The Protagoras Problem.

I have been recently going over a classic philosophical paradox, and I believe I might have solved it. I am not sure how sound my logic is thus far, but if you agree or disagree with me please comment on this post.

The paradox:

“Euathlos has learned from Protagoras how to be a lawyer, under a very generous arrangement whereby he doesn’t need to pay anything for his tuition until and unless he wins his first court case. Rather to Protagoras’ annoyance, however, after
giving up hours of his time training Euathlos, the pupil decides to become a musician and never takes any court cases. Protagoras demands that Euathlos pay him for his trouble and, when the musician refuses, decides to sue him in court.
Protagoras reasons that if Euathlos loses the case, he, Protagoras, will have won, in which case he will get his money back, and, furthermore, that even if he loses, Euathlos will then have won a case, despite his protestations about being a
musician now, and will therefore still have to pay up. Euathlos reasons a little differently however. If I lose, he thinks, then I will have lost my first court case, in which event, the original agreement releases me from having to pay any tuition fees. And, even if he wins, Protagoras will still have lost the right to enforce the contract, so he will not need to pay anything.

They can’t both be right. So who’s making the mistake?”

(p. 4, ‘101 Philosophy Problems’. Cohen, Martin 2001)
My solution. Euthalos owes Protagoras. If we look at Protagoras’ court demands they appear sound. If Euthalos loses, then Protagoras reaps the court benefits. If Euthalos wins, he must honour the agreement with Protagoras (A little more difficult to justify).


Euthalos’ reasoning doesn’t hold. He believes that if he loses he will have lost his first court case. While this appears to be true on the surface, it appears we run into a fallacy of what is called a ‘definitional retreat’. “This occurs when someone changes the meaning of the words in order to deal with an objection raised against the original wording” (p46 ‘How to win every argument’, Pirie, Madsen 2006). So what we see is a confusion upon the word ‘first’. In the agreement between Protagoras and Euthalos it is understood that Euthalos pays nothing until he wins his first court case. Does ‘first’ here mean the first instance of winning in any sequence of cases, or does it mean the first case in his sequence of court cases? We don’t know due to a lack of information which were stated between both parties. However, an everyday example may shed some more light on the issue of why I think Euthalos needs to pay up. Perhaps I begin watching the opening game of my favourite baseball team. Unfortunately they lose this game, and to my dismay they lose the next four games in a terrible losing streak.  I travel to the stadium to show my support for game six. Amazinly my team wins. The front page of the newspaper the following day reads ‘The Detroit Tigers win their first game after a five game losing streak’.

We know that this was the Tiger’s sixth game in the sequence of the games they have played. It was their first instance of winning. To compare this to the Protagoras problem, we see a similar issue. If Euthalos loses his first court case, he will have only lost his first in the case of sequence. This does nothing to remove the burden of winning his first court case, for this would be his first instance of winning.

Another question we must ask is whether the contract changes after the verdict of the court case? If it  does, then if Euthalos wins against Protagoras, either the contract is  meaningless or he must honour some new guidelines set forth by the  judge. If Protagoras wins, then we must ask if the contract is  unchanged or if Euthalos must pay an amount now. Protagoras’ win does not guaruntee an immediate payment. So we can observe that this  argument has two important qualifications. First, what is implied in the agreement between Protagoras and Euthalos when we use the word  ‘first’. Do we mean here the first in a succession of first, second, third; or, do we instead mean ‘first’ as an instance or occurence or a quality, regardless of sequence. We have seen this in our baseball example. Once this beginning qualification has been made in the court case, it is necessary to focus on the change in the contract terms. It is
from this qualification that we can move from the original agreement to and honourable resolution to this much contested paradox.

Published in: Uncategorized on July 31, 2010 at 9:37 am  Leave a Comment  

The URI to TrackBack this entry is:

RSS feed for comments on this post.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: