I Presume That Few Who Have Paid

It Is Not Of The Essence Of Mathematics To Be Conversant With The Ideas Of Number And Quantity.

Probability Is Expectation Founded Upon Partial Knowledge. A Perfect Acquaintance With All The Circumstances Affecting The Occurrence Of An Event Would Change Expectation Into Certainty, And Leave Nether Room Nor Demand For A Theory Of Probabilities.

I Am Fully Assured, That No General Method For The Solution Of Questions In The Theory Of Probabilities Can Be Established Which Does Not Explicitly Recognize, Not Only The Special Numerical Bases Of The Science, But Also Those Universal Laws Of Thought Which Are The Basis Of All Reasoning, And Which, Whatever They May Be As To Their Essence, Are At Least Mathematical As To Their Form.

It Follows That The Word Probability, In Its Mathematical Acceptance, Has Reference To The State Of Our Knowledge Of The Circumstances Under Which An Event May Happen Or Fail. With The Degree Of Information We Possess Concerning The Circumstances Of An Event, The Reason We Have To Think That It Will Occur, Or, To Use A Single Term, Our Expectation Of It Will Vary. Probability Is The Expectation Founded Upon Partial Knowledge.

To Unfold The Secret Laws And Relations Of Those High Faculties Of Thought By Which All Beyond The Merely Perceptive Knowledge Of The World And Of Ourselves Is Attained Or Matured, Is A Object Which Does Not Stand In Need Of Commendation To A Rational Mind.