Ex fele quodlibet
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In today's Get Fuzzy, we learn about Bucky Katt's extension of the Principle of Explosion to the semantics of questions:
Ludwig Wittgenstein discussed a related case in his Lectures on the Foundations of Mathematics, and comes up with more or less the same answer that Rob does.
Wittgenstein and Alan Turing are said to have had an informal debate on the logic of contradiction in 1939. I have the impression that Wittgenstein thought he won the debate, and others have taken the same view, including Deirdre McCloskey, whose use of Hodges' description I've linked to. But Turing arguably had the last laugh, by using a form of reductio arguments as a key step in breaking the German enigma code, which resulted directly in sinking submarines if not in bringing down bridges.
Dan T. said,
June 18, 2009 @ 2:14 pm
What meaning is ultimately derived, if any, depends on what error-correction protocols are applied to the original statement, which is lexically and grammatically deficient.
Starting statement: "How duz your munky checkbook!"
Applying spelling correction: "How does your monkey checkbook!"
Re-punctuating as apparent question: "How does your monkey checkbook?"
Now you still have a grammatical problem in that the phrase expects a verb at the end but finds a noun. You can either suppose there to be a verb "checkbook" and try to surmise its meaning from the related noun (it could mean "maintains a checkbook", and refer to a query about how the monkey keeps his checking account balanced), or correct it to a multi-word phrase "check book", then insert an article to get "check the book", resulting in: "How does your monkey check the book?", which could be meaningful if the monkey has a job involving examining books of some sort (accounting or library).
Chris said,
June 18, 2009 @ 2:16 pm
Interesting! Does anyone know if there exist more complete accounts of this debate?
[(myl) I believe that the most complete account is here ]
mgh said,
June 18, 2009 @ 2:21 pm
Dan T, re: spelling correction, my iPhone corrects the phrase to "how did your junky checkbook" while Microsoft Word autocorrects it to "how dust your monkey checkbook". I believe the proper correction is "Honeycomb yuck kudzu rho wok".
Greg said,
June 18, 2009 @ 2:32 pm
I'm confused: where is the contradiction in 'How duz your munky checkbook'?
[(myl) There's none, of course — just a jocular analogy between the (serious) idea that everything follows from a contradiction, and the (silly) idea that an uninterpretable question has infinite meanings. ]
Karen said,
June 18, 2009 @ 2:39 pm
Clearly, the answer is "very well, thank you" or – if you're broke and your monkey checkbook is in sad shape – "not so well, I'm sad to say."
(compare to Ophelia's question "How does your lordship for this many a day?"
Bob Moore said,
June 18, 2009 @ 4:56 pm
I think the discussion here is missing the point. The issue here is not contradiction, but underspecification of meaning. Although I am not an expert on this approach to semantics, I know that there has been a fair amount of work on underspecified meaning representations. Bucky here seems to be espousing the radical view that if a string doesn't have *any* interpretation according to a semantic theory, it is infinitely ambiguous among all possible interpretations. This reveals a level of sophistication in thinking that I had not previously suspected in a creature once described in the same strip as a practioner of "claw-based communication".
Mark Liberman said,
June 18, 2009 @ 5:05 pm
Bob Moore: Bucky here seems to be espousing the radical view that if a string doesn't have *any* interpretation according to a semantic theory, it is infinitely ambiguous among all possible interpretations.
To be fair to Bucky, he only asserts that "as it's meaning hasn't been narrowly defined, I would say it's meaning is infinite".
Under most definitions, the set of possible meanings has room for infinitely many distinct (and even non-overlapping) infinite sets.
Stephen Downes said,
June 18, 2009 @ 5:58 pm
Wittgenstein was Austrian, not German, and was in London during the war, being bombed by Nazi aircraft while he worked as a volunteer at various hospital jobs. He would have considered Turing's accomplishment not a "last laugh" but rather some very clever engineering, and certainly not any sort of refutation of his views. The code broken by Turing was not Wittgenstein's and had nothing to do with him.
[(myl) Of course, W was not only Austrian but also Jewish, so I'm sure that his sympathies for the 3rd Reich were indeed minimal. Nor has anyone ever suggested that he had any role in the origin or development of the Chiffriermaschinen Aktien-Gesellschaft. The relevance of T's cryptanalytical work to the 1939 argument has nothing to either with W's politics nor with the background of the enigma cryptosystem.
The point is, W's arguments against T were in fact basically of the form "Your concerns about contradiction are entirely abstract, and will never have any practical application, and should therefore be ignored". And as of 1939, Turing was a pure mathematician, while Wittgenstein had been trained as an engineer (including enrolling in a PhD program in mechanical engineering at Manchester), and had served in an artillery regiment during WW I, including apparently some time in an artillery workshop; and later had designed and built a house, down to the doorknobs and radiators. So W was *much* more the engineer, at that point, than T was.
And thus it's fittingly ironic that very shortly after this conversation, T and his colleagues used the logic of reductio — exactly what W argued could never have any practical consequence — as part their method for finding enigma keys. ]
Russell said,
June 18, 2009 @ 6:37 pm
Hmm…someone confronted by an incomprehensible utterance might still wish to maintain the notion that there was genuine communicative intent behind it, so then the possible meanings could indeed be quite large. The presumption is still that the speaker had a single meaning in mind, though.
