This Sentence is False: An Introduction to Philosophical Paradoxes

232 Pages·2009·1.32 MB·English

by  Peter Cave

This Sentence is False
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This Sentence is False
An introduction to
philosophical paradoxes
Peter Cave
Continuum
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©PeterCave2009
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Contents
Preface vii
Acknowledgements xi
1 Welcometotherationalirrational–howtowin,
howtostarve,andhowtopumpmoney 1
2 Toocleverbyone-half–or,atleast,one-eighth 18
3 Lather,rinse,repeat–‘repeat’didyousay? 34
4 Infinity:withoutend,withoutbeginning–yetwith
aflea,aflyandabandit 52
5 Heapsandhaze,coloursandclocks–and1,001cats 70
6 Ravens,lotteries,medicalmatters–andagruesometale
ortwo 91
7 Moralityandpolitics–blackmail,buck-passingand
voting 108
8 EncounterswithGod–andhismysteriousways 129
9 Encounterswithourmysteriousways–love,luckandlife 147
10 Whentostop 168
Appendix1:Furtherreading 193
Appendix2:Notes,sourcesandreferences 195
Appendix3:Paradoxespurveyed 202
Bibliography 205
GeneralIndex 211
ForAngelaJoyHarvey,
BlueS.,SilverS.,andparadoxicalliveseverywhere,
withinandwithout.
Preface
Letusbehuman.
WhenfirsttoldthattheEarthbothspinsandorbitstheSun,wemay
find it paradoxical. After all, it looks as if just the Sun does the
moving.Whenwelaterreflectthatthingswouldlookexactlyasthey
do,withtheEarthorbitingasparadoxicallyclaimed,wemaystillfind
its movement surprising, for we feel neither rushes of air nor sen-
sations of dizziness – nor, for that matter, do we get anywhere. If
governments tell us, ‘Don’t panic’, paradoxically we may feel well
justifiedinpanic;and,onthosefewoccasionswhenahusbandbrings
his wife chocolates and roses wrapped with loving smiles, paradox-
icallyshemayquestionbothhusbandandwrapping.
The above are not philosophical but everyday cases of paradox.
They are simply instances of what at first seems unlikely, surprising
or casually incongruous. Indeed, in 1616 a certain John Bullokar
offeredasparadoxtheaffirmationthat‘theearthdothmooueround,
and the heauens stand still’.Today most people accept that the evi-
dence is in: the Earth both spins and orbits. Most of us recognize
that, human that we are, the ‘Don’t panic’ injunctions may suggest
events over which to panic – and when guilty behaviour is sensed,
sensed because of chocolates and roses, the gifts paradoxically may
stillpromotepeace.
Incontrasttosuchexplicablesurprises,theparadoxesofthisbook
arenearlyallphilosophical–oftenwithcontinuingdebateoverreso-
lution.Manyareclassical;mostarewellknowntothephilosophical
community, though a small number feature the author’s own spin.
Theyembraceallthemainareasofphilosophy:frommetaphysics–
thatis,understandingtheworld’snatureinmostgeneralterms–to
vii
viii Preface
reasoningandknowledge,tovalueswithinmoralityandmorewidely.
Indeed, paradoxes, generously understood and unlimited to the
logical, offer excellent pathways into the philosophical activity.
This is not surprising: key philosophical problems can be readily
seenasparadoxicalorpuzzling.
Iusetheterms‘paradox’and‘puzzle’moreorlessinterchangeably,
butwhenlabellingIreserve‘paradox’forthosetraditionallyknownas
such,with‘puzzle’or‘problem’fortherest–thoughthisisfarfrom
definitive.To provide foci for discussion, some paradoxes are high-
lighted in the text – and, when not too aberrant, I have resisted
addingtheword‘paradox’toeachname.
Withmanyoftheparadoxes,full-lengthbookscouldbewritten–
and they have. While this book covers many, many paradoxes –
includingvirtuallyalltheaccessiblekeyphilosophicalparadoxes–we
journeyslowlyoversomeparadoxicalterrains,yetspeedacrossothers
withlittlemorethanglimpses.
Philosophical paradoxes fill this book, save that the last few
thoughts of Chapters 1 and 6 outline a few probability ‘paradoxes’.
They are included because we are often surprised by probability
assessments, treating them as paradoxical. Humans typically reach
mistakenconclusionsaboutwhatismore,orless,probable;yethere,
once the mathematics is understood, there usually remains no dis-
pute.Partlybecausecontroversydoesnotrageforthoseintheprob-
abilityknow–andtheydonotimmediatelygeneratemorepuzzles–
I do not view them as philosophical, hence their relegation to little
morethanasides.
Thisisanintroductoryworkwith,Ihope,lightnessoftouch,but
also with notes to guide further and deeper reading.The aim is to
encouragereflectionabouttheparadoxesandwhatliesbehind.
The book is loosely arranged by means of types of underlying
probleminthefirstsixchapters,withthesubsequentthreechapters
orientatedtomorality,Godandtheselfrespectively.Thelastchapter
brings together some themes, while adding further thoughts and
paradoxes.Inphilosophytherearenosharpboundaries–‘allthings
conspire’ is the ancient saw – so there is some arbitrariness in the
groupings.Thereisaninterweavingofconcerns:laterchapterssome-
Preface ix
times loop round to problems of the earlier, and the last chapter
explicitly does this.The endnotes cover more than references; they
engageinalittlegossipandafewadditionalparadoxes.
Althoughthebookistentativeabouttheresolutionofsomepara-
doxes, with regard to others I quote the splendid and well-rounded
JohnMaynardKeynes:‘...theauthormust,ifheistoputhispoint
ofviewclearly,pretendsometimestoalittlemoreconvictionthanhe
feels’.
To the extent that there is a theme for paradoxical resolution in
thiswork,itisthedictum,‘Letusbehuman’–adictum,inoneway
or another, found in philosophers as diverse as Spinoza, Hume,
KierkegaardandWittgenstein.Weoftenforgetlife’sdifferentcolours
and shades of grey, mistakenly seeking the black and white, the
Yes/Noanswers.Weoftenforgetthat,whenapplyingabstractreason-
ingandconceptstotheworld,restraintisrequired.
We live, argue and reason on Earth, not in abstract heavens.
Philosophycanofferreminders.