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”:
Page 10 of the paper
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