Abstract

Consider a sequence of outcomes of descending value, A > B > C >... > Z. According to Larry Temkin, there are reasons to deny the continuity axiom in certain ‘extreme’ cases, i.e. cases of triplets of outcomes A, B and Z, where A and B differ little in value, but B and Z differ greatly. But, Temkin argues, if we assume continuity for ‘easy’ cases, i.e. cases where the loss is small, we can derive continuity for the ‘extreme’ case by applying the axiom of substitution and the axiom of transitivity. The rejection of continuity for ‘extreme’ cases therefore renders the triad of continuity in ‘easy’ cases, the axiom of substitution and the axiom of transitivity inconsistent.As shown by Arrhenius and Rabinowitz, Temkin's argument is flawed. I present a result which is stronger than their alternative proof of an inconsistency. However, this result is not quite what Temkin intends, because it only refers to an ordinal ranking of the outcomes in the sequence, whereas Temkin appeals to intuitions about the size of gains and losses. Against this background, it is argued that Temkin's trilemma never gets off the ground. This is because Temkin appeals to two mutually inconsistent conceptions of aggregation of value. Once these are clearly separated, it will transpire, in connection with each of them, that one of the principles to be rejected does not appear plausible. Hence, there is nothing surprising or challenging about the result; it is merely a corollary to Expected Utility Theory. View HTML Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.UNACCEPTABLE RISKS AND THE CONTINUITY AXIOMVolume 28, Issue 1Karsten Klint Jensen DOI: https://doi.org/10.1017/S0266267112000107Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. UNACCEPTABLE RISKS AND THE CONTINUITY AXIOMVolume 28, Issue 1Karsten Klint Jensen DOI: https://doi.org/10.1017/S0266267112000107Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. UNACCEPTABLE RISKS AND THE CONTINUITY AXIOMVolume 28, Issue 1Karsten Klint Jensen DOI: https://doi.org/10.1017/S0266267112000107Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission.