tag:blogger.com,1999:blog-3891434218564545511Tue, 29 Nov 2022 16:50:03 +0000Godprobabilitytimeinfinitylanguagemoralitycausationfree willmindloveevilnaturalismknowledgepresentismtruthmodalityexplanationdecision theoryBayesianismmathematicshumorscienceconsciousnessparadoxethicslyingbeliefdeterminismepistemologysexactionlogicreasonsChristianityPrinciple of Sufficient ReasonPrinciple of Double Effectintentionevolutionlaws of naturevirtueAristotelianismAristotleontologyproblem of evilquantum mechanicsassertiondualismPlatonismSt. Thomas Aquinasphysicalismspacepainfunctionalismprogrammingvaguenesscausal finitismmereologyA-theoryNatural Lawrationalitysubstancematerialismnormativityvalueresponsibilitycompatibilismcosmological argumentdeathkillingmultiverseontological argumentpunishmentchangecreationexistenceliar paradoxpromisesfreedomgroundingpersonal identityDeep Thoughtsbeautybooksdesirephysicspropositionsteleologygoodmurderset theoryLeibnizabortioncounterfactualseternalismqualiajusticemarriagecredencedivine simplicityAxiom of ChoiceDIYpropertiesfaithheavenperceptiontautologyMolinismafterlifeartificial intelligenceconditional probabilityevidencechoiceconditionalsinfinitesimalspartspersonssinlifescoring rulesB-theoryKantomniscienceincarnationRelativity TheorycomputersfundamentalityartdeontologyscepticismsimplicitytheodicyTrinityanimalsmatterutilitarianismCatholicismastronomyconsequentialisminductionnecessitynormspossibilityfour-dimensionalismgamestime travelmetaphysicsnonmeasurable setsreductionspacetimeutilityHumechancehellidentitylibertarianismparthoodtheismGoedelSt. Augustineartifactsbiologyconsenteducationopen futurereproductiontrustcompositioninternal timepleasurewell-beingChristEucharistSpinozadouble effectebooksformsgrowing blocklawpythonresurrectionsportsaccidentsamateur astronomyauthoritycardinalitycontraceptionessentiality of originseternityfriendshiphuman naturejustificationmemorymetaethicsnecessary beingphilosophyDescartesSt Thomas Aquinascommandsconscienceexistence of GodhyperrealsincompatibilismmiraclesperfectionprivationsoulsymmetrytropesvicewelfareMinecraftindependenceinfinite regresslocationmeaningpersonhoodquantifiersregularityreligionwarPlatoSpecial Relativityatheismbodycausal powerscircularitydisagreementhomosexualityintentionsobligationpossible worldsrandomnesssocial epistemologysuffering3D printingPascal's Wagerculpabilitydivine command theoryexpected utilityforgivenessprobability theorysetstruthmakersworldswrongdoingSocratesaestheticsanalogycountingdesigndesign argumentdivine command metaethicsepistemic utilityhiddennessmusicnaturalnessomnipotenceopen theismparticlesretributionsemanticsthoughttranssubstantiationBibleKalaam argumentabilityargumentsconjunctiondeliberationendseuthanasiaformhappinessincommensurabilityincompletenessmeansmysteryriskvirtue ethicsPopper functionsScriptureabstractaangelsanimalismdesiresdignitydiscriminationdutyfictionhumanityindeterminismperdurantismprayerprocreationproper functionteachingtrolley problemunionDavid LewisIntelligent DesignNewtonian physicsTarskiamateur sciencediscretenesserrorhaecceitieshylomorphismmedicinemereological universalismnaturepriorsproofproportionalityrealismrelationssentencessimultaneous causationsupervenienceAndroida prioriagencyatonementcharactercharitycontrastive explanationemotionseternal lifefieldsflourishingharmhopeindicative conditionalsinfinite lotteriesjust warlawsmodesmotionnatural kindsnominalismpermissibilitypersistencephilosophy of sciencepotentialitypredicationrelativismrequestssacrificesinceritysupererogationthe FalltheologyunderstandingArduinoBanach-Tarski ParadoxCOVID-19FrankfurtJesusKierkegaardagent causationautonomybeingbrainbrainscomparative probabilityconfirmationdiachronic identitydisabilitydisjunctionelectronicsfine-tuningfine-tuning argumentfinitudeforeknowledgegracegratitudeinfinite lotteryjobsliteraturematerial conditionalsmodal logicnonsensenumberspeer disagreementperdurancepolitical philosophyprudencequantificationregresssalvationself-sacrificeBohmGettierPrinciple of Alternate PossibilitiesSatancertaintycollapsecooperationcrossextended simplesfilmfissionfuturehuman beingsimplicatureindexicalsintentionalitymeaning of lifemonadsnormalcyoughtpraiseprevisionprovabilityrevelationspeciestestimonytryingvotingwellbeingAdamCalvinismEveJudaismMassPelagianismThomismThomson's lampWittgensteinZenoactualityaliensappreciationattempted murderattemptsbenevolencecomplexitycomputationcontextcontingencycontradictioncredencesdecisionsdemocracydispositionsdominationepistemicismevidentialismex nihilo nihil fitexperienceexternal timefree will defensefrequentismgenderguiltholinessidealisminstrumentalityintuitionmeasurementmultilocationnaturespacifismpanpsychismprobabilismracismrapereferencerelativityreligious experiencesceptical theismsexual ethicssubstancessuicideteleological argumenttemporary intrinsicstorturetranscendental unity of apperceptiontransubstantiationwillBaylorCatholicCausal PrincipleEuthyphroHumeanismInference to Best ExplanationIslamMaryS5Star Treka posterioriapplied ethicsapproximationbadbeatific visionbeliefscausal closurechildrenconceptsconsistencycontentcontinuitycontinuumcounterexamplescreationismdeceptiondefinitionsdespairdisjunctionsentailmentequalityessential propertieseventsexpected valuefalse belieffetusgrammargroupshumansinconsistencylottery paradoxmeasuremotivationnamesnatural numbersnovelsobedienceobservationomnirationalityparenthoodpastphenomenologypredicatespremarital sexprinciple of indifferenceprivacypropertypurgatoryreal numbersreasonrepresentationrewardrolessacrednesssimultaneitysyntaxtensevelocityDoomsday ArgumentDutch booksEverettInternetLaw of Large NumbersNewcomb ParadoxOckham's razorSleeping BeautySt. Anselmaccomplishmentadministrativealgorithmsaxiologybeatitudeblamebundle theorychaoschoicesclosurecolocationcolorcommitmentcommunityconglomerabilityconservationdilemmasdistancedivine commandempathyeschatologyexternalismfallacyfatalismfetusesgraph theorygravitygrim reaper paradoxhealthhedonismidentity of indiscerniblesimmutabilityimpairmentin vitro fertilizationinerranceinfallibilityinferencelotterieslotterymasksmortal sinmultiple realizabilitynowoccasionalismoverdeterminationpantheismparticipationper impossibile conditionalsphotographypolygamypreferenceprimary causationrefrainingself-defenseshapeslaverysoftwarespiritualitysubjunctive conditionalssupertasksupervaluationismtimelessnesstopologytransitivitytranslationvaluesvegetarianismwaterwomenwritingBrouwer axiomC. 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counterfactualsphysicianspoliticspredictionpriesthoodproofsprosthesesquestionsredemptionrelationalismresentmentrobotsrule utilitarianismsainthoodsame-sex marriagescience fictionscientific realismself-referencesizesleepsocial constitutionstipulationstochastic processessubjective obligationsubjective timesubstantivalismsuccessteleportationthe goodthefttimestokenstranscendencetriple effectuglinessviolencevirtuesvisionvowswishworshipzombiesBig BangCantorCentral Limit TheoremChurchCurry's ParadoxEinsteinEpicurusFreudGenesisHausdorff ParadoxKantianismKripkeMarxMcTaggartPalmPrisoner's DilemmaRawlsS4St AnselmSt. John of the CrossSt. PaulTorahWindowsWodehouseabstractionadditivityadulteryadvertisingageamnesiaanthropomorphismanti-realismarranged marriageawarenessbaptismbare particularsbasic goodsbecomingbenefitbivalencebodiesbrainwashingcategory theorychargecivic dutyclassical theismclockscloseness of descriptioncoauthorshipcoercioncogitocolorscommon goodcompositional 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effectLaTeXLatinMaimonedesMormonismNewtonOckhamOttoPopper functionPrincipal PrincipleProtestantismReformed theologyReidRussellRussell ParadoxSchellenbergScotusSearleSola ScripturaStalinSurprise Exam paradoxWilliam JamesWojtylaWordleZeno's paradox`Aqedahabsurdityabundanceact utilitarianismactionsactualismadoptionadverbsagapeagreementalcoholalternate possibilitiesanalytic philosophyanomalyanonymous Christianityanthropocentrismantiexplanationarbitrarinessargumentargumentationargumentum ex convenientiaarrowaseitybetrayalbioethicsbirthblowgunbrains in vatsbreathingcancapacitycapital punishmentcatscellular automatacerebrumschainschemistrycircular timecohabitationcoherencecollective actioncommon sensecommunioncommunitiescompassioncomplicitycompressionconceivabilityconcretaconcurrenceconditional intentionsconfidentialityconfusionconsequencesconsummationcontemplationcontingent beingcontinuous creationcopyingcosmoscriticismdangerdefinitiondeflationismdesertdesign argumentsdespitedifferencedirection of timedisjunctivismdispositiondisvaluedogseccentricityeconomy of salvationembarrassmentemergenceendorsementenduranceenemiesensuringentropyenvironmentepistemic authorityepistemic humilityepistemic rationalityequivalence classeserror theoryestimationevilmakingexclusionary reasonsexdurantismexpectationexplanatory priorityexpressivismextinctionfactsfairiesfairnessfalsityfamilyfantasiesfantasyfirst-order factsfoodforceforgettingfunninessfusionfusionsfuture individualsgeneragiftglorygoalsgradinggratuitous evilhairhateheterosexualityhidden variableshigher educationhistory of philosophyhobbiesidentificationidentity theoryill-beingimago Deiimperfect dutyimplicit desireincomprehensibilityindignityindividualsinequalityinfantsinsectsinspirationintegrationintellectual lifeintellectual propertyinteraction probleminterestsinternalismintersubjectivityintrinsic propertiesjudgmentknowability paradoxlanguageslaw enforcementlearningliteralismlove for Godlove of 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changeCanadaCantor ParadoxCarnapCategorical ImperativeChestertonChurch-Turing thesisClarkeContinuum HypothesisCopernicusCouncil of ChalcedonCouncil of EphesusDark Night of the SoulDavidDedekind infinityDiscworldDostoevskiiDr. SeussEddingtonElijahEnglishExemplifyFPGAFaustFive WaysGalileoGauniloGavagaiGeachGethsemaneGod's willGood SamaritanGorgiasGrandfather ParadoxGrim ReapersGuernicaHamiltonian mechanicsHolocaustHoly SpiritHortonIIsraelJamesJudasKaneLateran IVLebesgue measureLeibniz's LawLeslieLeviticusLewisLondon/LondresLord's PrayerLumen GentiumLysisM13MacintoshMaxwell's DemonMeditationsMeinongMillMinetestMosesMother TeresaMothere TeresaNapoleonNestorianismNewcomb's ParadoxOld TestamentPAPPDFParfitParmenidesPhaedoPolish languagePrinciple of Suffiicient ReasonPutnamPythagorasRepugnant ConclusionSamkaraSarahSatan's AppleSchadenfreudeShogiSkolem ParadoxSolomonoff priorsSorites paradoxSoviet UnionSpanishSpockSt Petersburg ParadoxSt. AthanasiusSt. Catherine of SienaSt. Gregory of NyssaSt. JeromeSt. Petersburg ParadoxSymposiumT-schemaTertullianThalesThomsonTolkienTuring machineUngerUriahVatican IIVerneVulcansWacoWeilWilde lecturesWilliam Lane CraigWycliffeXenophanesZeusa prioricityabsenceabsolute prohibitionsacademiaaccidentaccidental generalizationsaccretionachievementactivityactorsactual worldadditionadelphopoiesisadequacyadultsadventadverbialismadviceaestheticaffixesaimalienationalphabetsaltruismambiguityanaesthesiaanarchismanecdotal reasoninganisotropyannihilationanthropic principleantipresentismantireductionismappetiteappropriatenessappropriationarchivalargument by exampleargument from evilarithmeticarityaritycurryingarroganceart historyaspect ratioassertionsassociationsassumptionasymmetryasymptotic approachataraxiaatlatlattitudesaufhebungauthorsautographic artavaricebackwards causationbacteriabakingbaldnessbase rate fallacybatterybeginningsbelievebigotrybinarybirthdaysblindnessbloggingbriberybringing aboutbutterfliescanon lawcarecaringcarpentrycastigationcausa suicausal decision theorycausal loopscausalitycavescelibacycellscentral limit theorychain of beingchairscheatingcivic friendshipcivilityclassclassical physicsclassificationclergyclericalismcloningclothescloudsclumpscoffeecognitive