Question

By contradiction here, I don’t necessarily mean a logical contradiction, although perhaps that also does apply here.

My question is along the lines of this: Is the very notion of assigning a probability to uncertainty a contradiction, or if not, meaningless?

Assigning a probability to a proposition implies that different propositions can have different probabilities. But if different propositions have different probabilities, then you can be sure of certain propositions better than others.

But relative "suredness" implies knowledge. However, if one is uncertain of each proposition, then you are trying to know something that you don’t know. It is akin to knowing uncertainty. Isn’t this contradictory?

The only exception to this I can think of is you have an event X and Y where X includes Y. For example, betting on a dice landing on 2 instead of an even number seems ridiculous, but that is only because the former is a part of the latter.

Answer 1

Assigning a probability to uncertainty is not contradictory; it is a recognized method of describing our level of confidence in different propositions. It does not deliver absolute certainty but offers a gradation in the justification of beliefs, consistent with philosophical views that knowledge does not require certainty.

Step-by-step explanation:

The notion of assigning a probability to uncertainty is not a contradiction, but rather a method of expressing degrees of confidence in our knowledge based on available information. Probability allows us to make meaningful statements about the likelihood of various outcomes, even in the face of uncertainty. When we say that one proposition has a different probability than another, we indicate that our reasons to believe one over the other vary in strength. This does not imply knowledge in the absolute sense but reflects a gradation of justification behind our beliefs. Moore's argument against skepticism suggests that certainty is not required to claim knowledge; rather, justified belief in a true proposition suffices. Thus, statements about the external world can be justified without being certain, allowing us to use probabilities to manage uncertainty and guide decisions. It is not about 'knowing uncertainty' but quantifying our uncertainty. Assigning probabilities to events is based on patterns identified in the repetition of those events, supporting the view that we can be 'sure enough' of certain propositions to act upon them meaningfully.