Consider that we build a robot that thinks like us, except that it cannot make qualitative judgements. It can use only Aristotelian logic. What sort of fundamental desirable properties would its thinking have?
Desiderata I. Degrees of plausibility are represented by real numbers.
Desiderata II. Qualitative correspondence with common sense.
Desiderata III. Consistency:
- IIIa. If a conclusion can be reasoned out in more than one way, then every plausible way must lead to the same result.
- IIIb. The robot always takes into account all of the evidence it has relevant to a question. It does not arbitrarily ignore some of the information, basing its conclusions only on what remains. In other words, it is not ideological.
- IIIc. The robot always represents equivalent states of knowledge by equivalent plausibility assignments. That is, if in two problems the robot's state of knowledge is the same (except perhaps for the labeling of propositions), then it must assign the same plausibilities in both.
I (HS) will note that IIIb makes this robot a Bayesian, just like the rest of us.