sophisticationcoherentismcoincidencecoinstantiationcold warcommon descentcommunication boardscommunion of the saintscompactnesscompanionshipcomparisoncompatibilitycompensationcompetitioncompositionalitycompulsionconciliationismconcretenesscondemnationconditionals of free willconditionsconflict of interestconsciousconsconsciousnessconsecrationconsequence argumentconstrualconstructioncontestcontextualismcontinental philosophycontractscontrastcontrolconvenienceconventionalismconversionconvexityconvincingcoralscorporationscorrespondencecorruptionismcounselingcountable additivitycounterpartscouragecourtcreativitydark nebuladark nightdarknessdatadata consolidationde redebunking argumentsdegrees of freedomdenialdenotationdependancydeposit of faithdepressiondepthderelictionderivative valuederivativesdetractiondeviant logicdevilsdevotiondevotionsdiagonal lemmadialoguedictionariesdifferential equationsdimensiondisbeliefdisclosurediscoverydisgustdishonestydislikingdisquotationdissentditheringdivine permissiondivinitydoctrinedog whistlesdoxastic goodsdoxinsdraftdramadrivingdrunkennessduck-rabbitduct tapeduellingdurationduresseartheclipseeconomicsectopic pregnancyefficient causationegalitarianismembeddingembryosemergentismemotivismemphasisencryptionendendangermentenforcementengagementenhancementenlightenmentenmityens rationisentanglemententitiesenvironmental ethicsenvyepistemic harmepistemic injusticeepistemic possibilityeroseroteticsessenceessencesessentialismevagelicalismevangelicalismevangelizationexceptionsexclude middleexduranceexistentialismexobiologyexperiment philosophyexperimental philosophyexpressingfactory farmingfailurefaithfulnessfallibilismfalsemakersfamiliarityfelix culpafertilityfictional charactersfigurative speechfine-tunefinkingfishfive-dimensionalismfollowershipfootballforesightforgeryfour causesfunctionfunctionsfundamentalismfuture selvesgalaxiesgardeninggeneralizationsgenetic fallacygenetic manipulationgenocidegenregerrymanderinggivingglorificationgodsgraspgreedgriefgritgroup rightsgroup theoryguisesgunshackshaeecceitieshaeeceitieshalf-lifeharmonyhatredheirloomsheroismheuristicshierarchyhindsighthistory of scienceholodeckhomonymhomophobiahomosexual activityhousehold hintshtmlhumor?hungerhypnosishypochondriaiconsillucutionary forceimmoralityimmortalityimpanationimperativesimpositionimpossible attemptsimpressivenessin virtue ofincompatibilityinconstencyindexindicative conditionsindicativesindirect communicationinerrancyinerrantisminertiainfima speciesinfiniityinfinite utilityinfluenzainformationinitialisminitiationinsideinsinuationinstantiationintellectintellectual failureintensionintensityinternal spaceinterpretationintimacyintrinsic evilintroversionintuitionismirrealismis-ought gapislandsisotropyjavajokesjust-so storieskenosiskindskingdom of Godknowledge whatlacklaitylangaugelannguageleadershiplengthslesser evilletters of recommendationliarliberal theologyliberalismlibidolibrarieslight spotslikinglimbolimitslinksliverliverslocalitylogicismlooking downlucklunchluxurymachinesmagnetismmanipulationmannersmanymathematicalmatteringmaximalismmaximsmeditationmemesmentalmental powersmental statesmeta-ontologymetaepistemologymetametaethicsmetaphysicalmetaphysical seriousnessmicrophysicsmicroscopemilitary ethicsminimumminimum wagemisfortunemispronunciationmisspeakingmistakesmodal realismmoleculesmonoidmonophysitismmoral errormoral evilmoral excellencemoral particularismmoral philosophymoral realismmoral responsibilitymoral standingmoralsmultiplicationmultitaskingmysticismnarrativenationalismnaturaismnatural theologynaturalistnecessitismneednegandnewbornsnoisesnon-cognitivismnon-deductive reasoningnon-realismnonlocalitynormative statusnorms natural lawnothingnessnuclear weaponsnumbernuminousnuminousnessobjectivismobservable universeoff topicoffersoligonismomnipresence.operationalismoppositionoptimalismoptimizationoral contraceptionorderorder of experienceordinary languageorektinsorgan salesorganicismorganizationsorgansorientationoriginal valueoriginalsimoriginsorphansorthodoxyoscilloscopeoutsideoxygenpairspanentheismpanexperientialismpapal infallibilityparableparadiseparallel processingparameciaparticularspaternalismpeopleper se causal sequencesperfect beingperjurypersistent vegetative statepersonpersonal qualitative identitypersonality identitypersuasionperverse rewardsperversionpessimismpetsphenomenaphilosophical theologypiecesplayplaysplenitudepocket oraclepointingpollutionpolytheismpornographypositionpositive psychologypossessionspotato chipspovertypowerspracticespragmatic contradictionpragmatic encroachmentpragmaticspreemptionspreestablished harmonypresenitsmpresentismlpresocraticspresuppositionprevision.probabilityprimary qualitiesprintingpro tanto reasonsprobabilitiesprodigal sonprofessionprofessional philosophyprofessionalsprojectionpromulgationpronounspronunciationpropensityproperitespropositionprotestprotocolproverbsproxiesproxyprudential reasonspseudonymitypseudosciencepublic domainpublic goodpublic squarepunspurity of heartpurposepursuitqualitative differencequalitative probabilityquantifierquantitiesquasi-substancequestionraceradical translationrainrandom walkrather thanrationalismrattlesnakesreceivingreciprocityrecombinationredreductio ad absurdumreference classreference framereflectionrefutationreligious disagreementrepairsrepetitionrepresentationalismreptilesreputationrequestresistanceretinal imagesreverse enngineeringrhetoricriddlesriotsrisk compensationrocketsrunningsacerdotalitysame sex marriagesame-sex relationssame-sex sexual activitysayingscattered objectsscepticsscientismscrupulositysculpturesecond order desiresecond order quantificationsecond-order perceptionsecularismseductionseemingselection effectselfself-consciousnessself-defeatself-interestself-knowledgeself-locating beliefself-organizationselvessensationsentence typesserialseriousnesssermonssexismsexual ethissexualityshallownessshameshavingsicknessside-effectssilencingsimonyskillskillssmall governmentsnowflakesocial choicesocial interactionssocietysolid objectssophistrysoulmatessoundsovereigntyspecificationspeech actsspeedsperm donationspiessplittingspookinessstarsstatesstringsstrugglestubbornnessstupiditysubjunctivessublimesubsists insubstantial changesubtractionsuggestionsupernormalcysuperpositionsurprise examsurrealsswampmanswarmssymbolismsympathysynecdochesynonymtablestamingtaskstastetaxatelekinesistelevisiontemporal partstendencytensismtenuretextualismtheatertheistic Platonismtheistic determinismtheological virtuestheoremstheoretical reasontheoriatheorytheory choicetheosisthoughthrowing a matchtolerancetop-down causationtracestradeoffstragedytragedy of the commonstransitiontransworld identitytreatmenttruth paradoxturthmakingtwinningtypologyunificationunitarityunitsuniverseupbringingusefulnessusuryutility monstersutopiavampiresvarietyvectorsvegetaranismvicious circlevirtual partsvirtue epistemologyvisibilityvon Balthasarvoyeurismwaitingwallswave-particle dualityways of beingweak transitivityweirdnesswell-foundednesswhite lieswholeswickednesswinningwishful thinkingwordworkworkswrongxiangqizebraszero probabilityAlexander Pruss's Bloghttp://alexanderpruss.blogspot.com/noreply@blogger.com (Alexander R Pruss)Blogger3929125tag:blogger.com,1999:blog-3891434218564545511.post-7027947087422901710Tue, 29 Nov 2022 16:49:00 +00002022-11-29T10:49:11.847-06:00meaning of lifemoralitynormsoverridingnessprudenceNonoverriding morality<p>Some philosophers think that sometimes norms other than moral
norms—e.g., prudential norms or norms of the meaningfulness of life—take
precedence over moral norms and make permissible actions that are
morally impermissible. Let <span
class="math inline"><em>F</em></span>-norms be such norms.</p>
<p>A view where <em>F</em>-norms
<em>always</em> override moral norms does not seem plausible. In the
case of prudential or meaningfulness, it would point to a fundamental
selfishness in the normative constitution of the human being.</p>
<p>So the view has to be that sometimes <span
class="math inline"><em>F</em></span>-norms take precedence over moral
norms, but not always. There must thus be norms which are neither <span
class="math inline"><em>F</em></span>-norms nor moral norms that decide
whether <em>F</em>-norms or moral norms
take precedence. We can call these “overall norms of combination”. And
it is crucial to the view that the norms of combination themselves be
neither $F-norms nor moral norms.</p>
<p>But here is an oddity. Morality already combines <span
class="math inline"><em>F</em></span>-considerations and first order
paradigmatically moral considerations. Consider two actions:</p>
<ol type="1">
<li><p>Sacrifice a slight amount of <span
class="math inline"><em>F</em></span>-considerations for a great deal of
good for one’s children.</p></li>
<li><p>Sacrifice an enormous amount of <span
class="math inline"><em>F</em></span>-considerations for a slight good
for one’s children.</p></li>
</ol>
<p><em>Morality</em> says that (1) is obligatory but (2) is permitted.
Thus, morality already weighs <span
class="math inline"><em>F</em></span> and paradigmatically moral
concerns and provides a combination verdict. In other words, there
already are <em>moral</em> norms of combination. So the view would be
that there are moral norms of combination and overall norms of
combination, both of which take into account exactly the same first
order considerations, but sometimes come to different conclusions
because they weigh the very same first order considerations differently
(e.g., in the case where a moderate amount of <span
class="math inline"><em>F</em></span>-considerations needs to be
sacrificed for a moderate amount of good for one’s children).</p>
<p>This view violates Ockham’s razor: Why would we have moral norms of
combination if the overall norms of combination always override them
anyway?</p>
<p>Moreover, the view has the following difficulty: It seems that the
best way to define a type of norm (prudential, meaningfulness, moral,
etc.) is in terms of the types of consideration that the norm is based
on. But if the overall norms of combination take into account the very
same types of consideration as the moral norms of combination, then this
way of distinguishing the types of norms is no longer available.</p>
<p>Maybe there is a view on which the overall ones take into account not
the first-order moral and <span
class="math inline"><em>F</em></span>-considerations, but only the
deliverances of the moral and <span
class="math inline"><em>F</em></span>-norms of combination, but that
seems needlessly complex.</p>
http://alexanderpruss.blogspot.com/2022/11/nonoverriding-morality.htmlnoreply@blogger.com (Alexander R Pruss)0tag:blogger.com,1999:blog-3891434218564545511.post-1061265868089061841Mon, 28 Nov 2022 19:31:00 +00002022-11-28T13:33:11.107-06:00competitionenmityhateloveoppositionOppositional relationships<p>Here are three symmetric oppositional possibilities:</p>
<ol type="1">
<li><p>Competition: <em>x</em> and
<em>y</em> have shared knowledge that
they are pursuing incompatible goals.</p></li>
<li><p>Moral opposition: <em>x</em> and
<em>y</em> have shared knowledge that
they are pursuing incompatible goals and each takes the other’s pursuit
to be morally wrong.</p></li>
<li><p>Mutual enmity: <em>x</em> and
<em>y</em> have shared knowledge that
they each pursue the other’s ill-being for a reason other than the
other’s well-being.</p></li>
</ol>
<p>The reason for the qualification on reasons in 3 is that one might
say that someone who punishes someone in the hope of their reform is
pursuing their ill-being for the sake of their well-being. I don’t know
if that is the right way to describe reformative punishment, but it’s
safer to include the qualification in (3).</p>
<p>Note that cases of moral opposition are all cases of competition.
