#mathematicalphilosophy — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #mathematicalphilosophy, aggregated by home.social.
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We've computationally verified that Peano arithmetic emerges naturally from just two operators: Δ (distinction/branching) and Σ (connection/composition).
This isn't just coding — it's evidence for the Δ–Σ Turing Completeness Theorem: a system is Turing-complete iff it can be represented through Δ and Σ.
Code implements the proofs: https://github.com/muskin88/delta-sigma-peano/blob/main/Peano_from_deltasigma.py
Formal statement: https://zenodo.org/records/17895986
(Theorem 3)The implications are ontological: these operators appear inevitable for any non-trivial reality. The framework unites computation, mathematics, and fundamental ontology.
#CategoryTheory #FoundationsOfMath #Computation #Ontology #FormalMethods #TypeTheory #PeanoArithmetic #TuringCompleteness #MathematicalPhilosophy
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We've computationally verified that Peano arithmetic emerges naturally from just two operators: Δ (distinction/branching) and Σ (connection/composition).
This isn't just coding — it's evidence for the Δ–Σ Turing Completeness Theorem: a system is Turing-complete iff it can be represented through Δ and Σ.
Code implements the proofs: https://github.com/muskin88/delta-sigma-peano/blob/main/Peano_from_deltasigma.py
Formal statement: https://zenodo.org/records/17895986
(Theorem 3)The implications are ontological: these operators appear inevitable for any non-trivial reality. The framework unites computation, mathematics, and fundamental ontology.
#CategoryTheory #FoundationsOfMath #Computation #Ontology #FormalMethods #TypeTheory #PeanoArithmetic #TuringCompleteness #MathematicalPhilosophy
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Everyone exists on a unique plane that can only be distantly observed, never shared.
And no one can ever see our true (from our frame of reference) shape, only the distorted intersection with their plane.
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Everyone exists on a unique plane that can only be distantly observed, never shared.
And no one can ever see our true (from our frame of reference) shape, only the distorted intersection with their plane.