Two people might be in an argument with one another and disagree on the outcome.

Two people might be in an argument with one another and disagree on the outcome.

Two people might be in an argument with one another and disagree on the outcome. We might say that one person thinks the argument is sound, while another does not. That is to say, the argument depends upon some (possibly unknowable or undecidable) assumptions, and the two people disagree in their belief of whether the assumptions actually are true. Is it fair to say that any disagreement about the validity of an argument should always be reconcilable? Even if the disagreement is about the reasoning process itself, this disagreement should be reducible to axioms which both participants hold or don't hold arbitrarily. I am confused about why there is so much disagreement in philosophical circles. If arguments drew from fundamental assumptions (such as whether a being has natural rights), then it seems arguments should conclude quite reasonably with "Aha, well I see that you have an arbitrary belief in this, while I have an arbitrary belief in that". Unless the assumption of some argument is itself the subject of truth for some other argument (and some other assumptions), should not all arguments end in this way -- with understanding of both side's assumptions and an agreement on validity? I am confused why both sides should not recognize that the other is just as unknowably sound when described in terms of arbitrary assumptions. Are there philosophical arguments that don't fit this model? Is it simply that philosophical arguments are so complex that we cannot agree on whether any given argument is valid?

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