[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-detail-638998-en":59,"doc-seo-638998-105":80},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":5,"data":60},{"doc_id":61,"user_id":62,"nickname":63,"user_avatar":64,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":66,"doc_content":67,"file_id":68,"file_url":69,"file_type":70,"file_size":71,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":72,"language":73,"language_code":74,"site_id":75,"html_lang":74,"table_of_contents":76,"faqs":77,"seo_title":78,"seo_description":66,"update_tm":79,"read_time":39},638998,3985747870414,"ahduag","https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","A NEW GARBER-STYLE SOLUTION TO THE PROBLEM OF OLD EVIDENCE - Stephan Hartmann and Branden Fitelson","A Bayesian confirmation-theoretic framework is developed to address the “old evidence” problem concerning Einstein’s credences about Mercury’s perihelion. The text reviews Garber-style models, where learning X supports the target hypothesis H by linking it to evidence E through entailment-style constraints, then critiques Jeffrey’s and Earman’s reliance on strong assumptions about E and on interpreting X and Y as “H entails E” versus “H refutes E.” A new approach replaces entailment with explanatory adequacy, using X as adequate explanation of E and Y as the best competitor’s adequate explanation, aiming to relax prior certainty and entailment interpretations.","A NEW GARBER-STYLE SOLUTION TO THE PROBLEM OF OLD EVIDENCE  \nSTEPHAN HARTMANN AND BRANDEN FITELSON  \n1. Background: Garber, Jeffrey and Earman  \nBy the time Einstein had formulated the general theory of relativity (H), the evidence regarding the perihelion of Mercury (E)— which Newtonian theory was unable to adequately explain — had long been known (Roseveare 1982) . Indeed, it is not implausible to suppose that Einstein was certain (in 1915) that E was true. Nonetheless, it is widely accepted that Einstein learned some proposition X (in 1915) which had the effect of confirming H (i. e. , rationally raising Einstein's credence in H) .  \nGarber (1983) proposes that what Einstein learned was a logical fact (i. e. , that X 􀂃 “H entails E”) . By adding an additional atomic statement “X” to the H; Elanguage (and interpreting “X” extra-systematically as “H entails E”), Garber showed how it was possible to write down Bayesian models of this sort, having the following desired confirmation-theoretic property  \n(y) Pr􀂄H j X􀂅 > Pr􀂄H􀂅:  \nGarber did not, however, endorse specific constraints on Pr􀂄􀀁􀂅, which ensure (y) . Subsequently, Jeffrey (1992) and Earman (1992) offered such constraints. Their  \napproaches require the addition of X and a fourth atomic statement “Y” to the H; E-language, where Y is extra-systematically interpreted as “H entails :E” (viz. , H refutes E) . In these traditional Garber-style approaches, the background extrasystematic constraints on Pr􀂄􀀁􀂅 consist of the following pair of “modus ponens principles” for the extra-systematic entailment relation.1  \n(1) Pr􀂄E j H & X􀂅 􀂃 1  \n(2) Pr􀂄E & H & Y 􀂅 􀂃 0  \nIn addition to (1) and (2), Jeffrey offers the following extra-systematic constraint:  \n(3) Pr􀂄X _ Y 􀂅 􀂃 1  \nInformally,(3) expresses certainty in the disjunction: either H entails E or H refutes E. Given the background assumption that Pr􀂄E􀂅 􀂃 1, it is straightforward  \nDate: 06/10/15 . Draft: Final version to appear in Philosophy of Science.  \nWe would like to thank Fabrizio Cariani, Vincenzo Crupi, Kenny Easwaran, Aidan Lyon, Jan Sprenger, Mike Titelbaum and two anonymous referees for useful feedback on previous versions of this paper.  \n1Traditionally, Garber-style approaches also rest on the background assumption that Pr􀂄E􀂅 􀂃 1. In standard probability theory, this background assumption entails (1) . We have chosen to state (1) explicitly here, since it reflects the fact that X is (in traditional Garber-style approaches) couched in terms of entailment. In the next section, we explain how to relax both of these assumptions.  \n2 STEPHAN HARTMANN AND BRANDEN FITELSON  \nto show that (1)–(3) jointly entail the desired confirmation-theoretic conclusion (y) . This, in essence, was Jeffrey's Garber-style approach to the old evidence problem.  \nAs Earman rightly points out, Jeffrey's constraint (3) is not very plausible as a rational stricture on Einstein's credences, prior to his learning X (in 1915) . There was no good reason for Einstein to be certain (prior to learning X) that H either entails or refutes E. Earman offers the following alternative extra-systematic constraint:  \n(4) Pr􀂄H j X􀂅 > Pr􀂄H j :X & :Y 􀂅  \nEarman shows that — given the background assumption that Pr􀂄E􀂅 􀂃 1 —(1), (2) and (4) jointly entail (y); and, he argues that (4) is a plausible assumption regarding Einstein's credences (in 1915) . We agree that (4) is more plausible than Jeffrey's (3) . For one thing,(4) is not a numerical constraint, but merely an ordinal constraint on Einstein's 1915 credences. Moreover, because Einstein was (antecedently) certain of E , it is reasonable to suppose that he would have judged that X confers a greater probability on H than :X & :Y does. Having said that, we would prefer a more general approach, which (a) doesn't presuppose that Pr􀂄E􀂅 􀂃 1; and,(b) doesn't require interpreting X and Y in terms of entailment relations. In the next section, we describe just such an approach.  \n2. A New Garber-Style Approach  \nWe like Garber's idea ","cbCaifa8hCznAgcC","https://ap.wps.com/l/cbCaifa8hCznAgcC","pdf",92367,3,"English","en",105,"# Background: Garber, Jeffrey and Earman\n## Garber-style Bayesian models and constraints\n## Jeffrey’s disjunction constraint\n## Earman’s ordinal constraint and alternative approach\n# A New Garber-Style Approach\n## Explaining old evidence via explanatory adequacy","[{\"question\":\"What is the “old evidence” problem addressed in the paper?\",\"answer\":\"The paper focuses on how learning in 1915 could rationally increase Einstein’s credence in the general theory of relativity given prior knowledge of Mercury’s perihelion anomaly.\"},{\"question\":\"How do traditional Garber-style approaches interpret X and Y?\",\"answer\":\"They interpret X and Y using entailment relations, treating X as a supporter of H toward E (H entails E) and Y as a refuter (H refutes E), together with extra-systematic probability constraints.\"},{\"question\":\"What is the main change in the new Garber-style approach?\",\"answer\":\"X and Y are reinterpreted as explanatory adequacy: X means H adequately explains E, while Y means H’s best competitor adequately explains E. This aims to avoid presupposing Pr(E)=1 and avoid entailment-based interpretations.\"}]","A NEW GARBER-STYLE SOLUTION TO THE PROBLEM OF OLD EVIDENCE - Stephan Hartmann and Branden Fitelson | PDF",1792701055,{"code":4,"msg":81,"data":82},"ok",{"site_id":75,"language":74,"slug":83,"title":65,"keywords":84,"description":66,"schema_data":85,"social_meta":138,"head_meta":140,"extra_data":142,"updated_unix":79},"a-new-garber-style-solution-to-the-problem-of-old-evidence-stephan-hartmann-and-branden-fitelson","",{"@graph":86,"@context":137},[87,100,120],{"@type":88,"itemListElement":89},"BreadcrumbList",[90,94,96,98],{"item":91,"name":92,"@type":93,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":95,"name":9,"@type":93,"position":14},"https://docshare.wps.com/document/",{"item":97,"name":40,"@type":93,"position":72},"https://docshare.wps.com/document/research-report/",{"item":99,"name":65,"@type":93,"position":19},"https://docshare.wps.com/document/a-new-garber-style-solution-to-the-problem-of-old-evidence-stephan-hartmann-and-branden-fitelson/638998/",{"url":99,"name":65,"@type":101,"image":102,"author":107,"headline":65,"publisher":109,"fileFormat":112,"inLanguage":74,"description":66,"dateModified":113,"datePublished":114,"encodingFormat":112,"isAccessibleForFree":115,"interactionStatistic":116},"DigitalDocument",{"url":103,"@type":104,"width":105,"height":106},"https://docshare.wps.com/thumbnails/a-new-garber-style-solution-to-the-problem-of-old-evidence-stephan-hartmann-and-branden-fitelson/638998.png","ImageObject",300,407,{"name":63,"@type":108},"Person",{"url":91,"name":110,"@type":111},"DocShare","Organization","application/pdf","2026-10-29","2026-10-22",true,{"@type":117,"interactionType":118,"userInteractionCount":8},"InteractionCounter",{"@type":119},"ViewAction",{"@type":121,"mainEntity":122},"FAQPage",[123,129,133],{"name":124,"@type":125,"acceptedAnswer":126},"What is the “old evidence” problem addressed in the paper?","Question",{"text":127,"@type":128},"The paper focuses on how learning in 1915 could rationally increase Einstein’s credence in the general theory of relativity given prior knowledge of Mercury’s perihelion anomaly.","Answer",{"name":130,"@type":125,"acceptedAnswer":131},"How do traditional Garber-style approaches interpret X and Y?",{"text":132,"@type":128},"They interpret X and Y using entailment relations, treating X as a supporter of H toward E (H entails E) and Y as a refuter (H refutes E), together with extra-systematic probability constraints.",{"name":134,"@type":125,"acceptedAnswer":135},"What is the main change in the new Garber-style approach?",{"text":136,"@type":128},"X and Y are reinterpreted as explanatory adequacy: X means H adequately explains E, while Y means H’s best competitor adequately explains E. This aims to avoid presupposing Pr(E)=1 and avoid entailment-based interpretations.","https://schema.org",{"og:url":99,"og:type":139,"og:title":65,"og:site_name":110,"og:description":66},"article",{"robots":141,"canonical":99},"index,follow",{"doc_id":61,"site_id":75}]