I have encountered this criticism on multiple occasions: the Protestant paradigm of Scripture leads to an inevitable subjectivism, where ultimately the individual decides on a whim what he or she wants to believe.
I always thought that adhering to a confessional tradition avoided this problem, after all you adhere to the articles of some confession that is not strictly up to you, but to trained teachers whom you can trust to correctly interpret the Scriptures, even on subjects you have not studied. You have a “magisterium”.
But why trust the Reformed tradition to have the truth, rather than trusting the Lutheran, Anglican, Orthodox, or Roman Catholic tradition? Doesn't that lead to subjectivism as well? There are always eternal exegetical debates between all these camps. Every answer has a counter-answer, practically ad-infinitum, and if so, is there any objective reason to decide between one or the other? The romanists say yes, “the pope”, what do we have?
For nearly two millennia, creeds, confessions, and catechisms have provided the necessary constraints against ignorance and instability. But if they aren't infallible, why even use them?
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This is an old philosophical problem, as Jacob alluded to. It basically says that without a firm foundation for all of our knowledge we can't be sure of any of it. Like math, 1+1=2 right? We have a complete arithmetic that is absolutely true no matter what, but that's not true either. So what do we do now?
Don't get hung up on the math example but I only bring it up to show that even in the one place that we would expect to find absolute TRUTH we can't. So do we reject certainty? Well as Jacob pointed out only if we are operating under that Cartesian sort of knowing.
But as others have pointed out even the RCC has this problem. The Magisterium can and does change, despite what they say. They have slippery words to describe it in ways that make it sound different than it is.
So they have the same problems everyone else has but only if that Cartesian model is correct. There's no shortage of criticisms on why that's wrong (the Cartesian model), so what do we do? Well, accepting that we are finite/sinful creatures and will never be without error in our theology (or anything else) there is another route.
The Bible is the objective word of God to finite/sinful men and women. It is that absolutely inerrant and infallible revelation of God to human beings. Therefore it's authority is self attesting because it needs no other foundation for it's own authority, no human institution.
Now human (read finite/sinful humans here) interpretations can and have been wrong before but we have tradition as an inferior and subordinate authority to scripture. That makes us different than Catholics and superior.
We can and should change our Confessions if they are wrong but that's a very hard process (and it should be) . We don't need slippery words to hide what we're doing, like Catholics, because we're honest and upfront about the finite/sinful situation we're in. Also we're honest about the trail of authority, the self-attesting scripture to the subordinate creeds and confessions, to the subordinate theological tradition judged by our church courts to be in accord with Scripture and the Creeds and Confessions.
But the faith didn't fall out of heaven here and now. We have a history of finite/sinful men who have studied the Word and mined it for a theology that we know can be true. But how do we judge them? Well the church courts judge them within the denominations in the same fashion. We accept the confession as being true in it's interpretation of Scripture (the one self-attesting foundation for truth) , so our courts judge teachings against that and in our Confessions.
So you see the levels of authority laid out for us. The self-attesting scriptures first. Than the Creeds and Confessions being finite/sinful interpretations of the scriptures. Then below that our theological tradition, judged against both by our church courts. That's a lot, if anything doesn't make sense then ask. But think about this, is this practically even a problem?
The RCC in theory is different than us because tradition is equal (but actually superior) to Scripture and like Scripture can't change, but it does. So they're taking out both sides of their mouth because they are stuck in that Cartesian model warts and all. We have a superior model that moves from God to the Scriptures, to the Creeds and Confessions, to our tradition judged by the courts of the church against both.