Cases of mutual enmity are also cases of competition, except in rare
cases, such as when a party suffers from depression or acedia which
makes them not be opposed to their own ill-being.</p>
<p>I suspect that most cases of mutual enmity are also cases of moral
opposition, but I am less clear on this.</p>
<p>Both competition and moral opposition are compatible with mutual
love, but mutual enmity is not compatible with either direction of
love.</p>
<p>Additionally, there is a whole slew of less symmetric options.</p>
<p>I think loving one’s competitors could be good practice for loving
one’s (then necessarily non-mutual) enemies.</p>
http://alexanderpruss.blogspot.com/2022/11/oppositional-relationships.htmlnoreply@blogger.com (Alexander R Pruss)0tag:blogger.com,1999:blog-3891434218564545511.post-5419642577340721895Mon, 28 Nov 2022 19:13:00 +00002022-11-28T13:13:45.641-06:00consequentialismgamessportsGames and consequentialism<p>I’ve been thinking about who competitors, opponents and enemies are,
and I am not very clear on it. But I think we can start with this:</p>
<ol type="1">
<li><em>x</em> and <span
class="math inline"><em>y</em></span> are competitors provided that they
knowingly pursue incompatible goals.</li>
</ol>
<p>In the ideal case, competitors both rightly pursue the incompatible
goals, and each knows that they are both so doing.</p>
<p>Given externalist consequentialism, where the right action is the one
that actually would produce better consequences, ideal competition will
be extremely rare, since the only time the pursuit of each of two
incompatible goals will be right is if there is an exact tie between the
values of the goals, and that is extremely rare.</p>
<p>This has the odd result that on externalist consequentialism, in most
sports and other games, at least one side is acting wrongly. For it is
extremely rare that there is an exact tie between the values of one side
winning and the value of the other side winning. (Some people enjoy
victory more than others, or have somewhat more in the way of fans,
etc.)</p>
<p>On internalist consequentalism, where the right action is defined by
expected utilities, we would expect that if both sides are unbiased
investigators, in most of the games, at least one side would at take the
expected utility of the other side’s winning to be higher. For if both
sides are perfect investigators with the same evidence and perfect
priors, then they will assign the same expected utilities, and so at
least one side will take the other’s to have higher expected utility,
except in the rare case where the two expected utilities are equal. And
if both sides assign expected utilities completely at random, but
unbiasedly (i.e., are just as likely to assign a higher expected utility
to the other side winning as to themselves), then bracketing the rare
case where a side assigns equal expected utility to both victory
options, any given side will have a probability of about a half of
assigning higher expected utility to the other side’s victory, and so
there will be about a 3/4 chance that at least one side will take the
other side’s victory to be more likely. And other cases of unbiased
investigators will likely fall somewhere between the perfect case and
the random case, and so we would expect that in most games, at least one
side will be playing for an outcome that they think has lower expected
utility.</p>
<p>Of course, in practice, the two sides are not unbiased. One might
overestimate the value of oneself winning and the underestimate the
value of the other winning. But that is likely to involve some epistemic
vice.</p>
<p>So, the result is that either on externalist or internalist
consequentialism, in most sports and other competitions, at least one
side is acting morally wrongly or is acting in the light of an epistemic
vice.</p>
<p>I conclude that consequentialism is wrong.</p>
http://alexanderpruss.blogspot.com/2022/11/games-and-consequentialism.htmlnoreply@blogger.com (Alexander R Pruss)0tag:blogger.com,1999:blog-3891434218564545511.post-7918792721305751156Mon, 28 Nov 2022 18:27:00 +00002022-11-28T12:27:02.956-06:00hyperrealslengthsmeasurePrecise lengths<p>As usual, write <span
class="math inline">[<em>a</em>,<em>b</em>]</span> for the interval of
the real line from <em>a</em> to <span
class="math inline"><em>b</em></span> including both <span
class="math inline"><em>a</em></span> and <span
class="math inline"><em>b</em></span>, <span
class="math inline">(<em>a</em>,<em>b</em>)</span> for the interval of
the real line from <em>a</em> to <span
class="math inline"><em>b</em></span> excluding <span
class="math inline"><em>a</em></span> and <span
class="math inline"><em>b</em></span>, and <span
class="math inline">[<em>a</em>, <em>b</em>)</span> and <span
class="math inline">(<em>a</em>, <em>b</em>]</span> respectively for the
intervals that include <em>a</em> and
exclude <em>b</em> and vice versa.</p>
<p>Suppose that you want to measure the size <span
class="math inline"><em>m</em>(<em>I</em>)</span> of an interval <span
class="math inline"><em>I</em></span>, but you have the conviction that
single points matter, so <span
class="math inline">[<em>a</em>,<em>b</em>]</span> is bigger than <span
class="math inline">(<em>a</em>,<em>b</em>)</span>, and you want to use
infinitesimals to model that difference. Thus, <span
class="math inline"><em>m</em>([<em>a</em>,<em>b</em>])</span> will be
infinitesimally bigger than <span
class="math inline"><em>m</em>((<em>a</em>,<em>b</em>))</span>.</p>
<p>Thus at least some intervals will have lengths that aren’t real
numbers: their length will be a real number plus or minus a (non-zero)
infinitesimal.</p>
<p>At the same time, intuitively, <em>some</em> intervals from <span
class="math inline"><em>a</em></span> to <span
class="math inline"><em>b</em></span> should have length
<em>exactly</em> <span
class="math inline"><em>b</em> − <em>a</em></span>, which is a real
number (assuming <em>a</em> and <span
class="math inline"><em>b</em></span> are real). Which ones? The choices
are [<em>a</em>,<em>b</em>], <span
class="math inline">(<em>a</em>,<em>b</em>)</span>, <span
class="math inline">[<em>a</em>, <em>b</em>)</span> are <span
class="math inline">(<em>a</em>, <em>b</em>]</span>.</p>
<p>Let <em>α</em> be the non-zero
infinitesimal length of a single point. Then <span
class="math inline">[<em>a</em>,<em>a</em>]</span> is a single point.
Its length thus will be <em>α</em>, and
not <em>a</em> − <em>a</em> = 0. So
[<em>a</em>,<em>b</em>] can’t
<em>always</em> have real-number length <span
class="math inline"><em>b</em> − <em>a</em></span>. But maybe at least
it can in the case where <span
class="math inline"><em>a</em> < <em>b</em></span>? No. For suppose
that <span
class="math inline"><em>m</em>([<em>a</em>,<em>b</em>]) = <em>b</em> − <em>a</em></span>
whenever <em>a</em> < <em>b</em>.
Then <span
class="math inline"><em>m</em>((<em>a</em>,<em>b</em>]) = <em>b</em> − <em>a</em> − <em>α</em></span>
whenever <em>a</em> < <em>b</em>,
since (<em>a</em>, <em>b</em>] is
missing exactly one point of <span
class="math inline">[<em>a</em>,<em>b</em>]</span>. But then let <span
class="math inline"><em>c</em> = (<em>a</em>+<em>b</em>)/2</span> be the
midpoint of [<em>a</em>,<em>b</em>].
Then:</p>
<ol type="1">
<li><span
class="math inline"><em>m</em>([<em>a</em>,<em>b</em>]) = <em>m</em>([<em>a</em>,<em>c</em>]) + <em>m</em>((<em>c</em>,<em>b</em>]) = (<em>c</em>−<em>a</em>) + (<em>b</em>−<em>c</em>−<em>α</em>) = <em>b</em> − <em>a</em> − <em>α</em></span>,</li>
</ol>
<p>rather than <span
class="math inline"><em>m</em>([<em>a</em>,<em>b</em>])</span> as was
climed.</p>
<p>What about (<em>a</em>,<em>b</em>)?
Can that always have real number length <span
class="math inline"><em>b</em> − <em>a</em></span> if <span
class="math inline"><em>a</em> < <em>b</em></span>? No. For if we had
that, then we would absurdly have:</p>
<ol start="2" type="1">
<li><span
class="math inline"><em>m</em>((<em>a</em>,<em>b</em>)) = <em>m</em>((<em>a</em>,<em>c</em>)) + <em>α</em> + <em>m</em>((<em>c</em>,<em>b</em>)) = <em>c</em> − <em>a</em> + <em>α</em> + <em>b</em> − <em>c</em> = <em>b</em> − <em>a</em> + <em>α</em></span>,</li>
</ol>
<p>since (<em>a</em>,<em>b</em>) is
equal to the disjoint union of <span
class="math inline">(<em>a</em>,<em>c</em>)</span>, the point <span
class="math inline"><em>c</em></span> and $(c,b).</p>
<p>That leaves [<em>a</em>, <em>b</em>)
and (<em>a</em>, <em>b</em>]. By
symmetry if one has length <span
class="math inline"><em>b</em> − <em>a</em></span>, surely so does the
other. And in fact Milovich gave me <a
href="https://mathoverflow.net/questions/108170/hyperreal-finitely-additive-measure-on-0-1-assigning-b-a-to-a-b-or-a-b">a
proof</a> that there is no contradiction in supposing that <span
class="math inline"><em>m</em>([<em>a</em>,<em>b</em>)) = <em>m</em>((<em>b</em>,<em>a</em>]) = <em>b</em> − <em>a</em></span>.</p>
http://alexanderpruss.blogspot.com/2022/11/precise-lengths.htmlnoreply@blogger.com (Alexander R Pruss)0tag:blogger.com,1999:blog-3891434218564545511.post-1460987582795887654Tue, 22 Nov 2022 19:54:00 +00002022-11-22T19:12:52.688-06:00expected valuehyperrealsprevisionprobabilityHyperreal expected value<p>I think I have a hyperreal solution, not entirely satisfactory, to
three problems.</p>
<ol type="1">
<li><p>The problem of how to value the St Petersburg paradox. The
particular version that interests me is one from <a
href="https://philarchive.org/rec/RUSINP-2">Russell and Isaacs</a> which
says that any finite value is too small, but any infinite value violates
strict dominance (since, no matter what, the payoff will be less than
infinity).</p></li>
<li><p>How to value gambles on a countably infinite fair lottery where
the gamble is positive and asymptotically approaches zero at infinity.
The <a
href="http://alexanderpruss.blogspot.com/2022/11/dominance-and-countably-infinite-fair.html">problem</a>
is that any positive non-infinitesimal value is too big and any
infinitesimal value violates strict dominance.</p></li>
<li><p>How to evaluate expected utilities of gambles whose values are
hyperreal, where the probabilities may be real or hyperreal, which I
raise in Section 4.2 of my paper on <a
href="http://philsci-archive.pitt.edu/21251/">accuracy in infinite
domains</a>.</p></li>
</ol>
<p>The apparent solution works as follows. For any gamble with values in
some real or hyperreal field <em>V</em>
and any finitely-additive probability <span
class="math inline"><em>p</em></span> with values in <span
class="math inline"><em>V</em></span>, we generate a hyperreal expected
value <em>E</em><sub><em>p</em></sub>,
which satisfies these plausible axioms:</p>
<ol start="4" type="1">
<li><p>Linearity: <span
class="math inline"><em>E</em><sub><em>p</em></sub>(<em>a</em><em>f</em>+<em>b</em><em>g</em>) = <em>a</em><em>E</em><sub><em>p</em></sub><em>f</em> + <em>b</em><em>E</em><sub><em>p</em></sub><em>g</em></span>
for <em>a</em> and <span
class="math inline"><em>b</em></span> in <span
class="math inline"><em>V</em></span></p></li>
<li><p>Probability-match: <span
class="math inline"><em>E</em><sub><em>p</em></sub>1<sub><em>A</em></sub> = <em>p</em>(<em>A</em>)</span>
for any event <em>A</em>, where <span
class="math inline">1<sub><em>A</em></sub></span> is <span
class="math inline">1</span> on <span
class="math inline"><em>A</em></span> and <span
class="math inline">0</span> elsewhere</p></li>
<li><p>Dominance: if <span
class="math inline"><em>f</em> ≤ <em>g</em></span> everywhere, then
<span
class="math inline"><em>E</em><sub><em>p</em></sub><em>f</em> ≤ <em>E</em><sub><em>p</em></sub><em>g</em></span>,
and if <em>f</em> < <em>g</em>
everywhere, then <span
class="math inline"><em>E</em><sub><em>p</em></sub><em>f</em> < <em>E</em><sub><em>p</em></sub><em>g</em></span>.</p></li>
</ol>
<p>How does this get around the arguments I link to in (1) and (2) that
seem to say that this can’t be done? The trick is this: the expected
value has values in a hyperreal field <span
class="math inline"><em>W</em></span> which will be larger than <span
class="math inline"><em>V</em></span>, while (4)–(6) only hold for
gambles with values in <em>V</em>. The
idea is that we distinguish between what one might call primary values,
which are particular goods in the world, and what one might call
distribution values, which specify how much a random distribution of
primary values is worth. We do not allow the distribution values
themselves to be the values of a gamble. This has some downsides, but at
least we can have (4)–(6) on <em>all</em> gambles.</p>
<p>How is this trick done?</p>
<p>I think like this. First it looks like the <a
href="https://en.wikipedia.org/wiki/Hahn%E2%80%93Banach_theorem">Hahn-Banach
dominated extension theorem</a> holds for <span
class="math inline"><em>V</em><sub>2</sub></span>-valued <span
class="math inline"><em>V</em><sub>1</sub></span>-linear functionals on
<em>V</em><sub>1</sub>-vector spaces
<span
class="math inline"><em>V</em><sub>1</sub> ⊆ <em>V</em><sub>2</sub></span>
are real or hyperreal field, except that our extending functional may
need to take values in a field of hyperreals even larger than <span
class="math inline"><em>V</em><sub>2</sub></span>. The crucial thing to
note is that any subset of a real or hyperreal field has a supremum in a
larger hyperreal field. Then where the proof of the Hahn-Banach theorem
uses infima and suprema, you move to a larger hyperreal field to get
them.</p>
<p>Now, embed <em>V</em> in a hyperreal
field <em>V</em><sub>2</sub> that
contains a supremum for every subset of <span
class="math inline"><em>V</em></span>, and embed <span
class="math inline"><em>V</em><sub>2</sub></span> in <span
class="math inline"><em>V</em><sub>3</sub></span> which has a supremum
for every subset of <span
class="math inline"><em>V</em><sub>2</sub></span>. Let <span
class="math inline"><em>Ω</em></span> be our probability space.</p>
<p>Let <em>X</em> be the space of
bounded <em>V</em><sub>2</sub>-valued
functions on <em>Ω</em> and let <span
class="math inline"><em>M</em> ⊆ <em>X</em></span> be the subspace of
simple functions (with respect to the algebra of sets that <span
class="math inline"><em>Ω</em></span> is defined on). For <span
class="math inline"><em>f</em> ∈ <em>M</em></span>, let <span
class="math inline"><em>ϕ</em>(<em>f</em>)</span> be the integral of
<em>f</em> with respect to <span
class="math inline"><em>p</em></span>, defined in the obvious way. The
supremum on <em>V</em><sub>2</sub>
(which has values in <span
class="math inline"><em>V</em><sub>3</sub></span>) is then a seminorm
dominating <em>ϕ</em>. Extend <span
class="math inline"><em>ϕ</em></span> to a <span
class="math inline"><em>V</em></span>-linear function <span
class="math inline"><em>ϕ</em></span> on <span
class="math inline"><em>X</em></span> dominated by <span
class="math inline"><em>V</em><sub>2</sub></span>. Note that if <span
class="math inline"><em>f</em> > 0</span> everywhere for <span
class="math inline"><em>f</em></span> with values in <span
class="math inline"><em>V</em></span>, then <span
class="math inline"><em>f</em> > <em>α</em> > 0</span> everywhere
for some <span
class="math inline"><em>α</em> ∈ <em>V</em><sub>2</sub></span>, and
hence <span
class="math inline"><em>ϕ</em>(−<em>f</em>) ≤ − <em>α</em></span> by
seminorm domination, hence <span
class="math inline">0 < <em>α</em> ≤ <em>ϕ</em>(<em>f</em>)</span>.
Letting <em>E</em><sub><em>p</em></sub>
be <em>ϕ</em> restricted to the <span
class="math inline"><em>V</em></span>-valued functions, our construction
is complete.</p>
<p>I should check all the details at some point, but not today.</p>http://alexanderpruss.blogspot.com/2022/11/hyperreal-expected-value.htmlnoreply@blogger.com (Alexander R Pruss)0tag:blogger.com,1999:blog-3891434218564545511.post-1022390940343671986Mon, 21 Nov 2022 17:38:00 +00002022-11-28T09:15:46.560-06:00dominationinfinite lotteryprevisionprobabilityDominance and countably infinite fair lotteries<p>Suppose we have a finitely-additive probability assignment <span
class="math inline"><em>p</em></span> (perhaps real, perhaps hyperreal)
for a countably infinite lottery with tickets <span
class="math inline">1, 2, ...</span> in such a way that each ticket has
infinitesimal probability (where zero counts as an infinitesimal). Now
suppose we want to calculate the expected value or previsio <span
class="math inline"><em>E</em><sub><em>p</em></sub><em>U</em></span> of
any bounded wager <em>U</em> on the
outcome of the lottery, where we think of the wager as assigning a value
to each ticket, and the wager is bounded if there is a finite <span
class="math inline"><em>M</em></span> such that <span
class="math inline">|<em>U</em>(<em>n</em>)| < <em>M</em></span> for
all <em>n</em>.</p>
<p>Here are plausible conditions on the expected value:</p>
<ol type="1">
<li><p>Dominance: If <span
class="math inline"><em>U</em><sub>1</sub> < <em>U</em><sub>2</sub></span>
everywhere, then <span
class="math inline"><em>E</em><sub><em>p</em></sub><em>U</em><sub>1</sub> < <em>E</em><sub><em>p</em></sub><em>U</em><sub>2</sub></span>.</p></li>
<li><p>Binary Wagers: If <em>U</em> is
0 outside <span
class="math inline"><em>A</em></span> and <span
class="math inline"><em>c</em></span> on <span
class="math inline"><em>A</em></span>, then <span
class="math inline"><em>E</em><sub><em>p</em></sub><em>U</em> = <em>c</em><em>P</em>(<em>A</em>)</span>.</p></li>
<li><p>Disjoint Additivity: If <span
class="math inline"><em>U</em><sub>1</sub></span> and <span
class="math inline"><em>U</em><sub>2</sub></span> are wagers supported
on disjoint events (i.e., there is no <span
class="math inline"><em>n</em></span> such<br />
that <em>U</em><sub>1</sub>(<em>n</em>)
and <em>U</em><sub>2</sub>(<em>n</em>)
are both non-zero), then <span
class="math inline"><em>E</em><sub><em>p</em></sub>(<em>U</em><sub>1</sub>+<em>U</em><sub>2</sub>) = <em>E</em><sub><em>p</em></sub><em>U</em><sub>1</sub> + <em>E</em><sub><em>p</em></sub><em>U</em><sub>2</sub></span>.</p></li>
</ol>
<p>But we can’t. For suppose we have it. Let <span
class="math inline"><em>U</em>(<em>n</em>) = 1/(2<em>n</em>)</span>. Fix
a positive integer <em>m</em>. Let
<em>U</em><sub>1</sub>(<em>n</em>) be
2 for <span
class="math inline"><em>n</em> ≤ <em>m</em> + 1</span> and <span
class="math inline">0</span> otherwise. Let <span
class="math inline"><em>U</em><sub>2</sub>(<em>n</em>)</span> be <span
class="math inline">1/<em>m</em></span> for <span
class="math inline"><em>n</em> > <em>m</em> + 1</span> and <span
class="math inline">0</span> for <span
class="math inline"><em>n</em> ≤ <em>m</em> + 1</span>. Then by Binary
Wagers and by the fact that each ticket has infinitesimal probability,
<span
class="math inline"><em>E</em><sub><em>p</em></sub><em>U</em><sub>1</sub></span>
is an infinitesimal <em>α</em> (since
the probability of any finite set will be infinitesimal). By Binary
Wagers and Dominance, <span
class="math inline"><em>E</em><sub><em>p</em></sub><em>U</em><sub>2</sub> ≤ 1/(<em>m</em>+1)</span>.
Thus by Disjoint Additivity, <span
class="math inline"><em>E</em><sub><em>p</em></sub>(<em>U</em><sub>1</sub>+<em>U</em><sub>2</sub>) ≤ <em>α</em> + 1/(<em>m</em>+1) < 1/<em>m</em></span>.
But <span
class="math inline"><em>U</em> < <em>U</em><sub>1</sub> + <em>U</em><sub>2</sub></span>
everywhere, so by Dominance we have <span
class="math inline"><em>E</em><sub><em>p</em></sub><em>U</em> < 1/<em>m</em></span>.
Since 0 < <em>U</em> everywhere, by
Dominance and Binary Wagers we have <span
class="math inline">0 < <em>E</em><sub><em>p</em></sub><em>U</em></span>.</p>
<p>Thus, <span
class="math inline"><em>E</em><sub><em>p</em></sub><em>U</em></span> is
a non-zero infinitesimal <em>β</em>.
But then <span
class="math inline"><em>β</em> < <em>U</em>(<em>n</em>)</span> for
all <em>n</em>, and so by Binary Wagers
and Dominance, <span
class="math inline"><em>β</em> < <em>E</em><sub><em>p</em></sub><em>U</em></span>,
a contradiction.</p>
<p>I think we should reject Dominance.</p>
http://alexanderpruss.blogspot.com/2022/11/dominance-and-countably-infinite-fair.htmlnoreply@blogger.com (Alexander R Pruss)2tag:blogger.com,1999:blog-3891434218564545511.post-771457543126287691Mon, 21 Nov 2022 15:17:00 +00002022-11-21T09:17:40.857-06:00corruptionismheavenhellpurgatoryCorruptionism and care about the soul<p>According to Catholic corruptionists, when I die, my soul will
continue to exist, but I won’t; then at the Resurrection, I will come
back into existence, receiving my soul back. In the interim, however, it
is my soul, not I, who will enjoy heaven, struggle in purgatory or
suffer in hell.</p>
<p>Of course, for any thing that enjoys heaven, strugges in purgatory or
suffers in hell, I should care that it does so. But should I have that
kind of special care that we have about things that happen to ourselves
for what happens to the soul? I say not, or at most slightly. For
suppose that it turned out on the correct metaphysics that my matter
continues to exist after death. Should I care whether it burns, decays,
or is dissected, with that special care with which we care about what
happens to ourselves? Surely not, or at most slightly. Why not? Because
the matter won’t be a part of me when this happens. (The “at most
slightly” flags the fact that we can care about “dignitary harms”, such
as nobody showing up at our funeral, or us being defamed, etc.)</p>
<p>But clearly heaven, purgatory and hell in the interim state is
something we should care about.</p>
http://alexanderpruss.blogspot.com/2022/11/corruptionism-and-care-about-soul.htmlnoreply@blogger.com (Alexander R Pruss)2tag:blogger.com,1999:blog-3891434218564545511.post-3705237815842570436Fri, 18 Nov 2022 17:29:00 +00002022-11-21T08:57:58.423-06:00probabilityqualitative probabilitysocial choiceSocial choice principles and invariance under symmetries<p>A comment by a referee of a recent paper of mine that one of my
results in decision theory didn’t actually depend on numerical
probabilities and hence could extend to social choice principles made me
realize that this may be true for some other things I’ve done.</p>
<p>For instance, in the past I’ve proved theorems on qualitative
probabilities. A qualitative probability is a relation <span
class="math inline">≼</span> on the subsets of some sample space <span
class="math inline"><em>Ω</em></span> such that:</p>
<ol type="1">
<li><p>≼ is transitive and
reflexive.</p></li>
<li><p>⌀ ≼ <em>A</em></p></li>
<li><p>if <span
class="math inline"><em>A</em> ∩ <em>C</em> = <em>B</em> ∩ <em>C</em> = ⌀</span>,
then <em>A</em> ≼ <em>B</em> iff <span
class="math inline"><em>A</em> ∩ <em>C</em> ≼ <em>B</em> ∩ <em>C</em></span>
(additivity).</p></li>
</ol>
<p>But need not think of <em>Ω</em> as
a space of possibilities and of ≼ as a
probability comparison. We could instead think of it as a set of people
who are candidates for getting some good thing, with <span
class="math inline"><em>A</em> ≼ <em>B</em></span> meaning that it’s at
least as good for the good thing to be distributed to the members of
<em>B</em> as to the members of <span
class="math inline"><em>A</em></span>. Axioms (1) and (2) are then
obvious. And axiom (3) is an independence axiom: whether it is at least
as good to give the good thing to the members of <span
class="math inline"><em>B</em></span> as to the members of <span
class="math inline"><em>A</em></span> doesn’t depend on whether we give
it to the members of a disjoint set <span
class="math inline"><em>C</em></span> at the same time.</p>
<p>Of course, for a general social choice principle we need more than
just a decision whether to give one and the same good to the members of
some set. But we can still formalize those questions in terms of
something pretty close to qualitative probabilities. For a general
framework, suppose a population set <span
class="math inline"><em>X</em></span> (a set of people or places in
spacetime or some other sites of value) and a set of values <span
class="math inline"><em>V</em></span> (this could be a set of types of
good, or the set of real numbers representing values). We will suppose
that <em>V</em> comes with a transitive
and reflexive (preorder) preference relation <span
class="math inline">≤</span>. Now let <span
class="math inline"><em>Ω</em> = <em>X</em> × <em>V</em></span>. A value
distribution is a function <em>f</em>
from <em>X</em> to <span
class="math inline"><em>V</em></span>, where <span
class="math inline"><em>f</em>(<em>x</em>) = <em>v</em></span> means
that <em>x</em> gets something of value
<em>v</em>.</p>
<p>We want to generate a reflexive and transitive preference ordering
≼ on the set <span
class="math inline"><em>V</em><sup><em>X</em></sup></span> of value
distributions.</p>
<p>Write <em>f</em> ≈ <em>g</em> when
<em>f</em> ≼ <em>g</em> and <span
class="math inline"><em>g</em> ≼ <em>f</em></span>, and <span
class="math inline"><em>f</em> ≺ <em>g</em></span> when <span
class="math inline"><em>f</em> ≼ <em>g</em></span> but not <span
class="math inline"><em>g</em> ≼ <em>f</em></span>. Similarly for values
<em>v</em> and <span
class="math inline"><em>w</em></span>, write <span
class="math inline"><em>v</em> < <em>w</em></span> if <span
class="math inline"><em>v</em> ≤ <em>w</em></span> but not <span
class="math inline"><em>w</em> ≤ <em>v</em></span>.</p>
<p>Here is a plausible axiom on value distributions:</p>
<ol start="4" type="1">
<li>Sameness independence: if <span
class="math inline"><em>f</em><sub>1</sub>, <em>f</em><sub>2</sub>, <em>g</em><sub>1</sub>, <em>g</em><sub>2</sub></span>
are value distributions and <span
class="math inline"><em>A</em> ⊆ <em>X</em></span> is such that
(a) <span
class="math inline"><em>f</em><sub>1</sub> ≼ <em>f</em><sub>2</sub></span>,
(b) <span
class="math inline"><em>f</em><sub>1</sub>(<em>x</em>) = <em>f</em><sub>2</sub>(<em>x</em>)</span>
and <span
class="math inline"><em>g</em><sub>1</sub>(<em>x</em>) = <em>g</em><sub>2</sub>(<em>x</em>)</span>
if <em>x</em> ∉ <em>A</em>, (c) <span
class="math inline"><em>f</em><sub>1</sub>(<em>x</em>) = <em>g</em><sub>1</sub>(<em>x</em>)</span>
and <span
class="math inline"><em>f</em><sub>2</sub>(<em>x</em>) = <em>g</em><sub>2</sub>(<em>x</em>)</span>
if <em>x</em> ∈ <em>A</em>.</li>
</ol>
<p>In other words, the mutual ranking between two value distributions
does not depend on what the two distributions do to the people on whom
the distributions agree. If it’s better to give $4 to Jones than to give
$2 to Smith when Kowalski is getting $7, it’s still better to give $4 to
Jones than to give $2 to Smith when Kowalski is getting $3. There is
probably some other name in the literature for this property, but I know
next to nothing about social choice literature.</p>
<p>Finally, we want to have some sort of symmetries on the population.
The most radical would be that the value distributions don’t care about
permutations of people, but more moderate symmetries may be required.
For this we need a group <em>G</em> of
permutations acting on <em>X</em>.</p>
<ol start="5" type="1">
<li>Strong <em>G</em>-invariance: if
<em>g</em> ∈ <em>G</em> and <span
class="math inline"><em>f</em></span> is a value distribution, then
<span
class="math inline"><em>f</em> ∘ <em>g</em> ≈ <em>f</em></span>.</li>
</ol>
<p>Here, <em>f</em> ∘ <em>g</em> is the
value distribution where site <span
class="math inline"><em>x</em></span> gets <span
class="math inline"><em>f</em>(<em>g</em>(<em>x</em>))</span>.</p>
<p>Additionally, the following is plausible:</p>
<ol start="6" type="1">
<li>Pareto: If <span
class="math inline"><em>f</em>(<em>x</em>) ≤ <em>g</em>(<em>x</em>)</span>
for all <em>x</em> with <span
class="math inline"><em>f</em>(<em>x</em>) < <em>g</em>(<em>x</em>)</span>
for some <em>x</em>, then <span
class="math inline"><em>f</em> ≺ <em>g</em></span>.</li>
</ol>
<p><strong>Theorem:</strong> Assume the Axiom of Choice. Suppose <span
class="math inline">≤</span> on <span
class="math inline"><em>V</em></span> is reflexive, transitive and
non-trivial in the sense that it contains two values <span
class="math inline"><em>v</em></span> and <span
class="math inline"><em>w</em></span> such that <span
class="math inline"><em>v</em> < <em>w</em></span>. There exists a
reflexive, transitive preference ordering <span
class="math inline">≼</span> on the value distributions satisfying
(4)–(6) if and only if there is such an ordering that is total if and
only if <em>G</em> has locally finite
action on <em>X</em>.</p>
<p>A group of symmetries <em>G</em> has
locally finite action a set <em>X</em>
provided that for each finite subset <span
class="math inline"><em>H</em></span> of <span
class="math inline"><em>G</em></span> and each <span
class="math inline"><em>x</em> ∈ <em>X</em></span>, applying finite
combinations of members of <em>G</em>
to <em>x</em> generates only a finite
subset of <em>X</em>. (More precisely,
if ⟨<em>H</em>⟩ is the subgroup
generated by <em>G</em>, then <span
class="math inline">⟨<em>H</em>⟩<em>x</em></span> is finite.)</p>
<p>If <em>X</em> is finite, then local
finiteness of action is trivial. If <span
class="math inline"><em>X</em></span> is infinite, then it will be
satisfies in some cases but not others. For instance, it will be
satisfied if <em>G</em> is permutations
that only move a finite number of members of <span
class="math inline"><em>X</em></span> at a time. It will on the other
hand fail if <em>X</em> is a infinite
bunch of people regularly spaced in a line and <span
class="math inline"><em>G</em></span> is shifts.</p>
<p>The trick to the proof of the Theorem is to reduce preferences
between distributions to comparisons of subsets of <span
class="math inline"><em>X</em> × <em>V</em></span> and to reduce
comparisons of subsets of <em>X</em> to
preferences between binary distributions.</p>
<p><strong>Proof of Therem:</strong> Suppose that <span
class="math inline"><em>G</em></span> has locally finite action. Define
<em>Ω</em> = <em>X</em> × <em>V</em>.
