[30 March 2009]
For some reason, lately I’ve found an old remark of Allen Renear’s running through my head.
“We can disagree about many things; but can we disagree about everything?
“Or would that be like positing the existence of an airline so small, it has no nonstop flights?”
[Memory tells me that he said this at a meeting of the Society for Textual Scholarship; Google, aided by Robin Cover’s Cover Pages, tells me that it was in April 1995.]
It’s on my mind, perhaps, because with Claus Huitfeldt and Yves Marcoux I’ve been doing some work on a formal model of transcription, and when we have examined how multiple divergent transcriptions of the same exemplar look in our model, it has proven much harder than I would have thought possible to make the transcriptions actually contradict one another. (More on this in another post, perhaps.)
I suppose it depends on what “flight” means.
From the customer’s point of view, a nonstop flight is one that makes no stops between the customer’s origin and the customer’s destination. But to the airline, a nonstop flight is one that comes into revenue service at one point, flies directly to another point without landing at any intermediate points, and goes out of service (perhaps only briefly while it is cleaned before being reloaded).
In the first sense, airlines must have nonstop flights. In the second sense, you could imagine an airline all of whose flights are puddle-jumpers from Eenie to Meenie to Minie to Mo and then out of service before returning the same way to Eenie.
Ray Smullyan’s knights (who only speak truths) and knaves (who only speak falsehoods) do disagree on all points, at least if you take “disagree” to refer to verbal expressions rather than beliefs. A simple knight-knave puzzle: you are looking for John on Knight-Knave Island, but you can’t tell the knights from the knaves. What 3-word question can you ask an inhabitant to find out if he is John or not?
John,
I suppose it may depends on what one means by “disagree”.
If you assert the sentence “Socrates is mortal,” I can disagree by saying “No, Socrates is not mortal.” But both of these sentences entail the existence of Socrates; we cannot disagree about his mortality without agreeing that “Socrates” names an individual and that it’s meaningful to postulate or to deny the mortality of that individual.
If you assert, on the other hand, the sentence “Socrates is divisible by three”, I am disinclined to deny it by saying “No, Socrates is not divisible by three”. I am more apt to say that the sentence you have affirmed is guilty of a category error (or else assigns a meaning to some of its terms unfamilar to me). But in that case, I am disagreeing with the conversational implicature of your statement, namely with the implicit claim that the sentence “Socrates is divisible by three” can be asserted meaningfully. I don’t, however, seem to be disagreeing with the claim that Socrates is divisible by three; I don’t know how to do that, because I can assign no meaning to it.
I suppose it boils down to this: I expect two people to disagree by assigning different truth values to the same sentence; if one assigns no truth value to the sentence, it’s not clear to me that they are disagreeing, or at least not clear that they are disagreeing about the proposition (if any) uttered by the sentence.
Q. Why did the chicken cross the road?
A. Two: one to hold the giraffe, and one to fill the bathtub with brightly-colored machine tools.