Logic and Theism: Arguments For and Against Beliefs in God

667 Pages·2006·7.49 MB·English

LogicandTheism
ArgumentsForandAgainstBeliefsinGod
This is a wide-ranging book about arguments for and against belief
in God. Arguments for the existence of God analyzed in the first six
chaptersincludeontologicalargumentsfromAnselmthroughGo¨del,
the cosmological arguments of Aquinas and Leibniz, and arguments
fromevidencefordesignandmiracles.Followingthesechaptersaretwo
chaptersconsideringargumentsagainstthatexistence.Thelastchapter
examinesPascalianargumentsforandagainstbeliefregardlessofex-
istence.TherearediscussionsofCantorianproblemsforomniscience,
of challenges to divine omnipotence, and of the compatibility of ev-
erlastingcompleteknowledgeoftheworldwithfreewill.Forreaders
withatechnicalbackgroundinlogicthereareappendicesthatpresent
formalproofsinasystemforquantifiedmodallogic,atheoryofpos-
sible worlds, notes on Cantorian set theory, and remarks concerning
nonstandardhyperrealnumbers.
This book will be a valuable resource for philosophers of religion
andtheologiansandwillinterestlogiciansandmathematiciansaswell.
Jordan Howard Sobel is Professor Emeritus in the Department of
PhilosophyattheUniversityofToronto.
Logic and Theism
Arguments For and Against Beliefs in God
JORDAN HOWARD SOBEL
UniversityofToronto
ThereisNoGod
‘ThereisnoGod,’thewickedsaith,
‘Andtrulyit’sablessing,
Forwhathemighthavedonewithus
It’sbetteronlyguessing.’
‘ThereisnoGod,’ayoungsterthinks,
‘Orreally,iftheremaybe,
Hesurelydidn’tmeanaman
Alwaystobeababy.’
‘ThereisnoGod,orifthereis,’
Thetradesmanthinks,‘twerefunny
Ifheshouldtakeitillinme
Tomakealittlemoney.’
‘Whethertherebe,’therichmansays,
‘Itmattersverylittle,
ForIandmine,thanksomebody,
Arenotinwantofvictual.’
Someothers,alsotothemselves,
Whoscarcesomuchasdoubtit,
Thinkthereisnone,whentheyarewell,
Anddonotthinkaboutit.
Butcountryfolkswholivebeneath
Theshadowofthesteeple;
Theparsonandtheparson’swife,
Andmostlymarriedpeople;
Youthsgreenandhappyinfirstlove,
Sothankfulforillusion;
Andmencaughtoutinwhattheworld
Callsguilt,infirstconfusion;
Andalmosteveryonewhenage
Disease,orsorrowsstrikehim,
InclinestothinkthereisaGod,
Orsomethingverylikehim.
AnthurHughClough
DoverBeach
Theseaiscalmto-night
Thetideisfull,themoonliesfair
Uponthestraits;–ontheFrenchcoastthelight
Gleamsandisgone;thecliffsofEnglandstand,
Glimmeringandvast,outinthetranquilbay.
Cometothewindow,sweetisthenight-air!
Only,fromthelonglineofspray
Wheretheseameetsthemoon-blanchedland,
Listen!youhearthegratingroar
Ofpebbleswhichthewavesdrawback,andfling,
Attheirreturn,upthehighstrand,
Begin,andcease,andthenagainbegin
Withtremulouscadenceslow,andbring
Theeternalnoteofsadnessin.
Sophocleslongago
HearditontheAegean,anditbrought
Intohismindtheturbidebbandflow
Ofhumanmisery;we
Findalsointhesoundathought,
Hearingitbythisdistantnorthernsea.
TheSeaofFaith
Wasonce,too,atthefull,androundearth’sshore
Laylikethefoldsofabrightgirdlefurled,
ButnowIonlyhear
Itsmelancholy,long,withdrawingroar,
Retreating,tothebreath
Ofthenight-wind,downthevastedgesdrear
Andnakedshinglesoftheworld.
Ah,love,letusbetrue
Tooneanother!fortheworld,whichseems
Toliebeforeuslikealandofdreams,
Sovarious,sobeautiful,sonew,
Hathreallyneitherjoy,norlove,norlight,
Norcertitude,norpeace,norhelpforpain;
Andwearehereasonadarklingplain
Sweptwithconfusedalarmsofstruggleandflight,
Whereignorantarmiesclashbynight.
