Rahm Emanuel, the sharp-tongued chair of the House Democratic Caucus, said this about our soon-to-be-ex attorney general: "Alberto Gonzales is the first attorney general who thought the truth, the whole truth and nothing but the truth were three different things".
Translate Emanuel's comment into higher-order predicate calculus. What is the minimum order of predicates that you need to quantify over?
Are these three phrases actually just different names for the same thing? If not, how do you explain the (redundant?) wording of the traditional oath? If the three phrases do name different concepts, give one example of each of the three categories from Gonzales' congressional testimony.
[ Tim Finin, who should be grading the quiz, offered an answer:
Here's my attempt at the first part. I'll leave it to others to others to see if AGAG followed the traditional oath, which I'll assume is something like: "AGAG promises to tell (1) the truth, (2) the whole truth and (3) nothing but the truth."
(1) If AGAG tells P, then P is true.
All(P) tell(AGAG,P) -> P.
(2) If AGAG tells P, then P is true and there is no sentence R that is not implied by P that is true.
All(P) tell(AGAG,P) -> P ^ ~ Exists(R) R ^ ~(P->R)
(3) Same as #1: If AGAG tells P, then P is true.
All(P) tell(AGAG,P) -> P.
I am assuming what I take to be a standard interpretation of what it means to "tell the truth", i.e., to make statements that are true and not to make any statements that are not true. Of course, the standard interpretation probably also involves saying things that you 'know' to be true, but I don't want to go there tonight.
So Tim thinks that the three phrases are only partly redundant, since the first and the third mean the same thing.
That's what I thought, too -- at first. But after a bit more thinking, I decided that it's not so clear. After all, if I promise to eat the pie, the whole pie, and nothing but the pie, all three clauses seem to be independent. ]
[Simon Cauchi brings a different semantic tradition to bear, according to which telling the truth is indeed like eating the pie:
"The truth" means just that. It's not qualified in any way.
"The whole truth" expressly disavows suppressio veri.
"Nothing but the truth" expressly disavows suggestio falsi.
[Barbara Partee comments:
Only time for a quick response: I think the best way to see them all as non-redundant (and to make the "whole truth" one fulfillable!) is to think of them all in the context of answering questions.
That limits the domain of potentially relevant propositions -- I'm not taking time to work this out carefully -- we're about to leave for a few days getaway -- but it narrows down the first one so that it's not about everything you say but about giving a true answer to the question. And 'whole truth' doesn't then mean that you have to give an answer that specifies all the true propositions about the whole actual world (which Tim's requires), but just a complete answer rather than a partial answer. And then the 'nothing but' is also no longer redundant, I guess, because it means you don't add on anything false.
Wait, or does it mean that you don't add anything irrelevant? You don't add anything that isn't implied by a complete true answer to the given question? Hmm, nothing irrelevant or just nothing that's both irrelevant and false? (A clever answerer can still make hay with implicatures -- I don't think the rule says anything about not implicating anything false, only about not actually saying anything false.)
[Rory Turnbull writes:
After reading your Language Log post on the semantics of "the truth, the whole truth, and nothing but the truth", it struck me that it's really just an oath to obey Gricean conversational maxims.
The truth - maxim of quality
The whole truth - maxim of quantity
Nothing but the truth - maxim of relation
]Posted by Mark Liberman at August 28, 2007 08:39 PM