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The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

And in what follows we’ll see the great power that arises from using this to combine the achievements and intuitions of physics and mathematics—and how this lets us think about new “general laws of mathematics”, and view the ultimate foundations of mathematics in a different light. So how about logic, or, more specifically Boolean algebra ?

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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

Instead, what happens is that the universe evolves by virtue of lots of elementary updating events happening throughout the network. How do we achieve this? Let’s say that we’re trying to achieve the objective of having an efficient transportation system for carrying people around. Last[#][[1]]], GrayLevel[0.5,

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The Concept of the Ruliad

Stephen Wolfram

For example, we know (as I discovered in 2000) that (( b · c ) · a ) · ( b · (( b · a ) · b )) = a is the minimal axiom system for Boolean algebra , because FindEquationalProof finds a path that proves it. elementary updating events) in physical space.

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