MatthewArnold
Contents
Preface pagexvii
divinity
I. ‘God’,‘god’,andGod 3
1. Existenceandessencequestions 3
2. Namesinquestionsofexistenceandbelief 4
3. Etymologyandsemantics 6
4. ThecoreattitudinalconceptionofGod 9
5. Thephilosophers’conceptionofGod–Godasa
perfectbeing 11
6. Thecommonconceptionoftraditionaltheology 12
7. Mighttherebeagod,evenifthereisnotaperfectbeing? 19
8. Mighttherenotbeagod,evenifthereisaperfectbeing? 24
arguments for the existence of god
II. ClassicalOntologicalArguments 29
1. Introduction 29
2. PartOne:Rene´Descartes’sontologicalproof 31
3. PartTwo:“Mr.Spinoza,meetMr.Russell” 40
4. PartThree:St.Anselm’sargumentofProslogionII 59
5. PartFour:ImmanuelKant’scritiqueofDescartes’s
ontologicalargument 66
AppendixA.Symbolsandsymbolizations 70
AppendixB.Derivationsandmodels 71
AppendixC.Rulesofinferenceandformsofderivations 78
ix
x Contents
III. ModernModalOntologicalArguments 81
1. NormanMalcolm’sargument 81
2. CharlesHartshorne’sargument 82
3. Aflyintheointment? 86
4. OtherAnselmianarguments 88
5. ‘It’sthepossibility!’ 89
6. Foesofontologicalargumentssaythattheir
possibility-premisesbegquestions 90
7. Friendsofontologicalargumentsrespond 91
8. Butthat–thatconceivabilityentailspossibility–issimply
nottrue! 92
9. Ademotionoftheargumentfromaproof,toa
licensetobelieve 96
AppendixA.‘Possibleworlds ’99
A1.Worldsenough 99
A2.Truthandactualityatpossibleworlds 101
A3.Modalrealismwithouttears 102
A4.Thisisnotastory 103
A5.Alogicforpossibleworlds 103
Appendix B.Modallogic 105
B1.Sententialmodallogic 105
B2.Hartshorne’smodalontologicalargument 108
B3.Quantifiedmodallogic 110
IV. KurtGo¨del’sOntologischerBeweis 115
1. Introduction 115
2. Languageandlogic 117
3. Axioms,definitions,andtwotheorems 118
4. ThatitisnecessarythatthereisaGod-likebeing 125
5. WouldthatbeGod,coulditbeGod? 128
6. Modalcollapse 132
7. Concludingrecommendations 135
Appendix A.NotesinKurtGo¨del’shand 144
Appendix B.NotesinDanaScott’shand 145
Appendix C.Mainlyderivations 146
C1.AlogicforGo¨del’ssystem 146
C2.Twopromisedderivations 148
C3.DerivationsoftheoremsinGo¨del’ssystem 149
C4.DerivationsforAnderson’semendationof
Go¨del’ssystem 157
V. FirstCauses:“TheSecondWay” 168
1. Part1,Question2,ofSummaTheologica–
“TheExistenceofGod” 168
Contents xi
2. AnarticulationoftheSecondWay 170
3. ‘Efficientcauses’intheargument–sustaining,orgenerating? 175
4. Theinfiniteandinfiniteregresses 181
5. Thepreliminaryconclusion 190
6. Thereisagapintheargument 192
7. Ontheultimateconclusion,thatGodexists:Whetherthis
wouldfollowevenifallwaswellintheargumenttoit 193
AppendixA.NotesonAquinas’sotherways 195
AppendixB.Bangsandinfiniteregressesofcauses 198
B1.Bigbang!! 198
B2.Ablastfromtherecentpast–WilliamLaneCraig’s
kala¯mcausalargument 198
VI. UltimateReasons:Proofsacontingentiamundi 200
1. Classicalsources 200
2. ALeibniziancosmologicalargument 208
3. Onthepremises,andterminology 209
4. Comparisonswithontological,andagainwithfirstcause,
arguments 214
5. Cleanthes’objection 215
6. A‘smallproblem’withourLeibnizianargument 217
7. That‘smallproblem’withtheargumentgoesintobigger
problemsforits‘ambition’ 218
8. Proofsacontingentiamundi–whatanicebadidea 222
AppendixA.Leibniz’sproblemwithnecessity 228
A1.What,accordingtoLeibniz,isthereasonforthe
existenceoftheWorld? 228
A2.Hashegivenasufficientreason? 228
A3.Leibniz’s‘trilemma’ 229
