Prologue We usually treat mathematical structures as things we look at—diagrams on a page, symbols in a line, objects to be manipulated by the intellect. But they are not objects. They are environments. They are the invisible architectures that determine what is possible, what is impossible, and what is necessary. You do not just solve … Continue reading The Axiom Engine: A Phenomenology of Abstract Structures
Tag: philosophy
Frame-Switching: The Hidden Pattern in Pointless Arguments
The One-Inch Frame Two friends argue heatedly about whether a hot dog is a sandwich. One insists it is—bread on both sides, filling in the middle. The other insists it isn't—ask any deli. After twenty minutes, neither has moved an inch. How to Disagree About Categories In March 2008, Paul Graham published "How to Disagree," … Continue reading Frame-Switching: The Hidden Pattern in Pointless Arguments
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