e iff $E\in \mathcal{E}_{S}$, Q-false iff $E\in \mathcal{E}_{S}^{\bot }$). It is then important to observe that the characterizations of $\mathcal{E}_{S}$ and $\mathcal{E}_{S}^{\bot }$ provided in Sec. 2.3 show that, for every $S\in \mathcal{S}$, one can deduce from theoretical laws of QM whether a property $E$ belongs to $\mathcal{E}_{S}\cup \mathcal{E}_{S}^{\bot }$. In particular, $E$ belongs to $\mathcal{E}_{S}$ ($\mathcal{E}_{S}^{\bot }$) iff it has probability 1 (0) for every $x$ in the state $S$. Hence, one can predict, for every $E\in \mathcal{E}$ and $x$ in the state $S$, whether $E(x)$ is Q-true, Q-false or meaningless. This result shows that standard QM is a semantically complete theory$^{(12)}$ and, together with proposition TF, explains the definition of *true* as *certain*, or *predictable*, which occurs in some approaches to QM.$^{(13,14)}$

Nonobjectivity versus objectivity in QM
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The position expounded in Sec. 2.4 about the truth value of sentences of the form $E(x)$, with $E\in \mathcal{E}$, is sometimes summarized by saying, briefly, that physical properties are *nonobjective* in standard QM (to be precise, only the properties in $\mathcal{E}_{S}^{I}$ should be classified as nonobjective for a given $S\in \mathcal{S}$).

Nonobjectivity of properties is supported by a number of arguments. Some of them are based on empirical results (e.g., the two-slits experiment), some follow from seemingly reasonable epistemological choices (e.g., the adoption of a verificationist position, together with the indeterminacy principle) and some take the form of theorems deduced from the mathematical apparatus of QM. These last arguments are usually considered conclusive in the literature. We remind here the Bell-Kochen-Specker and Bell’s theorems$^{(15-18)}$ which seem to prove that it is impossible to assign classical truth values to all sentences of the form $E(x)$, with $E\in \mathcal{E}$, without contradicting the predictions of QM.

However, all arguments which show t