On one hand, arguments are supposed to be objective – something which is true is always true, for everyone. On the other hand, if person says “P exists because X,Y,Z”, while he personally has seen the evidence (x,y,z) for P, and another person says “P exists because X,Y,Z” and he has only read about X,Y,Z from second sources – their knowledge is actually very different. Where is that difference (crucial one) reflected in logic?

I think your question is rooted in the fact that we generally consider two distinguishably different subjects under the umbrella of logic. The first is the art of argument as it takes place in natural[…]

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I would take a standard textbook on math, where all the propositions are correct. Write down 99 correct mathematical statements. And then add “Zeus exists”, and compile a text. Then I would argue, that if we have a box, from which we sample randomly 99 balls and they are have the property of being black, we can think with good reason that the next one will be black. And therefore, since 99 of the math propositions in the texts are have the property of being correct, there is good reason to think that “Zeus exists” is also correct. It seems wrong somewhere. But where?

No matter how strong an inductive argument is, it cannot guarantee results the same way a deductive argument can. It is always theoretically possible for the premises of an inductive argument to be true and[…]

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