Logic is not always a surefire way to come to a sound conclusion nor is it a new idea. It's useful but it is always corrupted by personal biases
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Logic correctly done with enough correct information is true. If it's not, then it's not logic or there is not enough information yet, which is constantly a growing resource. People change their beliefs with evidence all the time. If it is not logical, it's not true.
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Is it logical to trust in your logic?
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If you study it and think it has coherent reasoning. Unless you're trying to be all trippy.
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How much correct information is enough
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We constantly search for new information. We base our deductions off of the knowledge we have currently, and change it if new information requires that we do.