And What, Then, Is Belief? It Is

A Pair Of Statements May Be Taken Conjunctively Or Disjunctively; For Example, "it Lightens And It Thunders ," Is Conjunctive, "it Lightens Or It Thunders" Is Disjunctive. Each Such Individual Act Of Connecting A Pair Of Statements Is A New Monad For The Mathematician .

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.

A Quality Is Something Capable Of Being Completely Embodied. A Law Never Can Be Embodied In Its Character As A Law Except By Determining A Habit. A Quality Is How Something May Or Might Have Been. A Law Is How An Endless Future Must Continue To Be.

A Sign, Or Representamen, Is Something Which Stands To Somebody For Something In Some Respect Or Capacity. It Addresses Somebody,that Is, Creates In The Mind Of That Person An Equivalent Sign, Or Perhaps A More Developed Sign. That Sign Which It Creates I Call The Interpretant Of The First Sign. The Sign Stands For Something, Its Object. It Stands For That Object, Not In All Respects, But In Reference To A Sort Of Idea, Which I Have Sometimes Called The Ground Of The Representamen.

Mathematics Is Purely Hypothetical: It Produces Nothing But Conditional Propositions.