TY - JOUR
T1 - Internality, transfer, and infinitesimal modeling of infinite processes
AU - Bottazzi, Emanuele
AU - Katz, Mikhail G.
N1 - Publisher Copyright:
© 2020 The Authors [2020]. Published by Oxford University Press. All rights reserved.
PY - 2021/6/1
Y1 - 2021/6/1
N2 - A probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal probabilities are underdetermined. The claim is based upon external hyperreal-valued measures. We show that internal hyperfinite measures are not underdetermined. The importance of internality stems from the fact that Robinson's transfer principle only applies to internal entities. We also evaluate the claim that transferless ordered fields (surreals, Levi-Civita field, Laurent series) may have advantages over hyperreals in probabilistic modeling. We show that probabilities developed over such fields are less expressive than hyperreal probabilities.
AB - A probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal probabilities are underdetermined. The claim is based upon external hyperreal-valued measures. We show that internal hyperfinite measures are not underdetermined. The importance of internality stems from the fact that Robinson's transfer principle only applies to internal entities. We also evaluate the claim that transferless ordered fields (surreals, Levi-Civita field, Laurent series) may have advantages over hyperreals in probabilistic modeling. We show that probabilities developed over such fields are less expressive than hyperreal probabilities.
UR - http://www.scopus.com/inward/record.url?scp=85110641120&partnerID=8YFLogxK
U2 - 10.1093/philmat/nkaa033
DO - 10.1093/philmat/nkaa033
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85110641120
SN - 0031-8019
VL - 29
SP - 256
EP - 277
JO - Philosophia Mathematica
JF - Philosophia Mathematica
IS - 2
ER -