Appendix B.ContingencyinJohnLeslie’sAxiarchism 233
AppendixC.RobertC.Koons’s‘NewLook’cosmological
argument 234
C1.Astart-upproblem 234
C2.Aterminalproblem 236
VII. Look’Round!–ArgumentsfromDesign 238
1. TheargumentoftheDialogues–firststatement 239
2. Onassessingargumentsforcausalexplanations 243
3. Probabilities,plainandconditional 247
4. Bayes’stheorems 252
5. A‘particulardiscussionoftheevidence’–theDialogues,
Parts5–8,10,and11 258
6. Part12oftheDialogues:Hume’s‘philosophicaltheism’ 264
7. Newfactsandnewtheories 272
xii Contents
8. Theargumentfromdesign–millennialeditions 277
9. ItisbesttoleaveGod-likebeingsoutofotherwisenatural
explanations 287
Appendix.Swinburne’steleologicalargument,andhis
cumulativeargument,fortheexistenceofGod 288
A1.Swinburne’steleologicalargument 288
A2.The‘logic’ofthisargument 289
A3.TheargumentcomparedwithCleanthes’ 290
A4.‘Cumulativeconfirmation’–‘Don’ttrythisathome!’ 291
A5.OnSwinburne’scumulativeargumentforthe
existenceofGod 294
VIII. CloudsofWitnesses–“OfMiracles” 298
Introductoryandprefatoryremarks 298
1. ‘Miracles’ 302
2. ‘Lawsofnature’ 305
3. Evidenceformiracles,andforGod 309
4. OnthefirstpartofHume’sgeneralmaxim 312
5. Aconditionthatisnotonlynecessary,butalsosufficient,
fortestimonysufficienttoestablishamiracle 318
6. OnthesecondpartofHume’smaxim 319
7. Bayes’stheoremfortheevidenceoftestimony 319
8. ThomasBayesandBayes’stheorems 321
9. RichardPrice 322
10. Lotteries–Pricethoughttheymadehiscase 324
11. Hume,‘Imustweighthis’ 327
12. Twoexperiments 328
13. Responsestotheseresults 329
AppendixA.AproofofHume’stheorem 331
AppendixB.Condorcet’srule,witnessreliability,and‘last
degreesofassurance’ 333
B1.BayesingCondorcet’srule 333
B2.Witnessreliability 335
B3.Onlastdegreesofassurance 336
on two parts of the common conception
IX. RomancingtheStone 345
1. Onthe‘commonnames’ofGod 345
2. Omnipotence 346
3. ‘Essentialproperties’? 350
4. Onwhetheromnipotenceispossible 353
5. Onessentialomnipotence 361
Contents xiii
6. Onnecessarilyeverlastingexistenceconjoinedwith
essentialomnipotence 364
7. Onomnipotenceconjoinedwithotherconditions
andattributes 364
8. WhatisleftforGodofomnipotence? 365
Appendix.AformalarticulationoftheargumentofSection5 367
X. ‘GodKnows(GoFigure)’ 369
1. Introduction 369
2. Theprimaryargumentfromtheimpossibilityofasetof
thereflectivepartsofanomniscient’sknowledge 370
3. ‘Totalities’ 374
4. Theargumenttrimmed 374
5. Subtotalities,mappings,morethan,andCantorfor
totalities 375
6. Onkindsofmultiplicities 378
7. Takingthemeasureofthesechallengestoomniscience 380
8. Alltruthsandpossibilitiesforomniscience 382
9. Divineknowledge,aguardedrecommendation 386
10. Takingstock,tomoveon 388
11. Grim’sradicalargumentagainstomniscience 389
12. Conclusions 391
Appendix.NotesonCantoriansettheory 394
A1.Powersets 394
A2.Cardinalities 394
A3.Cantor’sTheorem 395
A4.Cardinalitiesofpowersets 397
arguments against the existence of god
XI. Atheologies,DemonstrativeandEvidential 401
1. ‘Thatthat’ssawceforagooseissawceforagander’ 401
2. Ambitiousatheisticdemonstrations 403
3. Modestatheisticdemonstrations 404
4. Hume’sargumentinPart11oftheDialogues 405
5. TheevidentialargumentfromevilofRowe(1986) 409
6. TheevidentialargumentsfromevilofRowe(1988)
and(1996) 413
7. ABayesianissueforevidenceofevil 427
8. Anotherskeptic 429
9. Itcanbedifferentstrokesfordifferentfolks 432
Appendix.Promisedderivations 432