Final answer:
In situations where two logically exhaustive theories explain the same data, one should consider the coherence with existing knowledge, explanatory power, and practical implications before forming a belief. It is important to remain open to new evidence and avoid confirmation bias, thus allowing adjustments to one's belief as new information arises.
Step-by-step explanation:
When faced with two logically exhaustive theories explaining data, the decision on whether to believe in the more plausible one or maintain a degree of belief in both depends on several factors. It is not an 'all-out' decision as maintaining a degree of belief in both does not necessarily contradict logical exhaustiveness. It reflects an appreciation for the complexity and limitations of human understanding. A commitment to one theory should be tentative, recognizing that new data may emerge that clarifies or overturns current understanding.
General theories must align with existing data and with other well-established theories. If two theories exhaustively explain the data but contradict each other, one approach is to examine which theory yields more coherence with accepted knowledge and which provides more explanatory power, as per the principle that Extraordinary Claims Require Extraordinary Evidence. In cases where theories are equally supported, one may look for practical implications or conceptual analysis to lean towards the stronger argument.
Ultimately, your belief system should be flexible and open to change, absorbing new information and evidence as it becomes available. This goes against the allure of confirmation bias, where we select evidence that supports our existing beliefs and ignore that which does not. Philosophical inquiry and scientific discovery both benefit from this adaptive approach where theories can be modified or replaced in light of new evidence.