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Title of Journal: Synthese

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Abbravation: Synthese

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Springer Netherlands

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10.1007/0-387-25590-7_25

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1573-0964

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Why follow the royal rule

Authors: Franz Huber
Publish Date: 2016/01/05
Volume: 194, Issue: 5, Pages: 1565-1590
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Abstract

This note is a sequel to Huber Synthese 1912167–2193 2014 It is shown that obeying a normative principle relating counterfactual conditionals and conditional beliefs viz the royal rule is a necessary and sufficient means to attaining a cognitive end that relates true beliefs in purely factual nonmodal propositions and true beliefs in purely modal propositions Along the way I will sketch my idealism about alethic or metaphysical modalityI am grateful to Jonathan Weisberg as well as three anonymous reviewers for their constructive feedback and to Kevin Kuhl for proofreading an earlier version of this paper My research was supported by the Canadian SSHRC through its Insight program and by the Connaught Foundation through its New Researcher programSomeone interested in studying safety and not bothered by Huber’s 2014 thought that it is important to distinguish between the factual components f w and the modal components r w of a possible world w will find the following models more elegant left Wleft R wright win Wleft S wright win Wright where W is a nonempty set of possible worlds left R wright win W is a family of arbitrary functions from wp left Wright into mathbb Ncup left infty right and left S wright win W is a family of regular subjective ranking functions from wp left Wright into mathbb Ncup left infty right In this setup instead of considering cases omega one considers possible worlds w=left llbracket rrbracket wR wS wright Sensitivity says for all vin W and all Asubseteq W all Aworlds w that are R vminimal are such that S wleft Aright =0 Adherence says for all vin W and all Asubseteq W all Aworlds w that are R vminimal are such that S wleft Wsetminus Aright 0 Safety says for all vin W and all Asubseteq W A is true in all R vminimal worlds w in which S wleft Wsetminus Aright 0These conditional versions consider the truth about the modal status of A in the word w the agent is in Quite different conditional versions consider the truth about the modal status of A in the world v where the counterfactual conditional is evaluated The conditions studied in this paper considered if the agent believes A in w conditional on what is true about the modal status of A in the world w she is in The different conditions consider if she believes A in w conditional on what is true about the modal status of A elsewhere in a different possible world vOne way to think of the former conditions is in terms of what is true from the first person perspective of the agent and to think of the latter conditions in terms of what is true from the third person perspective of some trackingascriber The latter conditional versions of sensitivity and adherence and safety say for all vin W and all Asubseteq W all Aworlds w that are R vminimal are such that S wleft Amid left xin WR xleft Aright =R vleft Aright right cap Eright =0 for all “v Aadmissible” Esubseteq W And for all vin W and all Asubseteq W all Aworlds w that are R vminimal are such that S wleft Wsetminus Amid left xin WR xleft Wsetminus Aright =R vleft Wsetminus Aright right cap Eright 0 for all “vleft Wsetminus Aright admissible” Esubseteq W As well as for all vin W and all Asubseteq W A is true in all R vminimal worlds w in which S wleft Wsetminus Amid left xin WR xleft Wsetminus Aright =R vleft Wsetminus Aright right cap Eright 0 for some “vleft Wsetminus Aright admissible” Esubseteq WThe objective chance is high that one’s subjective credence in A conditional on the truth about the objective chance of A is high given that A is true For all Asubseteq W and all vin W and all “v Aadmissible” Esubseteq W ch vleft crleft Amid left xin Wch xleft Aright =ch vleft Aright right cap Eright =highmid Aright =highThe objective chance equals c that A is true given that one’s subjective credence in A conditional on the truth about the objective chance of A equals c For all Asubseteq W and all vin W and all “ v Aadmissible” Esubseteq W ch vleft Amid crleft Amid left xin Wch xleft Aright =ch vleft Aright right cap Eright =cright =cOf course in this more elegant and general setup it is not possible anymore to say that admissible information is purely modal information as we have done in this paper The reason is that in this more elegant and general setup the very distinction between factual information and modal information cannot be drawn without further assumptions Admissibility now is relative to a proposition and a world and of course a credence function and this is only the tip of the iceberg that is known as the “big bad bug” Rachael 2009 and that is the reason for Huber’s 2014 complicated setup in the first place11

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