By Theorem 2 of my invariance of <a
href="https://arxiv.org/abs/2010.07366">non-classical probabilities
paper</a>, there is a strongly <span
class="math inline"><em>G</em></span>-invariant regular (i.e., <span
class="math inline">⌀ ≺ <em>A</em></span> if <span
class="math inline"><em>A</em></span> is non-empty) qualitative
probability ≼ on <span
class="math inline"><em>Ω</em></span>. Given a value distribution <span
class="math inline"><em>f</em></span>, let <span
class="math inline"><em>f</em><sup>*</sup> = {(<em>x</em>,<em>v</em>) : <em>v</em> ≤ <em>f</em>(<em>x</em>)}</span>
be a subset of <em>Ω</em>. Define <span
class="math inline"><em>f</em> ≼ <em>g</em></span> iff <span
class="math inline"><em>f</em><sup>*</sup> ≼ <em>g</em></span>.</p>
<p>Totality, reflexivity, transitivity and strong <span
class="math inline"><em>G</em></span>-invariance for value distributions
follows from the same conditions for subsets of <span
class="math inline"><em>Ω</em></span>. Regularity of <span
class="math inline">≼</span> on the subsets of <span
class="math inline"><em>Ω</em></span> and additivity implies that if
<em>A</em> ⊂ <em>B</em> then <span
class="math inline"><em>A</em> ≺ <em>B</em></span>. The Pareto condition
for ≼ on the value distributions
follows since if <em>f</em> and <span
class="math inline"><em>g</em></span> satisfy are such that <span
class="math inline"><em>f</em>(<em>x</em>) ≤ <em>g</em>(<em>x</em>)</span>
for all <em>x</em> with strict
inequality for some <em>x</em>, then
<span
class="math inline"><em>f</em><sup>*</sup> ⊂ <em>g</em><sup>*</sup></span>.
Finally, the complicated sameness independence condition follows from
additivity.</p>
<p>Now suppose there is a (not necessarily total) strongly <span
class="math inline"><em>G</em></span>-invariant reflexive and transitive
preference ordering ≼ on the value
distributions satisfying (4)–(6). Given a subset <span
class="math inline"><em>A</em></span> of <span
class="math inline"><em>X</em></span>, define <span
class="math inline"><em>A</em><sup>†</sup></span> to be the value
distribution that gives <em>w</em> to
all the members of <em>A</em> and <span
class="math inline"><em>v</em></span> to all the non-members, where
<em>v</em> < <em>w</em>. Define
<em>A</em> ≼ <em>B</em> iff <span
class="math inline"><em>A</em><sup>†</sup> ≼ <em>B</em><sup>†</sup></span>.
This will be a strongly <span
class="math inline"><em>G</em></span>-invariant reflexive and transitive
relation on the subsets of <em>X</em>.
It will be regular by the Pareto condition. Finally, additivity follows
from the sameness independence condition. Local finiteness of action of
<em>G</em> then follows from Theorem 2
of my paper. ⋄</p>
<p>Note that while it is natural to think of <span
class="math inline"><em>X</em></span> has just a set of people or of
locations, <a
href="https://www.google.com/url?q=https%3A%2F%2Fwww.dropbox.com%2Fs%2Fdklfwsl2ql1rt6s%2FAggregation.pdf%3Fraw%3D1&sa=D&sntz=1&usg=AOvVaw2nfKx0sldlPHYVX-lddt22">inspired
by Kenny Easwaran</a> one can also think of it as a set <span
class="math inline"><em>Q</em> × <em>Ω</em></span> where <span
class="math inline"><em>Ω</em></span> is a probability space and <span
class="math inline"><em>Q</em></span> is a population, so that <span
class="math inline"><em>f</em>(<em>x</em>,<em>ω</em>)</span> represents
the value <em>x</em> gets at location
<em>ω</em>. In that case, <span
class="math inline"><em>G</em></span> might be defined by symmetries of
the population and/or symmetries of the probability space. In such a
setting, we might want a weaker Pareto principle that supposes
additionally that <span
class="math inline"><em>f</em>(<em>x</em>,<em>ω</em>) < <em>g</em>(<em>x</em>,<em>ω</em>)</span>
for some <em>x</em> and <em>all</em>
<em>ω</em>. With that weaker Pareto
principle, the proof that the existence of a <span
class="math inline"><em>G</em></span>-invariant preference of the right
sort on the distributions implies local finiteness of action does not
work. However, I think we can still prove local finiteness of action in
that case if the symmetries in <span
class="math inline"><em>G</em></span> act only on the population (i.e.,
for all <em>x</em> and <span
class="math inline"><em>ω</em></span> there is an <span
class="math inline"><em>y</em></span> such that <span
class="math inline"><em>g</em>(<em>x</em>,<em>ω</em>) = (<em>y</em>,<em>ω</em>)</span>).
In that case, given a subset <em>A</em>
of the population <em>Q</em>, we define
<em>A</em><sup>†</sup> to be the
distribution that gives <em>w</em> to
all the persons in <em>A</em> with
certainty (i.e., everywhere on <span
class="math inline"><em>Ω</em></span>) and gives <span
class="math inline"><em>v</em></span> to everyone else, and the rest of
the proof should go through, but I haven’t checked the details.</p>
http://alexanderpruss.blogspot.com/2022/11/social-choice-principles-and-invariance.htmlnoreply@blogger.com (Alexander R Pruss)1tag:blogger.com,1999:blog-3891434218564545511.post-7475963915875327610Thu, 17 Nov 2022 19:41:00 +00002022-11-17T13:41:20.905-06:00animalismanimalscerebrumsrattlesnakesCerebrums and rattles<p>Animalists think humans are animals. Suppose I am an animalist and I
think that I go with my cerebrum in cerebrum-transplant cases. That may
seem weird. But suppose we make an equal opportunity claim here: all
animals that have cerebra go with their cerebra. If your dog Rover’s
cerebrum is transplanted into a robotic body, then the cerebrumless
thing is not Rover. Rather, Rover inhabits a robotic body or that body
comes to be a part of Rover, depending on views about prostheses. And
the same is true for any animal that has a cerebrum.</p>
<p>It initially seems weird to say that some animals can survive reduced
to a cerebrum and others cannot. But it’s not that weird when we add
that the ones that can’t survive reduced to a cerebrum are animals that
don’t <em>have</em> a cerebrum.</p>
<p>The person who thinks survival reduced to a cerebrum is implausible
for an animal might, however, say that this is what’s odd about it. An
animal reduced to cerebrum lacks internal life support organs (heart,
lungs, etc.) It is odd to think that some animals can survive without
internal life support and others cannot.</p>
<p>But compare this: Some animals can partly exist in spatial locations
where they have no living cells, and others cannot. The outer parts of
my hairs are parts of me, but there are no living cells there. If my
hair is in a room, then I am partly in that room, even if no living
cells of mine are in the room. But on the other hand, there are some
animals (at least the unicellular ones, but maybe also some soft
invertebrates) that can only exist where they have a living cell.</p>
<p>One might object that the spatial case and the temporal case are
different, because in the spatial case we are talking of partial
presence and in the temporal case of full presence. But a
four-dimensionalist will disagree. To exist at a time is to be partly
present at that time. So to a four-dimensionalist the analogy is pretty
strict.</p>
<p>Finally, compare this. Suppose Snaky a rattlesnake stretched along a
line in space. Now suppose we simultaneously annihilate everything in
Snaky. Now, “simultaneously” is presumably defined with respect to some
reference frame <em>F</em><sub>1</sub>.
Let <em>z</em> be a point in Snaky’s
rattle located just prior (according to <span
class="math inline"><em>F</em><sub>1</sub></span>) to Snaky’s
destruction. Then Snaky is partly present at <span
class="math inline"><em>z</em></span>. But with a bit of thought, we can
see that there is another reference frame <span
class="math inline"><em>F</em><sub>2</sub></span> where the only parts
of Snaky simultaneous with <em>z</em>
are parts of the rattle: all the non-rattle parts of Snaky have already
been annihilated at <span
class="math inline"><em>F</em><sub>2</sub></span>, but the rattle has
not. Then in <em>F</em><sub>2</sub> the
following is true: there is a time at which Snaky exists but nothing
outside of Snaky’s rattle exists. Hence Snaky can exist as just a
rattle, albeit for a very, very short period of time.</p>
<p>Hence even a snake can exist without its life-support organs, but
only for a short period of time.</p>
http://alexanderpruss.blogspot.com/2022/11/cerebrums-and-rattles.htmlnoreply@blogger.com (Alexander R Pruss)0tag:blogger.com,1999:blog-3891434218564545511.post-8746384043583707599Mon, 14 Nov 2022 19:18:00 +00002022-11-14T13:18:43.546-06:00goodmoral reasonsreasonsreductionReducing goods to reasons?<p>In my <a
href="http://alexanderpruss.blogspot.com/2022/11/the-2018-belgium-vs-brazil-world-cup.html">previous
post</a> I cast doubt on reducing moral reasons to goods.</p>
<p>What about the other direction? Can we reduce goods to reasons?</p>
<p>The simplest story would be that goods reduce to reasons to promote
them.</p>
<p>But there seem to be goods that give no one a reason to promote them.
Consider the good fact that there exist (in the eternalist sense:
existed, exist now, will exist, or exist timelessly) agents. No agent
can promote the fact that there exist agents: that good fact is part of
the agent’s thrownness, to put it in Heideggerese.</p>
<p>Maybe, though, this isn’t quite right. If Alice is an agent, then
Alice’s existence is a good, but the fact that some agent or other
exists isn’t a good as such. I’m not sure. It seems like a world with
agents is better for the existence of agency, and not just better for
the particular agents it has. Adding <em>another</em> agent to the world
seems a lesser value contribution than just ensuring that there is
agency at all. But I could be wrong about that.</p>
<p>Another family of goods, though, are necessary goods. That God exists
is good, but it is necessarily true. That various mathematical theorems
are beautiful is necessarily true. Yet no one has reason to promote a
necessary truth.</p>
<p>But perhaps we could have a subtler story on which goods reduce not
just to reasons to promote them, but to reasons to “stand for them”
(taken as the opposite of “standing against them”), where promotion is
one way of “standing for” a good, but there are others, such as
celebration. It does not make sense to promote the existence of God, the
existence of agents, or the Pythagorean theorem, but celebrating these
goods makes sense.</p>
<p>However, while it might be the case that something is good just in
case an agent should “stand for it”, it does not seem right to think
that it is good <em>to the extent that</em> an agent should “stand for
it”. For the degree to which an agent should stand for a good is
determined not just by the magnitude of the good, but the agent’s
relationship to the good. I should celebrate my children’s
accomplishments more than strangers’.</p>
<p>Perhaps, though, we can modify the story in terms of goods-for-<span
class="math inline"><em>x</em></span>, and say that <span
class="math inline"><em>G</em></span> is good-for-<span
class="math inline"><em>x</em></span> to the extent that <span
class="math inline"><em>x</em></span> should stand for <span
class="math inline"><em>G</em></span>. But that doesn’t seem right,
either. I should stand for justice for all, and not merely to the degree
that justice-for-all is good-for-me. Moreover, there goods that are good
for non-agents, while a non-agent does not have a reason to do
anything.</p>
<p>I love reductions. But alas it looks to me like reasons and goods are
not reducible in either direction.</p>
http://alexanderpruss.blogspot.com/2022/11/reducing-goods-to-reasons.htmlnoreply@blogger.com (Alexander R Pruss)0tag:blogger.com,1999:blog-3891434218564545511.post-3583630516974995818Mon, 14 Nov 2022 18:45:00 +00002022-11-15T12:22:21.046-06:00axiologymoral reasonsmoralitysportsvalueThe 2018 Belgium vs Brazil World Cup game<p>In 2018, the Belgians beat the Brazilians 2-1 in the 2018 World Cup
soccer quarterfinals. There are about 18 times as many Brazilians and
Belgians in the world. This raises a number of puzzles in value theory,
if for simplicity we ignore everyone but Belgians and Brazilians in the
world.</p>
<p>An order of magnitude more people <em>wanted</em> the Brazilians to
win, and getting what one wants is good. An order of magnitude more
people would have felt significant and appropriate <em>pleasure</em> had
the Brazilians won, and an appropriate pleasure is good. And given both
wishful thinking as well as reasonable general presumptions about there
being more talent available in a larger population base, we can suppose
that a lot more people <em>expected</em> the Brazilians to win, and it’s
good if what one thinks is the case is in fact the case.</p>
<p>You might think that the good of the many outweighs the good of the
few, and Belgians are few. But, clearly, the above facts gave very
little moral reason to the Belgian players to lose. One might respond
that the above facts gave lots of reason to the Belgians to lose, but
these reasons were outweighed by the great value of victory to the
Belgian players, or perhaps the significant intrinsic value of playing a
sport as well as one can. Maybe, but if so then just multiply both
countries’ populations by a factor of ten or a hundred, in which case
the difference between the goods (desire satisfaction, pleasure and
truth of belief) is equally multiplied, but still makes little or no
moral difference to what the Belgian players should do.</p>
<p>Or consider this from the point of view of the Brazilian players.
Imagine you are one of them. Should the good of Brazil—around two
hundred million people caring about the game—be a crushing weight on
your shoulders, imbuing everything you do in practice and in the game
with a great significance? No! It’s still “just a game”, even if the
value of the good is spread through two hundred million people. It would
be weird to think that it is a minor pecadillo for a Belgian to slack
off in practice but a grave sin for a Brazilian to do so, because the
Brazilian’s slacking hurts an order of magnitude more people.</p>
<p>That said, I do think that the larger population of Brazil imbues the
Brazilians’ games and practices with <em>some</em> not insignificant
additional moral weight than the Belgians’. It would be odd if the
pleasure, desire satisfaction and expectations of so many counted for
<em>nothing</em>. But on the other hand, it should make no significant
difference to the Belgians whether they are playing Greece or Brazil:
the Belgians shouldn’t practice less against the Greeks on the grounds
that an order of magnitude fewer people will be saddened when the Greeks
lose than when Brazilians do.</p>
<p>However, these considerations seem to me to depend to some degree on
which decisions one is making. If Daniel is on the soccer team and
deciding how hard to work, it makes little difference whether he is on
the Belgian or Brazilian team. But suppose instead that Daniel is has
two talents: he could become an excellent nurse or a top soccer player.
As a nurse, he would help relieve the suffering of a number of patients.
As a soccer player, in addition to the intrinsic goods of the sports, he
would contribute to his fellow citizens’ pleasure and desire
satisfaction. In <em>this</em> decision, it seems that the number of
fellow citizens <em>does</em> matter. The number of people Daniel can
help as a nurse is not very dependent on the total population, but the
number of people that his soccer skills can delight varies linearly with
the total population, and if the latter number is large enough, it seems
that it would be quite reasonable for Daniel to opt to be a soccer
player. So we could have a case where if Daniel is Belgian he should
become a nurse but if Brazilian then a soccer player (unless Brazil has
a significantly greater need for nurses than Belgium, that is). But once
on the team, it doesn’t seem to matter much.</p>
<p>The map from axiology to moral reasons is quite complex, contextual,
and heavily agent-centered. The hope of reducing moral reasons to
axiology is very slim indeed.</p>
http://alexanderpruss.blogspot.com/2022/11/the-2018-belgium-vs-brazil-world-cup.htmlnoreply@blogger.com (Alexander R Pruss)0tag:blogger.com,1999:blog-3891434218564545511.post-2885390719796222853Fri, 11 Nov 2022 21:53:00 +00002022-11-11T15:53:39.158-06:00AristotelianismflourishingspeciesSpecies flourishing<p>As an Aristotelian who believes in individual forms, I’m puzzled
about cases of species-level flourishing that don’t seem reducible to
individual flourishing. On a biological level, consider how some species
(e.g., social insects, slime molds) have individuals who do not
reproduce. Nonetheless it is important to the flourishing of the
<em>species</em> that the species include some individuals that do
reproduce.</p>
<p>We might handle this kind of a case by attributing to other
individuals their <em>contribution</em> to reproduction of the species.
But I think this doesn’t solve the problem. Consider a non-biological
case. There are things that are achievements of the human species, such
as having reached the moon, having achieved a four minute mile, or
having proved the Poincaré conjecture. It seems a stretch to try to
individualize these goods by saying that we all contributed to them.
(After all, many of us weren’t even alive in 1969.)</p>
<p>I think a good move for an Aristotelian who believes in individual
forms is to say that “No man or bee is an island.” There is an external
flourishing in virtue of the species at large: it is a part of
<em>my</em> flourishing that humans landed on the moon. Think of how
members of a social group are rightly proud of the achievements of some
famous fellow-members: we Poles are proud of having produced Copernicus,
Russians of having launched humans into space, and Americans of having
landed on the moon.</p>
<p>However, there is still a puzzle. If it is a part of every human’s
good that “I am a member of a species that landed on the moon”, does
that mean the good is multiplied the more humans there are, because
there are more instances of this external flourishing? I think not.
External flourishing is tricky this way. The goods don’t always
aggregate summatively between people in the case of external
flourishing. If external flourishing were aggregated summatively, then
it would have been better if Russia rather than Poland produced
Copernicus, because there are more Russians than Poles, and so there
would have been more people with the external good of “being a citizen
of a country that produced Copernicus.” But that’s a mistake: it is a
good that each Pole has, but the good doesn’t multiply with the number
of Poles. Similarly, if Belgium is facing off Brazil for the World Cup,
it is not the case that it would be way better if the Brazilians won,
just because there are a lot more Brazilians who would have the external
good of “being a fellow citizen with the winners of the World Cup.”</p>
http://alexanderpruss.blogspot.com/2022/11/species-flourishing.htmlnoreply@blogger.com (Alexander R Pruss)0tag:blogger.com,1999:blog-3891434218564545511.post-6825891679519407542Fri, 11 Nov 2022 17:36:00 +00002022-11-11T11:36:45.372-06:00consequentialismdecision theoryinfinityparadoxMore on the interpersonal Satan's Apple<p>Let me take another look at the <a
href="http://alexanderpruss.blogspot.com/2022/11/the-interpersonal-satans-apple.html">interpersonal
moral Satan’s Apple</a>, but start with a finite case.</p>
<p>Consider a situation where a <em>finite</em> number <span
class="math inline"><em>N</em></span> of people independently make a
choice between <em>A</em> and <span
class="math inline"><em>B</em></span> and some disastrous outcome
happens if the number of people choosing <span
class="math inline"><em>B</em></span> hits a threshold <span
class="math inline"><em>M</em></span>. Suppose further that if you fix
whether the disaster happens, then it is better you to choose <span
class="math inline"><em>A</em></span> than <span
class="math inline"><em>B</em></span>, but the disastrous outcome
outweighs all the benefits from all the possible choices of <span
class="math inline"><em>B</em></span>.</p>
<p>For instance, maybe <em>B</em> is
feeding an apple to a hungry child, and <span
class="math inline"><em>A</em></span> is refraining from doing so, but
there is an evil dictator who likes children to be miserable, and once
enough children are not hungry, he will throw all the children in
jail.</p>
<p>Intuitively, you should do some sort of expected utility calculation
based on your best estimate of the probability <span
class="math inline"><em>p</em></span> that among the <span
class="math inline"><em>N</em> − 1</span> people other than you, <span
class="math inline"><em>M</em> − 1</span> will choose <span
class="math inline"><em>B</em></span>. For if fewer or more than <span
class="math inline"><em>M</em> − 1</span> of them choose <span
class="math inline"><em>B</em></span>, your choice will make no
difference, and you should choose <span
class="math inline"><em>B</em></span>. If <span
class="math inline"><em>F</em></span> is the difference between the
utilities of <em>B</em> and <span
class="math inline"><em>A</em></span>, e.g., the utility of feeding the
apple to the hungry child (assumed to be fairly positive), and <span
class="math inline"><em>D</em></span> is the utility of the disaster
(very negative), then you need to see if <span
class="math inline"><em>p</em><em>D</em> + <em>F</em></span> is positive
or negative or zero. Modulo some concerns about attitudes to risk, if
<em>p</em><em>D</em> + <em>F</em> is
positive, you should choose <em>B</em>
(feed the child) and if its negative, you shouldn’t.</p>
<p>If you have a uniform distribution over the possible number of people
other than you choosing <em>B</em>, the
probability that this number is <span
class="math inline"><em>M</em> − 1</span> will be <span
class="math inline">1/<em>N</em></span> (since the number of people
other than you choosing <em>B</em> is
one of 0, 1, ..., <em>N</em> − 1). Now,
we assumed that the benefits of <span
class="math inline"><em>B</em></span> are such that they don’t outweigh
the disaster even if everyone chooses <span
class="math inline"><em>B</em></span>, so <span
class="math inline"><em>D</em> + <em>N</em><em>F</em> < 0</span>.
Therefore <span
class="math inline">(1/<em>N</em>)<em>D</em> + <em>F</em> < 0</span>,
and so in the uniform distribution case you shouldn’t choose <span
class="math inline"><em>B</em></span>.</p>
<p>But you might not have a uniform distribution. You might, for
instance, have a reasonable estimate that a proportion <span
class="math inline"><em>p</em></span> of other people will choose <span
class="math inline"><em>B</em></span> while the threshold is <span
class="math inline"><em>M</em> ≈ <em>q</em><em>N</em></span> for some
fixed ratio <em>q</em> between <span
class="math inline">0</span> and 1. If
<em>q</em> is not close to <span
class="math inline"><em>p</em></span>, then facts about the binomial
distribution show that the probability that <span
class="math inline"><em>M</em> − 1</span> other people choose <span
class="math inline"><em>B</em></span> goes approximately exponentially
to zero as <em>N</em> increases.
Assuming that the badness of the disaster is linear or at most
polynomial in the number of agents, if the number of agents is large
enough, choosing <em>B</em> will be a
good thing. Of course, you might have the unlucky situation that <span
class="math inline"><em>q</em></span> (the ratio of threshold to number
of people) and <em>p</em> (the
probability of an agent choosing <span
class="math inline"><em>B</em></span>) are approximately equal, in which
case even for large <em>N</em>, the
risk that you’re near the threshold will be too high to allow you to
choose <em>B</em>.</p>
<p>But now back to infinity. In the interpersonal moral Satan’s Apple,
we have infinitely many agents choosing between <span
class="math inline"><em>A</em></span> and <span
class="math inline"><em>B</em></span>. But now instead of the threshold
being a finite number, the threshold is an infinite cardinality (one can
also make a version where it’s a co-cardinality). And this threshold has
the property that other people’s choices can <em>never</em> be such that
your choice will put things above the threshold—either the threshold has
already been met without your choice, or your choice can’t make it hit
the threshold. In the finite case, it depended on the numbers involved
whether you should choose <em>A</em> or
<em>B</em>. But the exact same
reasoning as in the finite case, but now without <em>any</em>
statistical inputs being needed, shows that you should choose <span
class="math inline"><em>B</em></span>. For it literally cannot make any
difference to whether a disaster happens, no matter what other people
choose.</p>
<p>In my previous post, I suggested that the interpersonal moral Satan’s
Apple was a reason to embrace causal finitism: to deny that an outcome
(say, the disaster) can causally depend on infinitely many inputs (the
agents’ choices). But the finite cases make me less confident. In the
case where <em>N</em> is large, and our
best estimate of the probability of another agent choosing <span
class="math inline"><em>B</em></span> is a value <span
class="math inline"><em>p</em></span> not close to the threshold ratio
<em>q</em>, it still seems
counterintuitive that you should morally choose <span
class="math inline"><em>B</em></span>, and so should everyone else, even
though that yields the disaster.</p>
<p>But I think in the finite case one can remove the
counterintuitiveness. For there are mixed strategies that if adopted by
everyone are better than everyone choosing <span
class="math inline"><em>A</em></span> or everyone choosing <span
class="math inline"><em>B</em></span>. The mixed strategy will involve
choosing some number <span
class="math inline">0 < <em>p</em><sub>best</sub> < <em>q</em></span>
(where <em>q</em> is the threshold
ratio at which the disaster happens) and everyone choosing <span
class="math inline"><em>B</em></span> with probability <span
class="math inline"><em>p</em><sub>best</sub></span> and <span
class="math inline"><em>A</em></span> with probability <span
class="math inline">1 − <em>p</em><sub>best</sub></span>, where <span
class="math inline"><em>p</em><sub>best</sub></span> is carefully
optimized allow as many people to feed hungry children without a
significant risk of disaster. The exact value of <span
class="math inline"><em>p</em><sub>best</sub></span> will depend on the
exact utilities involved, but will be close to <span
class="math inline"><em>q</em></span> if the number of agents is large,
as long as the disaster doesn’t scale exponentially. Now our statistical
reasoning shows that when your best estimate of the probability of other
people choosing <em>B</em> is
<em>not</em> close to the threshold ratio <span
class="math inline"><em>q</em></span>, you should just straight out
choose <em>B</em>. And the worry I had
is that everyone doing that results in the disaster. But it does not
seem problematic that in a case where your data shows that people’s
behavior is not close to optimal, i.e., their behavior propensities do
not match <em>p</em><sub>best</sub>,
you need to act in a way that doesn’t universalize very nicely. This is
no more paradoxical than the fact that when there are criminals, we need
to have a police force, even though ideally we wouldn’t have one.</p>
<p>But in the infinite case, no matter what strategy other people adopt,
whether pure or mixed, choosing <span
class="math inline"><em>B</em></span> is better.</p>
http://alexanderpruss.blogspot.com/2022/11/more-on-interpersonal-satans-apple.htmlnoreply@blogger.com (Alexander R Pruss)2tag:blogger.com,1999:blog-3891434218564545511.post-2938107298701137238Fri, 11 Nov 2022 02:44:00 +00002022-11-10T20:44:33.750-06:00consequentialisminfinityparadoxThe interpersonal Satan's Apple<p>Consider a moral interpersonal version of <a
href="http://philsci-archive.pitt.edu/1595/1/15.1.bayesbind.pdf">Satan’s
Apple</a>: infinitely many people independently choose whether to give a
yummy apple to a (different) hungry child, and if infinitely many choose
to do so, some calamity happens to everyone, a calamity outweighing the
hunger the child suffers. You’re one of the potential apple-givers and
you’re not hungry yourself. The disaster strikes if and only if
infinitely many people <em>other than you</em> give an apple. Your
giving an apple makes no difference whatsoever. So it seems like you
<em>should</em> give the apple to the child. After all, you relieve one
child’s hunger, and that’s good whether or not the calamity happens.</p>
<p>Now, we deontologists are used to situations where a disaster happens
because one did the right thing. That’s because consequences are not the
only thing that counts morally, we say. But in the moral interpersonal
Satan’s Apple, there seems to be no deontology in play. It seems weird
to imagine that disaster could strike because everyone did what was
consequentialistically right.</p>
<p>One way out is causal finitism: Satan’s Apple is impossible, because
the disaster would have infinitely many causes.</p>
http://alexanderpruss.blogspot.com/2022/11/the-interpersonal-satans-apple.htmlnoreply@blogger.com (Alexander R Pruss)5tag:blogger.com,1999:blog-3891434218564545511.post-8124645336640246488Thu, 10 Nov 2022 15:05:00 +00002022-11-10T12:24:30.557-06:00decision theoryprobabilityMore on discounting small probabilities<p>In <a
href="http://alexanderpruss.blogspot.com/2022/11/how-to-discount-small-probabilities.html">yesterday’s
post</a>, I argued that there is something problematic about the idea of
discounting small probabilities, given that in a large enough lottery
<em>every</em> possibility with has a small probability. I then offered
a way of making sense of the idea by “trimming” the utility function at
the top and bottom.</p>
<p>This morning, however, I noticed that one can also take the idea of
discounting small probabilities more literally and still get the exact
same results as by trimming utility functions. Specifically, given a
probability function <em>P</em> and a
probability discount threshold <span
class="math inline"><em>ϵ</em></span>, we form a credence function <span
class="math inline"><em>P</em><sub><em>ϵ</em></sub></span> by letting
<span
class="math inline"><em>P</em><sub><em>ϵ</em></sub>(<em>A</em>) = <em>P</em>(<em>A</em>)</span>
if <span
class="math inline"><em>ϵ</em> ≤ <em>P</em>(<em>A</em>) ≤ 1 − <em>ϵ</em></span>,
<span
class="math inline"><em>P</em><sub><em>ϵ</em></sub>(<em>A</em>) = 0</span>
if <span
class="math inline"><em>P</em>(<em>A</em>) < <em>ϵ</em></span> and
<span
class="math inline"><em>P</em><sub><em>ϵ</em></sub>(<em>A</em>) = 1</span>
if <span
class="math inline"><em>P</em>(<em>A</em>) > 1 − <em>ϵ</em></span>.
