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Saying Mathematics ≠ Reality fails to capture a large portion of the story, since a subset of mathematics is clearly necessary to be able to encode science, and

• mpweiher 4y ago
  It's not necessary. It is empirically useful. Mathematics is about describing possible worlds. Given these assumptions (including the rules of the game), what follows? Science is about figuring out the real world. The real world has no obligation to be describable by mathematics. That it is so describable is fortuitous. "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning." https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
  • feanaro 4y ago
    > It's not necessary. I didn't mean "necessary" in the sense of modal logic, but in a more colloquial sense. Physical laws as known to us today are described using mathematics. We know of no other viable ways to describe them. In that sense, (a subset of) mathematics is necessary for this purpose. It was just meant as a restatement of the concept of unreasonable effectiveness of mathematics in a more natural language. > The real world has no obligation to be describable by mathematics. There is no obligation, but that it is so in our particular world is undeniable fact.