Why must degrees of plausibility be represented using real numbers when there are alternative number systems, which don’t have 1-to-1 correspondence to the reals, that satisfy transitivity and universal comparability?
Kevin S. Van Horn writes in his paper, “Constructing a Logic of Plausible Inference: A Guide to Cox’s Theorem”:
What’s so special about R? If we want our theory to have no holes then why don’t we use hyperreals or complex numbers? They also satisfy transitivity and universal comparability and I would argue that they have less holes than R
[Question] Why must plausibilities be represented using real numbers?
Professor Jaynes writes:
Why must degrees of plausibility be represented using real numbers when there are alternative number systems, which
don’thave 1-to-1 correspondence to the reals, that satisfy transitivity and universal comparability?Kevin S. Van Horn writes in his paper, “Constructing a Logic of Plausible Inference: A Guide to Cox’s Theorem”:
What’s so special about R? If we want our theory to have no holes then why don’t we use hyperreals or complex numbers? They also satisfy transitivity and universal comparability and I would argue that they have less holes than R