This discounts close-to-zero probabilities to zero and raises close-to-one
probabilities to one. (We shouldn’t forget the second or things won't work well.)</p>
<p>Of course, <span
class="math inline"><em>P</em><sub><em>ϵ</em></sub></span> is not in
general a probability, but it does satisfy the Zero, Non-Negativity,
Normalization and Monotonicity axioms, and we can now use LSI<span
class="math inline"><sup>↑</sup></span> <a
href="http://alexanderpruss.com/papers/InconsistentCredences.pdf">level-set
integral</a> to calculate utilities with <span
class="math inline"><em>P</em><sub><em>ϵ</em></sub></span>.</p>
<p>If <em>U</em><sub><em>ϵ</em></sub>
is the “trimmed” utility function from my previous post, then LSI<span
class="math inline"><sup>↑</sup><sub><em>P</em><sub><em>ϵ</em></sub></sub>(<em>U</em>) = <em>E</em>(<em>U</em><sub>2<em>ϵ</em></sub>)</span>,
so the two approaches are equivalent.</p>
<p>One can also do the same thing within <a
href="https://smile.amazon.com/Risk-Rationality-Lara-Buchak/dp/0198801289">Buchak’s
REU theory</a>, since that theory is equivalent to applying LSI<span
class="math inline"><sup>↑</sup></span> with a probability transformed
by a monotonic map of <span
class="math inline">[0,1]</span> to <span
class="math inline">[0,1]</span> keeping endpoints fixed, which is
exactly what I did when moving from <span
class="math inline"><em>P</em></span> to <span
class="math inline"><em>P</em><sub><em>ϵ</em></sub></span>.</p>
http://alexanderpruss.blogspot.com/2022/11/more-on-discounting-small-probabilities.htmlnoreply@blogger.com (Alexander R Pruss)3tag:blogger.com,1999:blog-3891434218564545511.post-7002448975859986156Wed, 09 Nov 2022 20:35:00 +00002022-11-09T15:15:03.397-06:00decision theoryinfinityprobabilityHow to discount small probabilities<p>A very intuitive solution to a variety of problems in infinite
decision theory is that “for possibilities that have very small
probabilities of occurring, we should discount those probabilities down
to zero” when making decisions (<a
href="https://quod.lib.umich.edu/cgi/p/pod/dod-idx/how-to-avoid-maximizing-expected-utility.pdf?c=phimp;idno=3521354.0019.018;format=pdf">Monton</a>).</p>
<p>Suppose throughout this post that <span
class="math inline"><em>ϵ</em> > 0</span> counts as our threshold of
“very small probabilities”. No doubt <span
class="math inline"><em>ϵ</em> < 1/100</span>.</p>
<p>In this post I want to offer a precise and friendly amendment to the
solution of neglecting small probabilities. But first why we need an
amendment. Consider a game where an integer <span
class="math inline"><em>K</em></span> is randomly chosen between <span
class="math inline"> − 1</span> and <span
class="math inline"><em>N</em></span> for some large fixed positive
<em>N</em>, so large that <span
class="math inline">1/(2+<em>N</em>) < <em>ϵ</em></span>, and you get
<em>K</em> dollars. The game is clearly
worth playing. But if you discount “possibilities that have very small
probabilities”, you are left with <em>nothing</em>: every possibility
has a very small probability!</p>
<p>Perhaps this is uncharitable. Maybe the idea is not that we discount
to zero <em>all</em> possibilities with small probabilities, but that we
discount such possibilities until the total discount hits the threshold
<em>ϵ</em>. But while this sounds like
a charitable interpretation of the suggestion, it leaves the theory
radically underdetermined. For <em>which</em> possibilities do we
discount? In my lottery case, do we start by discounting the
possibilities at the low end (<span
class="math inline"> − 1, 0, 1, ...</span>) until we have hit the
threshold? Or do we start at the high end (<span
class="math inline"><em>N</em>, <em>N</em> − 1, <em>N</em> − 2, ...</span>)
or somewhere in the middle?</p>
<p>Here is my friendly proposal. Let <span
class="math inline"><em>U</em></span> be the utility function we want to
evaluate the value of. Let <em>T</em>
be the smallest value such that <span
class="math inline"><em>P</em>(<em>U</em>><em>T</em>) ≤ <em>ϵ</em>/2</span>.
(This exists: <span
class="math inline"><em>T</em> = inf {<em>λ</em> : <em>P</em>(<em>U</em>><em>λ</em>) ≤ <em>ϵ</em>/2}</span>.)
Let <em>t</em> be the largest value
such that <span
class="math inline"><em>P</em>(<em>U</em><<em>t</em>) ≤ <em>ϵ</em>/2</span>
(i.e., <span
class="math inline"><em>t</em> = sup {<em>λ</em> : <em>P</em>(<em>U</em><<em>λ</em>) ≤ <em>ϵ</em>/2}</span>).
Take <em>U</em> and replace any values
bigger than <em>T</em> with <span
class="math inline"><em>T</em></span> and any values smaller than <span
class="math inline"><em>t</em></span> with <span
class="math inline"><em>t</em></span>, and call the resulting utility
function <span
class="math inline"><em>U</em><sub><em>ϵ</em></sub></span>. We now
replace <em>U</em> with <span
class="math inline"><em>U</em><sub><em>ϵ</em></sub></span> in our
expected value calculations. (In the lottery example, we will be
trimming from both ends at the same time.)</p>
<p>The result is a precise theory (given the mysterious threshold <span
class="math inline"><em>ϵ</em></span>). It doesn’t neglect all
possibilities with small probabilities, but rather it trims
low-probability outliers. The trimming procedure respects the fact that
often utility functions are defined up to positive affine
transformations.</p>
<p>Moreover, the trimming procedure can yield an answer to what I think
is the biggest objection to small-probability discounting, namely that
in a long enough run—and everyone should think there is a non-negligible
chance of eternal life—even small probabilities can add up. If you are
regularly offered the same small chance of a gigantic benefit during an
eternal future, and you turn it down each time because the chance is
negligible, you’re almost surely missing out on an infinite amount of
value. But we can apply the trimming procedure at the level of choice of
policies rather than of individual decisions. Then if small chances are
offered often enough, they won’t all be trimmed away.</p>
http://alexanderpruss.blogspot.com/2022/11/how-to-discount-small-probabilities.htmlnoreply@blogger.com (Alexander R Pruss)0tag:blogger.com,1999:blog-3891434218564545511.post-2362146137141300824Tue, 08 Nov 2022 21:38:00 +00002022-11-09T09:27:49.005-06:00decision theoryinfinityA principle about infinite sequences of decisions<p>There are <a
href="http://philsci-archive.pitt.edu/1595/1/15.1.bayesbind.pdf">many</a>
paradoxes of infinite sequences of decisions where the sequence of
individual decisions that maximize expected utility is unfortunate.
Perhaps the most vivid is Satan’s Apple, where a delicious apple is
sliced into infinitely many pieces, and Eve chooses which pieces to eat.
But if she greedily takes infinitely many, she is kicked out of
paradise, an outcome so bad that the whole apple does not outweigh it.
For any set of pieces Eve eats, another piece is only a plus. So she
eats them all, and is damned.</p>
<p>Here is a plausible principle:</p>
<ol type="1">
<li>If at each time you are choosing between a finite number of betting portfolios fixed in advance,
with the betting portfolio in each decision being tied to a set of
events wholly independent of all the later or earlier events or
decisions, with the overall outcome being just the sum or
aggregation of the outcomes of the betting portfolios, and with the utility of each
portfolio well-defined given your information, then you should
at each time maximize utility.</li>
</ol>
<p>In Satan’s Apple, for instance, the overall outcome is not just the
sum of the outcomes of the individual decisions to eat or not to eat,
and so Satan’s Apple is not a counterexample to (1). In fact, few of the
paradoxes of infinite sequences of decisions are counterexamples to
(1).</p>
<p>However, my <a
href="http://alexanderpruss.blogspot.com/2022/10/expected-utility-maximization.html">unbounded
expected utility maximization paradox</a> is.</p>
<p>I don’t know if there is something particularly significant about
a paradox violating (1). I think there is, but I can’t quite put my finger
on it. On the other hand, (1) is such a complex principle that it may just seem <i>ad hoc</i>.</p>
http://alexanderpruss.blogspot.com/2022/11/a-principle-about-infinite-sequences-of.htmlnoreply@blogger.com (Alexander R Pruss)3tag:blogger.com,1999:blog-3891434218564545511.post-6566217356214966087Wed, 02 Nov 2022 21:01:00 +00002022-11-02T16:01:35.743-05:00decision theorydominationinfinite lotteryMust we accept free stuff?<p>Suppose someone offers you, at no cost whatsoever, something of
specified positive value. However small that value, it seems irrational
to refuse it.</p>
<p>But what if someone offers you a random amount of positive value for
free. Strict dominance principles say it’s irrational to refuse it. But
I am not completely sure.</p>
<p>Imagine a lottery where some positive integer <span
class="math inline"><em>n</em></span> is picked at random, with all
numbers equally likely, and if <span
class="math inline"><em>n</em></span> is picked, then you get <span
class="math inline">1/<em>n</em></span> units of value. Should you play
this lottery for free?</p>
<p>The expected value of the lottery is zero with respect to any
finitely-additive real-valued probability measure that fits the
description (i.e., assign equal probablity to each number). And for any
positive number <em>x</em>, the
probability that you will get less than <span
class="math inline"><em>x</em></span> is one. It’s not clear to me that
it’s worth going for this.</p>
<p>If you like infinitesimals, you might say that the expected value of
the lottery is infinitesimal and the probability of getting less than
some positive number <em>x</em> is
1 − <em>α</em> for an infinitesimal
<em>α</em>. That makes it sound like a
better deal, but it’s not all that clear.</p>
<p>Of course, infinite fair lotteries are dubious. So I don’t set much
store by this example.</p>
http://alexanderpruss.blogspot.com/2022/11/must-we-accept-free-stuff.htmlnoreply@blogger.com (Alexander R Pruss)3tag:blogger.com,1999:blog-3891434218564545511.post-5245512503270114347Wed, 02 Nov 2022 17:08:00 +00002022-11-02T12:08:28.933-05:00friendshipvaluevirtueTwo different ways of non-instrumentally pursuing a good<p>Suppose Alice is blind to the intrinsic value of friendship and Bob
can see the intrinsic value of friendship. Bob then told Alice that
friendship is intrinsically valuable. Alice justifiedly trusts Bob in
moral matters, and so Alice concludes that friendship has intrinsic
value, even though she can’t “see” it. Alice and Bob then both pursue
friendship for its own sake.</p>
<p>But there is a difference: Bob pursues friendship because of the
particular ineffable “thick” kind of value that friendship has. Alice
doesn’t know what “thick” kind of value friendship has, but on the basis
of Bob’s testimony, she knows that it has some such value or other, and
that it is a great and significant value. As long as Alice knows what
kinds of actions friendship requires, she can pursue friendship without
that knowledge, though it’s probably more difficult for her, perhaps in
the way that it is more difficult for a tone-deaf person to play the
piano, though in practice the tone-deaf person could learn what kinds of
finger movements result in aesthetically valuable music without grasping
that aesthetic value.</p>
<p>The Aristotelian tradition makes the grasp of the particular thick
kind of value involved in a virtuous activity be a part of the full
possession of that virtue. On that view, Alice cannot have the full
virtue of friendship. There is something she is missing out on, just as
the tone-deaf pianist is missing out on something. But she is not, I
think, less praiseworthy than Bob. In fact Alice’s pursuit of friendship
involves the exercise of a virtue which Bob’s does not: the virtue of
faith, as exhibited in Alice’s trust in Bob’s testimony about the value
of friendship.</p>
http://alexanderpruss.blogspot.com/2022/11/two-different-ways-of-non.htmlnoreply@blogger.com (Alexander R Pruss)0tag:blogger.com,1999:blog-3891434218564545511.post-4710805261980258229Tue, 01 Nov 2022 21:06:00 +00002022-11-01T16:06:08.588-05:00instrumentalityintrinsic goodpursuittruthvaluePursuing a thing for its own sake<p>Suppose you pursue truth for its own sake. As we learn from
Aristotle, it does not follow that you don’t pursue truth for the sake
of something else. For the most valuable things are both intrinsically
and instrumentally valuable, and so they are typically pursued both for
their own sake and for the sake of something else.</p>
<p>What if you pursue something, but not for the sake of something else.
