The essence of mathematics lies precisely in its freedom.
Georg CantorRead
The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.
Interpretation
Fear of the infinite limits our understanding of the vast possibilities of existence.
In this quote, Georg Cantor highlights how fear and limited perception hinder our ability to grasp the concept of infinity. He suggests that while infinity in its purest form is essential to our existence, fear can blind us to its presence in various forms in our lives and thoughts, preventing us from appreciating the true depth and breadth of reality.
In practice
In a philosophical discussion about the nature of existence, this quote can highlight the dangers of limiting oneself to finite thinking.
The essence of mathematics lies precisely in its freedom.
I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.
Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.
A set is a Many that allows itself to be thought of as a One.
The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
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.
Not from the stars do I my judgement pluck, And yet methinks I have astronomy. But not to tell of good or evil luck, Of plagues, of dearths, or season's quality; Nor can I fortune to brief minutes tell ... Or say with princes if it shall go well.
If there is existence, there must be non-existence. And if there was a time when nothing existed, there must have been a time before that - when even nothing did not exist. Suddenly, when nothing came into existence, could one really say whether it belonged to the category of existence or non-existence?
I have always been full of lust - as I am now - but I have always been placing conceptual obstacles in my own path.
Each of us must turn inward and destroy in himself all that he thinks he ought to destroy in others.
Integrity is fundamental to being men. Integrity means being truthful, but it also means accepting responsibility and honoring commitments and covenants.
I wonder if it hurts to live, And if they have to try, And whether, could they choose between, They would not rather die.
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