Let&#x27;s start with something lighter: how do you categorize subjective states of mind? But we do through words like &quot;happy&quot;, &quot;sad&quot;, &quot;good-will&quot;. Additionally we can make statements as to the degree of sadness, or degree of happiness. Psychologists do this professionally with their survey instruments, but even the layman is capable of saying &quot;I was most happy at my wedding and least happy at my great-grandfather&#x27;s funeral&quot;, which sets bounds with two points of reference.<p>Oops! Anything with degrees of effect and bounds is basically a finite ordering. And a finite ordering can be given a rank, with numbers. So now we have given numbers to subjective states.<p>This is obviously quite handwavy, but the core ideas are here. I might be missing something. The big differences are that probability assigns a continuous measure to what we believe is Belief. How do you get an infinite, uncountable number of experiences?<p>One way is to have the acceptable accuracy be less than an infinite number of digits. That&#x27;s always going to happen in practice but it&#x27;s not quite what we&#x27;re looking for. One other way to do it is to use preferences and expected value. Do you think your knowledge is complete enough such that you&#x27;d be indifferent to betting an X amount of money on a roullette wheel with given probability of winning P? Then P is your degree of belief.<p>In the end there are very good reasons to doubt subjective probability estimates. But as long as one works with bounds and acceptable degrees of error, then you at least get a sense of how it is you&#x27;re going wrong.