Does it follow that you pursue the thing for its own sake? Maybe, but
it’s not as clear as it might seem. Imagine that you eat fiber for the
sake of preventing colon cancer. Then you hear a study that says that
fiber doesn’t prevent colon cancer. But you continue to eat fiber, out
of a kind of volitional inertia, without any reason to do so. Then you
are pursuing the consumption of fiber not for the sake of anything else.
But merely losing the instrumental reason for eating fiber doesn’t give
you a non-instrumentally reason. Rather, you are now eating fiber
irrationally, for no reason.</p>
<p>Perhaps it is impossible to do something for no reason. But even if
it is impossible to do something for no reason, it is incorrect to
<em>define</em> pursuing something for its own sake as pursuing it not
for the sake of something else. For that you <em>pursue something for
its own sake</em> states something positive about your pursuit, while
that you <em>don’t pursue it for the sake of anything else</em> states
something negative about your pursuit. There is a kind of valuing of the
thing for its own sake that is needed to pursue the thing for its own
sake.</p>
<p>It is tempting to say that you pursue a thing for its own sake
provided that you pursue it because of the intrinsic value you take it
to have. But that, too, is incorrect. For suppose that a rich benefactor
tells you that they will give you a ton of money if you gain something
of intrinsic value today. You know that truth is valuable for its own
sake, so you find out something. In doing so, you find out the truth
<em>because</em> the truth is intrinsically valuable. But your pursuit
of that truth is entirely instrumental, despite your reason being the
intrinsic value.</p>
<p>Hence, to pursue a thing for its own sake is not the same as to
pursue it because it has intrinsic value. Nor is it to pursue it not for
the sake of something else.</p>
<p>I suspect that pursuing a thing for its own sake is a primitive
concept.</p>
http://alexanderpruss.blogspot.com/2022/11/pursuing-thing-for-its-own-sake.htmlnoreply@blogger.com (Alexander R Pruss)6tag:blogger.com,1999:blog-3891434218564545511.post-4492072568340409261Tue, 01 Nov 2022 15:37:00 +00002022-11-01T10:37:50.766-05:00axiologymaterialismvalueHuman worth and materialism<ol type="1">
<li><p>A typical human being has much more intrinsic value than any 80
kg arrangement of atoms.</p></li>
<li><p>If materialism is true, a typical human being is an 80 kg
arrangement of atoms.</p></li>
<li><p>So, materialism is not true.</p></li>
</ol>
http://alexanderpruss.blogspot.com/2022/11/human-worth-and-materialism.htmlnoreply@blogger.com (Alexander R Pruss)25tag:blogger.com,1999:blog-3891434218564545511.post-7256153594092493302Mon, 31 Oct 2022 15:01:00 +00002022-10-31T10:01:27.389-05:00accidentsEucharistmagnetismsubstancetranssubstantiationTranssubstantiation and magnets<p>On Thomistic accounts of transsubstantiation, the accidents of bread
and wine continue to exist even when the substance no longer does
(having been turned into the substance of Christ’s body and blood). This
seems problematic.</p>
<p>Here is an analogy that occurred to me. Consider a magnet. It’s not
crazy to think of the magnet’s magnetic field as an accident of the
magnet. But the magnetic field extends spatially beyond the magnet.
Thus, it exists in places where the magnet does not.</p>
<p>Now, according to four-dimensionalism, time is rather like space. If
so, then an accident existing <em>when its substance does not</em> is
rather like an accident existing <em>where its substance does not</em>.
Hence to the four-dimensionalist, the magnet analogy should be quite
helpful.</p>
<p>Actually, if we throw relativity into the mix, then we can get an
even closer analogy, assuming still that a magnet’s field is an accident
of the magnet. Imagine that the magnet is annihilated. The magnetic
field disappears, but gradually, starting near the magnet, because all
effects propagate at most at the speed of light. Thus, even when the
magnet is destroyed, for a short period its magnetic field still
exists.</p>
<p>That said, I don’t know if the magnet’s field is an accident of it.
(Rob Koons in conversation suggested it might be.) But it’s
comprehensible to think of it as such, and hence the analogy makes
Thomistic transsubtantiaton comprehensible, I think.</p>
http://alexanderpruss.blogspot.com/2022/10/transsubstantiation-and-magnets.htmlnoreply@blogger.com (Alexander R Pruss)3tag:blogger.com,1999:blog-3891434218564545511.post-8919479568093308864Fri, 28 Oct 2022 15:36:00 +00002022-10-28T10:36:48.828-05:00beliefignoranceknowledgelearningDoes our ignorance always grow when we learn?<p>Here is an odd thesis:</p>
<ol type="1">
<li>Whenever you gain a true belief, you gain a false belief.</li>
</ol>
<p>This follows from:</p>
<ol start="2" type="1">
<li>Whenever you gain a belief, you gain a false belief.</li>
</ol>
<p>The argument for (2) is:</p>
<ol start="3" type="1">
<li><p>You always have at least one false belief.</p></li>
<li><p>You believe a conjunction if and only if you believe the
conjuncts.</p></li>
<li><p>Suppose you just gained a belief <span
class="math inline"><em>p</em></span>.</p></li>
<li><p>There is now some false belief <span
class="math inline"><em>q</em></span> that you have. (By (3))</p></li>
<li><p>Before you gained the belief <span
class="math inline"><em>p</em></span> you didn’t believe the conjunction
of <em>p</em> and <span
class="math inline"><em>q</em></span>. (By (4))</p></li>
<li><p>So, you just gained the belief in the conjunction of <span
class="math inline"><em>p</em></span> and <span
class="math inline"><em>q</em></span>. (By (5) and (7))</p></li>
<li><p>The conjunction of <em>p</em>
and <em>q</em> is false. (By
(6))</p></li>
<li><p>So, you just gained a false belief. (By (8) and (9))</p></li>
</ol>
<p>I am not sure I accept (4), though.</p>
http://alexanderpruss.blogspot.com/2022/10/our-ignorance-grows-when-we-learn.htmlnoreply@blogger.com (Alexander R Pruss)4tag:blogger.com,1999:blog-3891434218564545511.post-6834869573308450426Fri, 28 Oct 2022 15:08:00 +00002022-10-28T10:08:13.753-05:00“Accuracy, probabilism and Bayesian update in inﬁnite domains” <p>The paper has
just come out <a href="https://rdcu.be/cYqOw">online in
Synthese</a>.</p>
<p>Abstract: Scoring rules measure the accuracy or epistemic utility of
a credence assignment. A significant literature uses plausible
conditions on scoring rules on finite sample spaces to argue for both
probabilism—the doctrine that credences ought to satisfy the axioms of
probabilism—and for the optimality of Bayesian update as a response to
evidence. I prove a number of formal results regarding scoring rules on
infinite sample spaces that impact the extension of these arguments to
infinite sample spaces. A common condition in the arguments for
probabilism and Bayesian update is strict propriety: that according to
each probabilistic credence, the expected accuracy of any other credence
is worse. Much of the discussion needs to divide depending on whether we
require finite or countable additivity of our probabilities. I show that
in a number of natural infinite finitely additive cases, there simply do
not exist strictly proper scoring rules, and the prospects for arguments
for probabilism and Bayesian update are limited. In many natural
infinite countably additive cases, on the other hand, there do exist
strictly proper scoring rules that are continuous on the probabilities,
and which support arguments for Bayesian update, but which do not
support arguments for probabilism. There may be more hope for
accuracy-based arguments if we drop the assumption that scores are
extended-real-valued. I sketch a framework for scoring rules whose
values are nets of extended reals, and show the existence of a strictly
proper net-valued scoring rules in all infinite cases, both for f.a. and
c.a. probabilities. These can be used in an argument for Bayesian
update, but it is not at present known what is to be said about
probabilism in this case.</p>
http://alexanderpruss.blogspot.com/2022/10/accuracy-probabilism-and-bayesian.htmlnoreply@blogger.com (Alexander R Pruss)1tag:blogger.com,1999:blog-3891434218564545511.post-7857959486826622788Fri, 28 Oct 2022 15:00:00 +00002022-10-28T10:00:15.001-05:00contrastive explanationexplanationfree willlibertarianismPrinciple of Sufficient ReasonreasonsChoices on a spectrum<p>My usual story about how to reconcile libertarianism with the
Principle of Sufficient Reason is that when we choose, we choose on the
basis of incommensurable reasons, some of which favor the choice we made
and others favor other choices. Moreover, this is a kind of constrastive
explanation.</p>
<p>This story, though it has some difficulties, is designed for choices
between options that promote significantly different goods—say, whether
to read a book or go for a walk or write a paper.</p>
<p>But a different kind of situation comes up for choices of a point on
a spectrum. For instance, suppose I am deciding how much homework to
assign, how hard a question to ask on an exam, or how long a walk to go
for. What is going on there?</p>
<p>Well, here is a model that applies to a number of cases. There are
two incommensurable goods one better served as one goes in one direction
in the spectrum and the other better served as one goes in the other
direction in the spectrum. Let’s say that we can quantify the spectrum
as one from less to more with respect to some quantity <span
class="math inline"><em>Q</em></span> (amount of homework, difficulty of
a question or length of a walk), and good <span
class="math inline"><em>A</em></span> is promoted by less of <span
class="math inline"><em>Q</em></span> and incommensurable good <span
class="math inline"><em>B</em></span> is promoted by more of <span
class="math inline"><em>Q</em></span>. For instance, with homework,
<em>A</em> is the student’s having time
for other classes and for non-academic pursuits and <span
class="math inline"><em>B</em></span> is the student’s learning more
about the subject at hand. With exam difficulty, <span
class="math inline"><em>A</em></span> may be avoiding frustration and
<em>B</em> is giving a worthy
challenge. With a walk, <em>A</em> is
reducing fatigue and <em>B</em> is
increasing health benefits. (Note that the claim that <span
class="math inline"><em>A</em></span> is promoted by less <span
class="math inline"><em>Q</em></span> and <span
class="math inline"><em>B</em></span> is promoted by more <span
class="math inline"><em>Q</em></span> may only be correct within a
certain range of <em>Q</em>. A walk
that is too long leads to injury rather than health.)</p>
<p>So, now, suppose we choose <span
class="math inline"><em>Q</em> = <em>Q</em><sub>1</sub></span>. Why did
one choose that? It is odd to say that one chose <span
class="math inline"><em>Q</em></span> on account of reasons <span
class="math inline"><em>A</em></span> and <span
class="math inline"><em>B</em></span> that are opposed to each
other—that sounds inconsistent.</p>
<p>Here is one suggestion. Take the choice to make <span
class="math inline"><em>Q</em></span> equal to <span
class="math inline"><em>Q</em><sub>1</sub></span> to be the conjunction
of two (implicit?) choices:</p>
<ol type="a">
<li><p>Make <em>Q</em> at most <span
class="math inline"><em>Q</em><sub>1</sub></span></p></li>
<li><p>Make <em>Q</em> at least <span
class="math inline"><em>Q</em><sub>1</sub></span>.</p></li>
</ol>
<p>Now, we can explain choice (a) in terms of (a) serving good <span
class="math inline"><em>A</em></span> better than the alternative, which
would be to make <em>Q</em> be bigger
than <em>Q</em><sub>1</sub>. And we can
explain (b) in terms of (b) serving good <span
class="math inline"><em>B</em></span> better than the alternative of
making <em>Q</em> be smaller.</p>
<p>Here is a variant suggestion. Partition the set of options into two
ranges <em>R</em><sub>1</sub>,
consisting of options where <span
class="math inline"><em>Q</em> < <em>Q</em><sub>1</sub></span> and
<em>R</em><sub>2</sub>, where <span
class="math inline"><em>Q</em> > <em>Q</em><sub>1</sub></span>. Why
did I choose <span
class="math inline"><em>Q</em> = <em>Q</em><sub>1</sub></span>? Well, I
chose <em>Q</em> over all the choices
in <em>R</em><sub>1</sub> because <span
class="math inline"><em>Q</em></span> better promotes <span
class="math inline"><em>B</em></span> than anything in <span
class="math inline"><em>R</em><sub>1</sub></span>, and I chose <span
class="math inline"><em>Q</em></span> over all the choices in <span
class="math inline"><em>R</em><sub>2</sub></span> because <span
class="math inline"><em>Q</em></span> better promotes <span
class="math inline"><em>A</em></span> than anything in <span
class="math inline"><em>R</em><sub>1</sub></span>.</p>
<p>On both approaches, the apparent inconsistency of citing opposed
goods disappears because they are cited to explain different
contrasts.</p>
<p>Note that nothing in the above explanatory stories requires any
commitment to there being some sort of third good, a good of balance or
compromise between <em>A</em> and <span
class="math inline"><em>B</em></span>. There is no commitment to <span
class="math inline"><em>Q</em><sub>1</sub></span> being the best way to
position <em>Q</em>.</p>
http://alexanderpruss.blogspot.com/2022/10/choices-on-spectrum.htmlnoreply@blogger.com (Alexander R Pruss)0