Arguments that "prove a point" with a probability of X% (where X is low) is a slippery concept. I'm guessing that this means (using one interpretation of probability), that whenever arguments like this are used, they are found to prove the point 20% of the time. But that seems extremely odd.
I agree assigning probability (regarding proving a point) is suggestive, even if in some case, the use of algorithm can reduce the suggestive part.
It comes back to what it means to "prove a point," which is to make it certain or virtually certain that it is true. I could understand saying that I have an argument that has a 99% probability of proving a point. Maybe, in the past, arguments like this one (which have been checked by two people) have stood the test of time as arguments that prove the point.
In the domain of research on earliest Christianity, it is quasi impossible to have arguments with high probability, because for each one which has been made, there has been a lot of debate and opposition. So trying to make several independent arguments to "prove" the same point is not only commendable but also necessary.
Too many times, scholars (and others) are "proving" their point on only one argument (from one piece of evidence).
And also, many would reject a point because each one of several arguments (used to "prove" the point) is not accepted as "proving" beyond doubts, on its own, the point. However, I think it is wrong reasoning, according to the aforementioned equation.
But 20% chance to prove a point?
Yes, but if one has a large number of independent arguments with similar probabilities in order to make the same point, then those several 20%, put together, are not so ridiculous.
It's a startling claim. It's like saying that there's a 2% chance that a baby can guard Fort Knox with absolute security, or that there's a 4% chance that a crook can be trusted with your money with absolute confidence. It just sounds silly. Only under contrived circumstances could you make statements like that (e.g., maybe a computer program generating arguments could spit out proofs with probability 20% or something).
I agree trying to make a point with a 2% or 4% probability is ridiculous, even with a large numbers of arguments "proving" (with the same low probabilities) that same point.
First, if the probability is so low and cannot be accurately assessed (like most of assigned probabilities not resulting from strictly factual quantified data), it can as well be a 0%.
Second, you would need a lot of arguments in order to arrive to about an overall 50% total probability "proving" the same point; I calculated around 32 of these arguments with, for each, probability of 2%.
But for arguments with 20% probability, we need only three of them to arrive around this 50% overall probability.
Maybe there's a way to make use of these arguments, maybe a way to do so in a probabilistic setting, but they are not "proving" any points.
I would say, I have 6 independent arguments proving the same point. If you accept these arguments as 1) being independent, b) at least having a probability for each of 20% to prove the point, then these arguments put together will show my point is more likely to be valid than not valid.
We too easily allow ourselves to make contradictory assumptions when we let in slippery concepts like this. Imagine two people arguing a topic. Each has six arguments. Each of them insists that they must be allowed at least a 20% chance for their respective arguments to succeed (and that these probabilities are independent). Well, that's a contradiction. And our concept of "proving a point" or not, will not allow us to have an easy time of weighing both sides of an argument where there is uncertainty (not proof, only indications of a probabilistic nature).
I think the critique of the arguments of the first person made by the second person should lower the probabilities of the arguments from the first person. The second person should try to make his own arguments "showing" the opposite of the point made by the first person, and taking in account the critique of these arguments by the first person, which would lower the overall probability of the opposite point. That would be the best methodological way to discuss a point.
Math doesn't say anything about how we have to model things like this. (Creating a model requires domain knowledge. It's not just math.) So I'm not going to say that there is just one solution. But I think we need to try harder than this.
I think that equation makes a lot of sense, and is a part of a solution about proving points, but because it requires input data which are largely suggestive and debatable (cannot be scientifically quantified), it is far from being foolproof. But it allows to link mathematically different arguments about the same point.
Cordially, Bernard