Yes, it is possible for predicate properties to be neither true nor false. This concept is known as "indeterminacy" or "undecidability" in logic and mathematics.
This can occur when there is insufficient information or evidence to determine the truth or falsity of a statement. It can also happen when a statement is self-referential or paradoxical.
Yes, acknowledging and addressing indeterminacy is crucial in scientific research because it helps us understand the limits of our knowledge and the uncertainties in our findings. It also encourages critical thinking and promotes further investigation.
Yes, there are many examples of indeterminacy in science, such as the famous Schrödinger's cat thought experiment in quantum mechanics, the concept of free will in psychology, and the nature of time in physics.
It depends on the specific case. In some cases, further research and evidence may lead to a resolution of indeterminacy. In other cases, indeterminacy may be inherent in the nature of the question or statement, and therefore cannot be resolved definitively.