Logic Is An Old Subject, And Since

Our Argument Is Not Flatly Circular, But Something Like It. It Has The Form, Figuratively Speaking, Of A Closed Curve In Space.

The Lore Of Our Fathers Is A Fabric Of Sentences. In Our Hands It Develops And Changes, Through More Or Less Arbitrary And Deliberate Revisions And Additions Of Our Own, More Or Less Directly Occasioned By The Continuing Stimulation Of Our Sense Organs. It Is A Pale Gray Lore, Black With Fact And White With Convention. But I Have Found No Substantial Reasons For Concluding That There Are Any Quite Black Threads In It, Or Any White Ones.

The Mastery Of One's Phonemes May Be Compared To The Violinist's Mastery Of Fingering. The Violin String Lends Itself To A Continuous Gradation Of Tones, But The Musician Learns The Discrete Intervals At Which To Stop The String In Order To Play The Conventional Notes. We Sound Our Phonemes Like Poor Violinists, Approximating Each Time To A Fancied Norm, And We Receive Our Neighbor's Renderings Indulgently, Mentally Rectifying The More Glaring Inaccuracies.

The Totality Of Our So-called Knowledge Or Beliefs, From The Most Casual Matters Of Geography And History To The Profoundest Laws Of Atomic Physics Or Even Of Pure Mathematics And Logic, Is A Man-made Fabric Which Impinges On Experience Only Along The Edges. Or, To Change The Figure, Total Science Is Like A Field Of Force Whose Boundary Conditions Are Experience.

Irrefragability, Thy Name Is Mathematics.