In the popular example of "Schrödinger's cat" (see citation below), both polemic states of being alive and dead are accepted as true. Schrödinger presents a situation that, despite the seemingly inherent fact that if one is alive they are not dead (and vice versa), in the mathematical interpretation of a physical experiment you can have a "justified true belief" for both possibilities simultaneously. It is only until one opens the box that one becomes true and the other false.
This epistemological issue exists in the relationship to "Truth" and "Knowledge". While A and "not-A" cannot both be observably true, they can theoretically (mathematically) exist simultaneously given a closed system without an observer. This same issue is brought to light with similar thought experiments.
A man stands in a field full of barn facades. In the field there is one real (non-facade) barn. The man, under the impression that all the barns are real, points to the real barn and says, "That is a barn".
Though the man has a "true belief", the justification of that belief complicates the matter, because he has a false sense of the accuracy of his choice. However it does not in the end diminish the accuracy of his statement. Therefore, even with a fallacious premise ("the man believing all the barns were real") the truth of his statement remains intact. Just as the truth of the cat being simultaneous dead and alive remains intact, until an observer opens the box. These are examples of Logical Truths despite false premises.
...ridiculous cases [like, a] cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
~ Erwin Schrödinger, Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics), Naturwissenschaften
(translated by John D. Trimmer in Proceedings of the American Philosophical Society)
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