Paradox

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T W E N T Y - T H R E EWittgenstein andthe Depth of aGrammatical JokeThe problems arising through a misinterpretation of ourforms of language have the character of depth. They aredeep disquietudes; their roots are as deep in us as the formsof our language and their significance is as great as theimportance of our language.—Let us ask ourselves: whydo we feel a grammatical joke to be deep? (And that iswhat the depth of philosophy is.)(Wittgenstein 1958, 111)The logician and mathematician, Reverend Charles Dodgson,better known by his pseudonym, Lewis Carroll, is famousfor his linguistic humor. In Alice’s Adventures in Wonderland,the Duck inquires in vain for the referent of “it” in theMouse’s lecture: “Stigand, the patriotic archbishop of Canter-
334 A BRIEF HISTORY OF THE PARADOXbury, found it advisable . . . to go with Edgar Atheling. . . . ”The Duck assumes the “it” should be something particularsuch as a frog or a worm. But the Mouse is using “it” as adummy pronoun; it is inserted to appease a grammaticalhunger for an object term. If David Hume is correct, Descartesmay be like the Duck when searching for the referentof “I” in “I think, therefore, I exist.”Dodgson’s whimsy carried over to his recreationalmathematics. Interestingly, he believed these riddles couldserve the serious purpose of spiritual protection. In hisintroduction to Pillow Problems, he writes, “There aresceptical thoughts, which seem for the moment to uprootthe firmest faith: there are blasphemous thoughts, whichdart unbidden into the most reverent souls; there are unholythoughts, which torture, with their hateful presence, thefancy that would fain be pure. Against all these real mentalwork is a most helpful ally.” The puzzles should be challengingbut not too difficult. Veterans of sensory deprivationchambers recommend that you pass the time by posingintellectual challenges: reciting the alphabet backwards,listing all the prime numbers less than a hundred, etc. Theycaution that the problem must be definitely soluble. If youhave the misfortune of picking a question that you cannotanswer, you will not be able to switch the topic. You willcome to hate the question but will not be able to stopthinking about it.<strong>Paradox</strong>es parasitized the attention of Bertrand Russell’sprotégé, Ludwig Wittgenstein. Wittgenstein (1889-1951)was repulsed by philosophers who had actually grown fondof the Eternal Questions. He philosophizes only in the hopeof ending his compulsion to answer.
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A BRIEF HISTORYof theParadox
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A BRIEF HISTORYof theParadoxPHILOSO
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Tothose who neverhave a book dedica
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ContentsList of FiguresPrefaceixxiO
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List of Figures1.1 Canadian flag 71
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PrefaceMathematicians characterize
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PREFACExiiiHegel, Marx, and nowaday
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PREFACExvpermission to quote “Ant
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A BRIEF HISTORYof theParadox
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O N EAnaximander and theRiddle of O
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ANAXIMANDER AND THE RIDDLE OF ORIGI
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T W OPythagoras’s Searchfor the C
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PYTHAGORAS’S SEARCH FOR THE COMMO
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PARMENIDES ON WHAT IS NOT 29city th
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PARMENIDES ON WHAT IS NOT 31incredu
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PARMENIDES ON WHAT IS NOT 33differe
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PARMENIDES ON WHAT IS NOT 35Odysseu
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PARMENIDES ON WHAT IS NOT 37“Nobo
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PARMENIDES ON WHAT IS NOT 39tendenc
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PARMENIDES ON WHAT IS NOT 41Clinton
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PARMENIDES ON WHAT IS NOT 43cal abs
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SISYPHUS’S ROCK AND ZENO’S PARA
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SOCRATES: THE PARADOX OF INQUIRY 59
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S I XThe MegarianIdentity CrisisEuc
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THE MEGARIAN IDENTITY CRISIS 73Plat
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THE MEGARIAN IDENTITY CRISIS 75to l
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THE MEGARIAN IDENTITY CRISIS 77soul
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THE MEGARIAN IDENTITY CRISIS 79lear
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THE MEGARIAN IDENTITY CRISIS 81A =
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S E V E NEubulides and thePolitics
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EUBULIDES AND THE POLITICS OF THE L
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A FOOTNOTE TO “PLATO” 101becaus
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A FOOTNOTE TO “PLATO” 103human
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A FOOTNOTE TO “PLATO” 105tion o
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A FOOTNOTE TO “PLATO” 107Jumble
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A FOOTNOTE TO “PLATO” 109in the
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A FOOTNOTE TO “PLATO” 111refute
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A FOOTNOTE TO “PLATO” 113Graham
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A FOOTNOTE TO “PLATO” 115to me
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ARISTOTLE ON FATALISM 117Fig. 9.1pa
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ARISTOTLE ON FATALISM 119shooting u
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ARISTOTLE ON FATALISM 1214. Therefo
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ARISTOTLE ON FATALISM 123the Megari
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ARISTOTLE ON FATALISM 125Socrates w
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ARISTOTLE ON FATALISM 127not have r
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ARISTOTLE ON FATALISM 129THE MORAL
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CHRYSIPPUS ON PEOPLE PARTS 131Fig.
