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PNC and quantum mechanics - mathematical versus sensible realities

Is it possible to accept PNC as Aristotle states it and yet deal with the consequences that quantum states may have on the PNC? Perhaps a way around the problem of the PNC and quantum mechanics - specifically Schrödinger's Cat - is to say that the PNC deals with immediately sensible things and the epistemological effects thereof, whereas quantum mechanic's description of a quantum state is a mathematical reality that collapses when we try to observe it. In other words, there is no problem believing the reality of the paradox of a photon having both positive and negative spin before specific observation and still agreeing that it is not possible for one and the same thing both to have and not to have one and the same property at the same time.
Is this a slippery way away from having an example of a true contradiction - i.e. argument against PNC?

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