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Abbott and Costello meet Wittgenstein
Tim Madigan on some philosophical comedians.
“A mathematician is bound to be horrified by my mathematical comments, since he has always been trained to avoid indulging in thoughts and doubts of the kinds I develop.”
Ludwig Wittgenstein, Philosophical Grammar
The philosopher Saul Kripke, in his book Wittgenstein on Rules and Private Language, discusses what he calls “The Wittgensteinian Paradox.” A skeptic doggedly proclaims that 68 plus 57 equals not, as one might expect, 125, but 5. The skeptic has a ready answer for every dissent: what we think of as a ‘plus’ sign is really a ‘quus’ sign, to ‘count’ is really to ‘quount’ and ‘independence’ is really ‘quindependence’, at least until we reach the computation 68 + 57, wherein the old rules fail to apply. We blindly apply rules of addition without understanding the nature of those facts, and so cannot say that the answer ‘5’ is wrong without first appealing to a rule which is disputable. No amount of arguing will convince the skeptic otherwise.
While reading this particular passage, I was reminded of a similar case, wherein a man insists against the face of all opposing evidence that 13 x 7 = 28. The man in question, or more precisely the character he plays (named Pomeroy) is Lou Costello, member of the famous American comedy team Abbott and Costello. This particular routine occurs in their film In the Navy. Pomeroy, the ship’s cook, maintains to his sailor friends that all seven officers on board will get thirteen doughnuts apiece. His friends, seeing that there are exactly 28 doughnuts left (Pomeroy having eaten the rest), demur. The officers will get 4 doughnuts each, not 13. Pomeroy then goes into a convoluted explication as to why this is not so.
The major similarity between Kripke’s skeptic and Pomeroy is their versatility in rebutting all objections to the unorthodox sums they reach. In his computation, Pomeroy refuses to accept the given answer which everyone ‘knows’ to be true, namely 13 x 7 = 91, not 28. But Pomeroy goes even further than Kripke’s apocryphal skeptic does. He actually proves (to himself at least) that 28 is the correct answer, and does so by the use of addition, division and multiplication. Of course, his use of these functions differs greatly from that of everyone else around him, yet on his own terms he is quite convincing. He applies his own rules to the computation, and each time arrives at an answer satisfactory to him. If we follow Pomeroy’s rules of mathematics, then we must admit that 13 x 7 = 28. Pomeroy could easily claim that all the old rules of mathematics hold true until we reach the equation 13 x 7, in which case his rules take over.
However, the true test here is not so much a mathematical one as a practical one – the seven officers in question will not get thirteen doughnuts apiece no matter how inviolable Pomeroy’s arguments might be, unless he means by ‘thirteen’ what everyone else means by ‘four’. But, as Charles Peirce (a member of the famous comedy act Peirce and James) might say, what practical effect does this seeming difference in meaning have? Clearly none, since the officers will have the same number of doughnuts to eat, whether they choose to call them ‘four’ or ‘thirteen’ or ‘quour’ or ‘quirteen.’ The difference has no practical bearing, aside from the likelihood of Pomeroy’s being sent to the brig for pilfering.
The coupling of Abbott and Costello’s name with that of Wittgenstein is not as fanciful as it might first appear. Both the comedians and the philosopher were interested in the uses and abuses of language. Wittgenstein wrote: “the task of philosophy is not to create a new, ideal language, but to clarify the use of our language … its aim is to remove particular misunderstandings …” (‘Wittgenstein on the Nature of Philosophy’, in Wittgenstein and His Times, ed. Brian McGuinness, Blackwell, 1982, p.9). Abbott and Costello, famous for their verbal trickery and semantic manipulations, took advantage of such grammatical confusions for comic effect.
Kripke makes a further relevant point.
The fact is that, extreme cases of uneducability or insanity aside, almost all of us, after sufficient training, respond with roughly the same procedures to concrete addition problems. We respond unhesitatingly to such problems as “68 + 57”, regarding our procedure as the only comprehensible one, and we agree in the unhesitating responses we make. On Wittgenstein’s conception, such agreement is essential for our game of ascribing rules and concepts to each other. (Kripke, p.96)
This is what makes the comedy routine in question so amusing. Pomeroy is not playing the exact same language game as everyone else. Or perhaps it is better to say that he is playing a confused variation on the game. We know that, regardless of his ingenuity, there will not be thirteen doughnuts for every officer. “Beings who agreed in consistently giving bizarre quus-like responses would share in another form of life”, Kripke writes (ibid.) Such bizarreness is the basis for Abbott and Costello’s work. The main difference is that whereas Kripke and Wittgenstein can only stare at the skeptic uncomprehendingly, Abbott performs an act of closure – he slaps Costello hard across the face, and thereby brings the latter back into contact with the real world. Would that philosophical disputations could be solved so easily!
© Dr Timothy J. Madigan