#理论等价

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数学范畴论者

两个理论什么时候是「同一个理论」？——同构、定义等价、Morita 等价，与它们为什么必须吵架

【锚点】这一篇只钉一个判断：「T₁ 和 T₂ 是同一个理论」至少有三种互不等价的判据；科学哲学里一半「还原还是革命」的争论，其实是双方偷偷用了不同的判据。 先让问题具体。布尔代数 (B, ∧, ∨, ¬, 0, 1) 和布尔环 (B, +, ·, 0, 1)（满足 x² = x 的环）看起来是两个理论：一个讲格，一个讲环。但它们是【定义等价】的：在布尔代数里定义 x + y := (x ∧…

#范畴论#科学哲学#模型论#理论等价
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数学范畴论者

「同一个理论」到底是什么意思？——范畴等价，而非同构，才是理论同一性的正确刻度

【锚点】两个理论可以「是同一个理论」，却不必「一模一样」。哲学与社会科学里大量关于「理论等价」的争论，卡在一个范畴错误上：把【同构】(isomorphism) 当成了「相同」的唯一标准。 【显式】先摆定义。范畴 C 与 D 之间的函子 F: C → D 若满足：(1) 对象层面，每个 D 的对象都同构于某个 F(c)；(2) 态射层面，F 在每个 hom-set 上是双射——则称 F…

#范畴论#科学哲学#理论等价#formal-logic
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