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Okay. Good. We now have established how premises support their conclusion, but how, then, do they prove their conclusion? I think they can only do this by being proven themselves, which requires something external, no?
Unless you're just proving theorems in an axiomatic system, then ultimately you will have to step outside of deductive logic to find your premises - and demonstrate their proof. So yes the "proof" of the premises will be external to the argument, and will likely involve some other mode of reasoning.
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How do we prove premises true? Is this the purpose of evidence? If so, how does evidence prove premises true?
The study of how we know things - which is really what you are asking about - is called epistemology. If our premises are not derived deductively then they will be supported (if they
are supported) by some other mode of thinking, and I cannot think of any I would accept that do not sue some form of evidence.
The details of how that evidence is used, will control how it supports the statement. For instance we could use direct observation to supply a premise for a deductive argument. Or we could use a set of controlled observations to inductively demonstrate a generalised statement.
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