Unless we can take "its meaning is infinite" to mean not "it has the potential to mean anything" (and given enough information we could figure out what this token means) but instead "it means everything (at once)."
dr pepper said,
June 18, 2009 @ 8:04 pm
"Who does your monkey checkbook?"
"My accountant, Babs Boon, of course!"
Dan T. said,
June 18, 2009 @ 10:54 pm
Perhaps a zoo with separate budgets for different sections including the one for primates would have a "monkey checkbook" after all.
peter said,
June 19, 2009 @ 4:21 am
Mark —
Your response to Stephen Downe's comment requires a response. Although Alan Turing's current reputation has him cast as an other-worldly, head-in-the-clouds mathematician, the latest historical research of his role on the Enigma project and subsequent developments in early computing indicates that he was very much an engineer getting his hands dirty with the electronics. Part of his current reputation has arisen through misinformation about his role in the Manchester computer projects after WW II spread by Tom Kilburn and his supporters, misinformation which downplayed Turing's role and contributions. Being dead, Turing was not able to defend himself against this calumny. Since most of Turing's practical work was done at the British Government's WW II code-breaking group at Bletchley Park, and thus subject to the Official Secrets Act, others who knew of Turing's deep involvement in the practical side were also unable to defend him.
The person who has done the most to uncover the historical truth is philosopher Jack Copeland, of the University of Canterbury, New Zealand. Kilburn, for instance, is on record has having said that Turing's contribution to Kilburn's work in computing was not more than 30 minutes of conversation. Yet Copeland found that Turing had given a secret course of several weeks duration on the practical aspects of computing at the National Physical Laboratory in 1947, a course which Kilburn attended. Turing had been asked to give this course by the UK Ministry of Defence, who knew very well his role in both the theoretical and the practical aspects of the computers developed at Bletchley Park.
For whatever reason, the feelings against Turing by Kilburn and his supporters ran very deep. At a conference in Manchester in 2004 commemorating the 50th anniversary of Turing's death, I witnessed Copeland's presentation supporting Turing – and Turing himself – come under vitriolic attack from several elderly members of the audience, apparently still intent on minimizing Turing's contributions to practical computing. It is perhaps relevant to note that the Computer Science department at the University of Manchester is housed in a building named after Kilburn, not after Turing.
[(myl) I apologize for any misunderstanding. I've always read the historical accounts as making it clear that at Bletchley Park, and at Manchester after the war, Turing was heavily and effectively involved in practical as well as theoretical aspects of the work. I wasn't even aware of the contrary opinions that you cite.
In the debate with Wittgenstein, at least as it has come down to us, W presents himself as the practical man, defending common sense against T's concerns for abstract consistency. So when Stephen Downes wrote in an earlier comment that "[Wittgenstein] would have considered Turing's accomplishment not a 'last laugh' but rather some very clever engineering, and certainly not any sort of refutation of his views", I felt that he had that debate exactly backwards.
The point of my original remark was that in the end, Turing won both the abstract and the concrete sides of that argument. ]
Chris said,
June 19, 2009 @ 9:25 am
For whatever reason, the feelings against Turing by Kilburn and his supporters ran very deep.
The obvious suspect would be the reason the government, notwithstanding Turing's contributions to the war effort, persecuted him and drove him to suicide: his homosexuality.
It's not hard to believe that if the government (AFAIK democratic) was taking such actions against homosexuals, then a considerable number of private individuals must have been hostile to them too.
peter said,
June 19, 2009 @ 10:27 am
Chris — Do you know of conclusive evidence that Turing committed suicide? He died from eating a poisoned apple. But he ate an apple everyday, so anyone wishing to kill him would have had an easy way of arranging it. From what I can tell, the jury is still out on the cause of Turing's death.
Peter Gerdes said,
June 20, 2009 @ 10:25 am
IMO Wittgenstein got owned in that argument. Turing (from the brief snippet I read) didn't explain his point of view very clearly but he's clearly got the better of the argument.
Wittgenstein is just vacillating on the reasoning system being used. If indeed, as Wittgenstein asserts, we are unwilling to apply the results we derive from a contradictory system to yield problematic results (falling bridges etc..) that only shows we weren't really using that logical system. Instead we must have been making use of a more complicated rule of inference that takes formal contradictions in simpler system in stride (no contradiction in the logic we are truly using). If I was indeed truly working in the inconsistent logic itself as my ultimate means of reasoning I would have no choice but to accept every conclusion of that system since I would have no alternative means of reasoning underneath the contradictory one.
Of course Wittgenstein could be more reasonably interpreted as suggesting that, while actually truly accepting contradiction would be problematic, the mathematicians shouldn't be so worried about seeing that as a formal result when they play their symbol games. But no mathematician would suggest it's invalid to study the behavior of arbitrary symbol manipulation games. But as this is now a purely pragmatic point (both can be viewed as mathematical objects of study) this question just comes down to which gives the more productive setting for mathematics and contradiction free first order logic has won this fight handily.