It seems like my knowledge (confidence in my probability assessment) of the shape of a distribution is continuous
You are right. Knightian uncertainty isn’t a separate discrete category, it’s an endpoint of a particular interval on the other end of which sits uncertainty that you know everything about, e.g. the probability of drawing a red ball from an urn into which you have just placed 10 red and 10 black balls.
Knight himself called known uncertainty “risk” and unknown uncertainty “uncertainty”. He wrote: Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.… The essential fact is that ‘risk’ means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.… It will appear that a measurable uncertainty, or ‘risk’ proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all.”
You are right. Knightian uncertainty isn’t a separate discrete category, it’s an endpoint of a particular interval on the other end of which sits uncertainty that you know everything about, e.g. the probability of drawing a red ball from an urn into which you have just placed 10 red and 10 black balls.
Knight himself called known uncertainty “risk” and unknown uncertainty “uncertainty”. He wrote: Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.… The essential fact is that ‘risk’ means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.… It will appear that a measurable uncertainty, or ‘risk’ proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all.”