Tag: Philosophy of Mathematics
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Wonderful Language of Mathematics
Through the character Socrates in the dialogue Theaetetus, Plato states, “Wonder is the feeling of the philosopher, and philosophy begins in wonder.” Many centuries later in The Assayer, Galileo states, “Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first…
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Liar Paradox and Logicism
This statement is false. Here the opening statement must be false if it is true, and true if it is false. In other words, if the statement is false, then that means it must be true. But if the statement is true, then that means it must be false. The Liar Paradox is the paradox…
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Philosophy of Mathematics – Part 3: Discovered or Invented
In Part 1, we learned that the philosophy of mathematics is the branch of philosophy that relates to the foundation of mathematics. In Part 2, we learned that the philosophy of mathematics is also the branch of philosophy that deals with the nature of mathematics. Now in Part 3, we ponder whether mathematics is discovered…
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Philosophy of Mathematics – Part 2: Nature
As I stated earlier in Part 1, the philosophy of mathematics is the branch of philosophy that relates to the foundation of mathematics, deals with the nature of mathematics, and ponders whether mathematics is discovered or invented. Part 2 focuses upon the nature of mathematics. The books Arithmetic by Paul Lockhart and Beautiful Math: The…
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Philosophy of Mathematics – Part 1: Foundation
The branch of philosophy that relates to the foundation of mathematics, deals with the nature of mathematics, and ponders whether mathematics is discovered or invented is known as the philosophy of mathematics. Part 1 focuses upon the foundation of mathematics. The book One, Two, Three: Absolutely Elementary Mathematics by David Berlinski is a great source…