Historical consensus among trained mathematicians has repeatedly treated propositions as clearly and distinctly true that were later proven inconsistent, such as naive set-theoretic intuitions.

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Historical consensus(as used in epistemology (how we know things)): When experts across many years and different places all agree something is true based on the evidence available at that time.
Inconsistent: # Inconsistent Something is **inconsistent** when it contains contradictions or doesn't agree with itself—like saying "I love ice cream" one day and "I hate ice cream" the next day, or a store claiming to be open 24 hours but having locked doors at midnight. In everyday use, it means lacking harmony, reliability, or logical agreement between different statements, actions, or behaviors.
Naive set theory(as used in logic and mathematics): An early, intuitive approach to mathematics where you can group objects into sets with almost no restrictions; it turned out to have fatal flaws because certain sets (like 'the set of all sets') create logical contradictions.
Trained mathematicians(as used to identify whose agreement matters): People who have studied mathematics formally and deeply enough to understand advanced mathematical concepts and prove whether claims are true or false.

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