Do Numbers Exist? The Philosophy of Mathematics
Where do numbers live? Platonism: an eternal abstract realm. Intuitionism: we build them in the mind. From the foundational crisis to proofs-as-programs.
Steps
- 1
- Reading· ~11 min
Benacerraf's Two Puzzles: The Problem Nobody Has Solved
Paul Benacerraf's devastating 1973 paper identified two constraints that no philosophy of mathematics has yet satisfied simultaneously. This is genuinely unsolved.
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- Reading· ~9 min
The Unreasonable Effectiveness of Mathematics
Why mathematics, invented (or discovered) without any physical application in mind, keeps turning out to describe the physical world with uncanny precision.
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- Text Explore· ~8 min
Benacerraf's Dilemma
Examine the two constraints that define the central problem of philosophy of mathematics.
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- Argument Map· ~10 min
The Ontology of Mathematical Objects
Map the competing positions on mathematical existence and the arguments for and against each.
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- Dialogue· ~10 min
Dialogue: Is 7 Real?
The question that drives the whole debate, and why your answer commits you to a surprising amount.
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- Reflection· ~8 min
Reflection: Your Mathematical Reality
Philosophy of mathematics is not only for specialists, your implicit view of numbers reveals something about your metaphysics.
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