Imagine a graph where the x-axis represents our probability estimate for a given statement being true and the y-axis represents our certainty that our probability estimate is correct. So if, for example, we estimate a probability of .6 for a given statement to be true but we're only mildly certain of that estimate, then our belief graph would probably look like a shallow bell curve
I don't understand where the bell curve is coming from. If you have one probability estimate for a given statement with some certainty about it, you would depict it as a single point on your graph.
The bell curves in this context usually represent probability distributions. The width of that probability distribution reflects your uncertainty. If you're certain, the distribution is narrow and looks like a spike at the estimate value. If you're uncertain, the distribution is flat(ter). Probability distributions have to sum to 1 under the curve, so the smaller the width of the distribution, the higher the spike is.
How likely you are to discover new evidence is neither here nor there. Even if you are very uncertain of your estimate, this does not convert into the probability of finding new evidence.
I think you're referring to the type of statement that can have many values. Something like "how long will it take for AGI to be developed?". My impression (correct me if I'm wrong) is that this is what's normally graphed with a probability distribution. Each possible value is assigned a probability, and the result is usually more or less a bell curve with the width of the curve representing your certainty.
I'm referring to a very basic T/F statement. On a normal probability distribution graph that would indeed be represented as a single point - t...
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