Logic in quantum language (Sec. 3) | Logic in Wittgenstein’s theory (Sec. 4) |

Axiom 1 in Section 2.2 (what is a measurement?) the linguistic Copenhagen interpretation in Sec. 2.3 | Definition 17 (what is a proposition?) Naive set theory ( |

system, particle, object, tomato | object, thing, tomato |

state space (state) | logical space (case, fact,, atomic fact) |

[MV], measured value {1, 0} | [TV], truth value {T, F} |

classical binary projective measurement ${\text{M}}_{{L}^{\infty}\left(\Omega \mathrm{,}\nu \right)}\left({\text{O}}^{\Gamma}\equiv \left(X\left(=\left\{\mathrm{1,0}\right\}\right){\mathrm{,2}}^{X}\mathrm{,}{F}^{\Gamma}\right)\mathrm{,}{S}_{\left[\widehat{\omega}\left(t\right)\right]}\right)$ | proposition ${\text{P}}_{\Omega}\left(\Gamma \mathrm{,}{S}_{\left[\widehat{\omega}\left(t\right)\right]}\right)$ |

Theorem 11 (Syllogism in measurements) | Theorem 19 (Syllogism in propositions) |

elementary measurement | elementary proposition |

Theorem 13 (Remark 14) Elementary measurements are not fundamental | Theorem 23 (Remark 24) Elementary propositions are fundamental |