Unsettled ThoughtsPub Date : 2019-12-19DOI: 10.1093/oso/9780198833710.003.0003
J. Staffel
{"title":"Approximation Measures","authors":"J. Staffel","doi":"10.1093/oso/9780198833710.003.0003","DOIUrl":"https://doi.org/10.1093/oso/9780198833710.003.0003","url":null,"abstract":"The focus of Chapter 3 is the central Bayesian tenet that a thinker’s unconditional credences should be probabilistically coherent. Plausibly, thinkers who don’t have coherent credences can be more or less incoherent, i.e. their credences can diverge from complying with the probability axioms only a little, or quite substantially. We can capture this intuitive idea by representing a thinker’s credence function as a vector, and measuring its distance to the closest probabilistically coherent credence function that is defined over the same set of propositions. The problem that arises in this context is that there are many possible measures we can use to determine the distance from coherence, and those measures can deliver incompatible rankings. I present a representative range of such measures and illustrate the ways in which they differ.","PeriodicalId":446166,"journal":{"name":"Unsettled Thoughts","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122797738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Unsettled ThoughtsPub Date : 2019-12-19DOI: 10.1093/oso/9780198833710.003.0004
J. Staffel
{"title":"Why Approximate Coherence?","authors":"J. Staffel","doi":"10.1093/oso/9780198833710.003.0004","DOIUrl":"https://doi.org/10.1093/oso/9780198833710.003.0004","url":null,"abstract":"Chapter 4 begins to answer the question of how Bayesians can justify the claim that approximating probabilistic coherence is beneficial for non-ideal thinkers. Dutch book arguments are often put forth to argue that ideal rationality requires being coherent. I show that we can justify that it is better to be less incoherent by showing that decreased incoherence is associated with decreased losses from Dutch books. While incoherent thinkers can never be immune from Dutch book losses, the amount they stand to lose, given that we standardize bet sizes, is greater the more incoherent their credences are.","PeriodicalId":446166,"journal":{"name":"Unsettled Thoughts","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126393652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Unsettled ThoughtsPub Date : 2019-12-19DOI: 10.1093/oso/9780198833710.003.0009
J. Staffel
{"title":"How Do Beliefs Simplify Reasoning?","authors":"J. Staffel","doi":"10.1093/oso/9780198833710.003.0009","DOIUrl":"https://doi.org/10.1093/oso/9780198833710.003.0009","url":null,"abstract":"Chapter 9 examines how the proposed theory of epistemic rationality can accommodate outright beliefs, and what role such outright beliefs play in our epistemic conduct. It is argued that people need outright beliefs in addition to credences to simplify their reasoning. Outright beliefs do this by allowing thinkers to ignore small error probabilities. What is outright believed can change between contexts. When our beliefs change, we have to ask how related other beliefs, including beliefs representing uncertainties, change in light of this. It has been claimed that our beliefs change via an updating procedure resembling conditionalization. However, conditionalization is notoriously complicated. This claim is thus in tension with the explanation that the function of beliefs is to simplify our reasoning. We can resolve this puzzle by endorsing a different hypothesis about how beliefs change across contexts that better accounts for the simplifying role of beliefs.","PeriodicalId":446166,"journal":{"name":"Unsettled Thoughts","volume":"2015 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127311622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}