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 (≈Venn diagram: Figure 3)

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