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CHRYSIPPUS ON PEOPLE PARTS 133The h
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CHRYSIPPUS ON PEOPLE PARTS 135creat
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CHRYSIPPUS ON PEOPLE PARTS 137belon
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CHRYSIPPUS ON PEOPLE PARTS 139claim
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CHRYSIPPUS ON PEOPLE PARTS 141insta
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CHRYSIPPUS ON PEOPLE PARTS 143The s
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CHRYSIPPUS ON PEOPLE PARTS 145reass
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CHRYSIPPUS ON PEOPLE PARTS 147In Na
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SEXTUS EMPIRICUS AND THE INFINITE R
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AUGUSTINE’S PRAGMATIC PARADOXES 1
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T H I R T E E NAquinas: Can God Hav
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AQUINAS: CAN GOD HAVE A BIOGRAPHY?
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F O U R T E E NOckham andthe Insolu
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OCKHAM AND THE INSOLUBILIA 189merel
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OCKHAM AND THE INSOLUBILIA 191WHAT
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OCKHAM AND THE INSOLUBILIA 193Suppo
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OCKHAM AND THE INSOLUBILIA 195was l
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OCKHAM AND THE INSOLUBILIA 197With
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OCKHAM AND THE INSOLUBILIA 199of th
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BURIDAN’S SOPHISMS 201Buridan ban
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BURIDAN’S SOPHISMS 203recover the
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BURIDAN’S SOPHISMS 205respondent
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BURIDAN’S SOPHISMS 207BURIDAN’S
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BURIDAN’S SOPHISMS 209shows that
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BURIDAN’S SOPHISMS 211invalid bec
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BURIDAN’S SOPHISMS 213ers turned
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BURIDAN’S SOPHISMS 215The circumn
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PASCAL’S IMPROBABLE CALCULATIONS
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S E V E N T E E NLeibniz’s Princi
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LEIBNIZ’S PRINCIPLE OF SUFFICIENT
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HUME’S ALL-CONSUMING IDEAS 253Hum
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HUME’S ALL-CONSUMING IDEAS 255bel
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HUME’S ALL-CONSUMING IDEAS 257gen
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HUME’S ALL-CONSUMING IDEAS 259Loc
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HUME’S ALL-CONSUMING IDEAS 261Whe
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HUME’S ALL-CONSUMING IDEAS 263HUM
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HUME’S ALL-CONSUMING IDEAS 265was
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HUME’S ALL-CONSUMING IDEAS 267sta
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THE COMMON SENSE OF THOMAS REID 269
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Page 302 and 303: THE COMMON SENSE OF THOMAS REID 283
Page 304 and 305: KANT AND THE ANTINOMY OF PURE REASO
Page 322 and 323: T W E N T Y - O N EHegel’s World
Page 324 and 325: HEGEL’S WORLD OF CONTRADICTIONS 3
Page 336 and 337: RUSSELL’S SET 317THE HEGELIAN HUN
Page 338 and 339: RUSSELL’S SET 319Georg Cantor was
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Page 342 and 343: RUSSELL’S SET 323Fig. 22.2to have
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Page 348 and 349: RUSSELL’S SET 329Whitehead congra
Page 350 and 351: RUSSELL’S SET 331hires a secretar
Page 354 and 355: WITTGENSTEIN AND THE DEPTH OF A GRA
Page 368 and 369: T W E N T Y - F O U RQuine’s Ques
Page 370 and 371: QUINE’S QUESTION MARK 351doomsday
Page 372 and 373: QUINE’S QUESTION MARK 353concede
Page 374 and 375: QUINE’S QUESTION MARK 355rowed
Page 376 and 377: QUINE’S QUESTION MARK 357Quine sa
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Page 382 and 383: QUINE’S QUESTION MARK 363captivat
Page 384 and 385: QUINE’S QUESTION MARK 365To meet
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Page 388 and 389: QUINE’S QUESTION MARK 369GRADUALI
Page 390 and 391: QUINE’S QUESTION MARK 371definiti
Page 392 and 393: BibliographyAnscombe, G. E. M. (195
Page 394 and 395: BIBLIOGRAPHY 375Hegel, G. W. F. (18
Page 396 and 397: BIBLIOGRAPHY 377Miller, J. (1998).
Page 398 and 399: BIBLIOGRAPHY 379Skyrms, Brian (1975
Page 400 and 401: IndexNote: Page numbers in bold ref
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INDEX 383Carneades, 152Carroll, Lew
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INDEX 385ethics: of Aristotle, 97-9
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INDEX 387Jaynes, E. T., 250John XXI
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INDEX 389money and law of diminishi
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INDEX 391Poincaré, Henri, 325polit
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INDEX 393Socrates, 58-70; Augustine
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