nothing to do with quantum mechanics. And when $\Pi_b = \Pi_c$, we have $\Pi_b \& \Pi_c = \Pi_c$, hence $P_{abc}=\<a|\Pi_c|a\>=P_{ac}$, and turns out to be [*always*]{} true in the quantum logic calculus, in contrast to what Feynman claimed.

On the other hand, the statement $P_{abc}=0$ if $\Pi_b \ne \Pi_c$ seems somewhat counterintuitive, since if $\Pi_b\approx \Pi_c$ one might want to have $P_{abc}\approx P_{ac}$. In view of the fact that, unless $\Pi_b$ and $\Pi_c$ commute, there is no simple [*algebraic*]{} expression relating $\Pi_{bc}$ to $\Pi_b$ and $\Pi_c$, one is not compelled to adhere to the rigid assignment $\Pi_b \& \Pi_c = 0$ and might prefer to consider $\Pi_b \& \Pi_c$ to be undefined if $\Pi_b$ and $\Pi_c$ do not commute, interpreting this as an indication that $P_{abc}$ cannot be predicted (in principle) by the formalism of quantum theory (and thus may have any value).

In view of the fact that the counterintuitive abundance of zero projectors has further undesirable consequences to be discussed in Section \[path\], this would seem a more satisfactory solution of Feynman’s argument. A new quantum logic consistent with this interpretation is discussed in [Neumaier]{} [@Neu1].

Wigner’s claim {#wigner}
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Similar discussions as those given by Feynman usually 