# Should we think about superposition in a fuzzy or in a paraconsistent manner?

Suppose we define a predicate $$L$$ as "is alive." We then take Schrödinger's cat, $$c$$, and put it in its box and wait for a time for it to be equally likely for it to be dead and alive. How should we think about the sentence $$Lc\land\lnot Lc$$? If superposition is fuzzy, then we should find that:

$$Lc\land\lnot Lc \leftrightarrow \frac{1}{2}$$

But if superposition is instead paraconsistent we find:

$$Lc\land\lnot Lc \leftrightarrow \top$$

Is one more appropriate to superposition, or is there another logic we should use?

• You will need a kind of logic that can handle probability, and then also its complex analog in QM. Nov 26 '20 at 23:25
• Just a comment... in quantum mechanics, you never get into logical trouble if (a) you only ever talk about the outcomes of observations, and (b) you are comfortable with probabilistic statements, like "spin up will be measured 50% of the time." You only have problems if you start talking about things that are not measurable, like "which path did the electron take to get from the double slit to the measurement apparatus." My perspective is that from the point of view of physics, the most reasonable approach is to simply accept that we can't answer the question "what path did the electron take." Nov 26 '20 at 23:25
• Why are you representing “is alive” as a predicate rather than a hermitian operator? Recall that superposition refers to addition, not disjunction. Nov 27 '20 at 2:04
• @Sandejo but that's not really relevant to Schrodinger's cat, is it? Living/Not living isn't really a function per se at least not one that you can add (although you could paraphrase into the order of particles in the cat, or the order of particles in our perception of the cat; but that dismisses our rather Moorean concepts of life). Thus it makes more sense to use a predicate. But if you're insistent on using an operator, consider the question to be asking how the hermatian operator relates to predication. Dec 14 '20 at 20:56
• @tox123 The problem is that, in QM, it is not meaningful to ask whether the cat is alive, only whether it will be observed to be alive. If you wish to keep $L$ as a predicate, you would need to redefine it as something like "will be observed to be alive," in which case I think it would follow classical logic. Dec 14 '20 at 22:10