We Cannot Begin With Complete Doubt.

Notwithstanding All That Has Been Discovered Since Newton's Time, His Saying That We Are Little Children Picking Up Pretty Pebbles On The Beach While The Whole Ocean Lies Before Us Unexplored Remains Substantially As True As Ever, And Will Do So Though We Shovel Up The Pebbles By Steam Shovels And Carry Them Off In Carloads.

It Is... Easy To Be Certain. One Has Only To Be Sufficiently Vague.

...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.

If Man Were Immortal He Could Be Perfectly Sure Of Seeing The Day When Everything In Which He Had Trusted Should Betray His Trust, And, In Short, Of Coming Eventually To Hopeless Misery. He Would Break Down, At Last, As Every Good Fortune, As Every Dynasty, As Every Civilization Does. In Place Of This We Have Death.

We Cannot Begin With Complete Doubt.