Dear Peter,
Thank you for the very interesting essay.
I have given it a single read, but it will take more because it rapidly ramps-up with ideas coming at the reader at a fast and furious pace.
I have some concerns that have me thinking (always a good thing, so thank you!).
The three laws you look at are laws that apply to logical propositions, not objects. And I would worry about anyone seriously trying to apply them to objects. One should not expect them to apply to objects, as you deftly point out.
Incidentally, this is an issue in quantum mechanics where we implicitly (and wrongly) expect our logic of propositions to apply to experimental setups. In quantum mechanics, we quantify experimental setups (which is the terminology that Ariel Caticha has used), or measurement sequences (favored by my past co-author Philip Goyal), with two numbers. One can derive that the mathematics of this pair is equivalent to that of complex numbers, which we refer to as quantum amplitudes.
We assign amplitudes to experimental setups, and we use the relationships among experimental setups to calculate the amplitudes for more complex experiments via the Feynman rules. With the Born rule in hand, one can then calculate the probability associated with that setup (or measurement sequence).
In short, we use two types of measures in quantum mechanics, each operating in a separate space. In the space of experimental setups, or equivalently measurement sequences, we use complex amplitudes. These amplitudes quantify the relationships among experimental setups via the Feynman rules. The Born rule maps the resulting complex amplitude to a probability, which lives in the space of logical propositions about these experiments. Two different measures (quantifications), each with its own algebra and calculus, applied to two different, but coupled, spaces.
It is the lack of recognition that these two quantifications (complex amplitudes and probabilities) live in and quantify elements in two different spaces that have led people to claim that quantum mechanics does not obey Boolean algebra.
Well, what do you mean by quantum mechanics when you say that? Because quantum mechanics is a theory that works in two different, but coupled, spaces. Of course the theory is not Boolean! Only the space of propositions is Boolean! There is NO SINGLE ALGEBRA of QM. The whole thing results from confusion about what we are really doing.
And the way I am thinking about your three laws is that they do not apply to objects. I don't really see a need to rework things. But I do see a need to take more care!
I hope these comments make some sense. I would be happy to engage in a dialogue if you have any questions.
Thank you again for a thought-provoking essay!
Cheers
Kevin