there's no such thing as a "burden of proof", but demands of proof do definitely exist.
what is called burden of proof is a form of demand of proof which is dressed up as an obligation - but it is fallacious because it pre-supposes that the person the burden is placed on for some reason MUST convince the other; in most cases, they in fact have a choice.
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yes, that you're arguing a point does indicate you wish to convince the other person, but demands of proof can be goalpost-shifts; so when you make a demand of proof the other person has to decide whether it is worth it, and if you're arguing in good faith.
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thus the example of Thomas - doubting in good faith. "I wish to have more proof", and when provided, he believed. Those arguing in bad faith do one or both: shift again if evidence is provided, or purposely demand evidence they think cannot be provided.
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