Does quantum mechanics, due to the phenomenon of superposition (Schrodinger's cat is both dead and alive), give reasons to alter the laws of logic, specifically the principle of bivalance (something is either true or untrue). What would be the consequences of such a step?
It's an excellent question.
Heisenberg thought that QM forced us to modify the tertium non datur rule. So do many scientists. They are wrong, and here's why.
The principle of bivalence is not the issue here since it is unnecessary in dialectical logic that all statements are true or false, only that the statements we subject to our logical processes are. Aristotle builds this principle into his logic with his rule for contradictory pairs (RCP).
'Of every contradictory pair one member must be true and the other false.'
Notice that in order to apply the LEM or LNC we must know, before we begin, that one member is true and one false. How often do we forget this?
In QM this is not our situation. For instance, when we say an electron is a wave and also a particle there is no contradiction. This is because we know that an electron is not exclusively one or the other and must actually be neither but something capable of being either. The RCP is not satisfied so the LEM and LNC do not apply.
If you work through the various seemingly contradictory phenomena of QM you'll find that they can all be dealt with in this way. They may seem bafflingly contradictory but they are not actually so in formal logic. Or, at least, nobody has shown them to be so.
Logic allows us to combine false or partially true statements as we wish. Only when the RCP is satisfied do the 'laws of thought' come into play.
In QM and in metaphysics most of the dilemmas, (wave/particle, freewill/determinism, mind/matter and so forth) do not take a form that satisfies the RCP so they are not formal contradictions. For each of them a third option is possible. Heisenberg was wrong. What is needed for QM and metaphysics is not a modification to the LEM but a close examination of the rules for the dialectic.
In my opinion this simple point, once grokked, unlocks the secrets of metaphysics.
EDIT: The law of non-contradiction (LNC) states that for any A it is impossible for both A and ~A to be true. That is to say, if the assertion ‘x is square’ is true, then the assertion ‘x is-not square’ cannot also be true. The law of the excluded middle (LEM) states that it is necessary for one of A and ~A to be true and the other to be false. Either x is square or it is not, there is no third alternative. Where there is a third alternative then A and ~A are not a legitimate dialectical pair.
A common misinterpretation of quantum superposition (something being in two states that appear to be exclusive for perception, like dead and alive) is bivalence, where states are effectively exclusive. The term perception is a key factor, because a phenomenon of superposition does not mean something being in a state A OR B, and neither A AND B, but that quantum state A has multiple perceptible values, which are complementary with B. Quantum probabilities are therefore able to be expressed with imaginary numbers. Such mechanics are logic at the quantum scale of existence, but cannot be grasped by the mechanics of our macroscopic perception.
Bivalence is not at the same level: probabilities in the macroscopic world are a simple percentage. Bivalent states are also exclusive (XOR function: either A is true or false, not both, not none).
Therefore, only by altering the principles of perception it would be possible to grasp the principles of logic from the quantum domain (note that it's not the same as "altering the principles of logic": logic is just the same, except that our perception is not able to approach the logic of the quantum realm; a consequence of such problem is that quantum behavior cannot be described but by using math).