tried, Intelligent Guessing May Be Expected To Lead Us To One Which Will Support All Tests, Leaving The Vast Majority Of Possible Hypotheses Unexamined.

Kepler's Discovery Would Not Have Been Possible Without The Doctrine Of Conics. Now Contemporaries Of Kepler-such Penetrating Minds As Descartes And Pascal-were Abandoning The Study Of Geometry ... Because They Said It Was So Utterly Useless. There Was The Future Of The Human Race Almost Trembling In The Balance; For Had Not The Geometry Of Conic Sections Already Been Worked Out In Large Measure, And Had Their Opinion That Only Sciences Apparently Useful Ought To Be Pursued, The Nineteenth Century Would Have Had None Of Those Characters Which Distinguish It From The Ancien Régime.

The Percept Is The Reality. It Is Not In Propositional Form. But The Most Immediate Judgment Concerning It Is Abstract. It Is Therefore Essentially Unlike The Reality, Although It Must Be Accepted As True To That Reality. Its Truth Consists In The Fact That It Is Impossible To Correct It, And In The Fact That It Only Professes To Consider One Aspect Of The Percept.

It Is Certain That The Only Hope Of Retroductive Reasoning Ever Reaching The Truth Is That There May Be Some Natural Tendency Toward An Agreement Between The Ideas Which Suggest Themselves To The Human Mind And Those Which Are Concerned In The Laws Of Nature.