The Transfinite Numbers Are In A Sense

The Actual Infinite Arises In Three Contexts: First When It Is Realized In The Most Complete Form, In A Fully Independent Otherworldly Being, In Deo, Where I Call It The Absolute Infinite Or Simply Absolute; Second When It Occurs In The Contingent, Created World; Third When The Mind Grasps It In Abstracto As A Mathematical Magnitude, Number Or Order Type.

There Is No Doubt That We Cannot Do Without Variable Quantities In The Sense Of The Potential Infinite. But From This Very Fact The Necessity Of The Actual Infinite Can Be Demonstrated.

Every Transfinite Consistent Multiplicity, That Is, Every Transfinite Set, Must Have A Definite Aleph As Its Cardinal Number.

I Entertain No Doubts As To The Truths Of The Tranfinites, Which I Recognized With God's Help And Which, In Their Diversity, I Have Studied For More Than Twenty Years; Every Year, And Almost Every Day Brings Me Further In This Science.

A False Conclusion Once Arrived At And Widely Accepted Is Not Easily Dislodged And The Less It Is Understood The More Tenaciously It Is Held.