The Student's Paradox

The Student’s Paradox

1. If you know a subject (S), then you waste your time going to a teacher of S in order to learn S from her. [p(remise)]
2. You shouldn't waste your time (i.e. do less valuable things when you could be doing more valuable things). [p]
3. Therefore, if you know S, you shouldn't go to a teacher of S. [1,2]
4. If you don't know S, then you take an unreasonable risk (of acquiring false beliefs) in going to a "teacher" of S in order to learn S from her. [p]
5. You shouldn't take unreasonable risks. [p]
6. Therefore, if you don't know S, you shouldn't go to a teacher of S.
7. But there are only two possibilities: you either know S or you don't know S. [p]
8. Therefore, either way, you should never go to a teacher of any subject. [3,6,7]

This paradox is an old favorite of mine since it proves why one should never attend class. It was part of the first lesson of my ancient philosophy course. Fortunately for my professor everyone still attended pretty regularly for the rest of the semester so he still gets paid. This paradox works well enough that my entire philosophy class failed to refute it and we moved on to other things later in the week. For my part, I haven’t really tried since I was amused the entire time watching my professor argue with his students about why they shouldn’t attend his class. So I think I’ll take up refuting this paradox now. 1, 2, and 3, are all fairly reasonable arguments since if you know something you’d be wasting your time going to a teacher to learn it. The key to the paradox is in part 4 where learning from a teacher is put forth as an unreasonable risk of being taught something which is false. If risking learning a false belief is unreasonable then the paradox is true. If the risk, however, is reasonable then it fails to be a paradox. The problem for the student is that in going to a teacher to learn a subject, he places himself at risk of learning false information. The student has no way of judging the validity of any information from the teacher because he has no prior reference from which to judge the truth of the information. It seems to me that in order to be taking an unreasonable risk the student would have to be learning from an individual who has shown no prior indications of trustworthiness, or worse, indications of being untrustworthy. The student could judge whether or not to believe what the teacher tells him based upon what the teacher tells him about what he already knows to be truth. A teacher who is in agreement with the student about what the student already knows to be truth is thereby trustworthy and learning from him/her is not an unreasonable risk. Another method might be to compare the instruction of several scholars who claim to know the truth. If they agree then they are either all right or all wrong but one has a 50/50 chance to learn true beliefs from them. This is better odds than visiting a casino (unless you are betting on black or red at the roulette table or card counting at Blackjack) so I wouldn’t consider it an unreasonable risk to learn something from a teacher when all teachers are in agreement. In the case where teachers do not agree on the truth then the safe bet is to bet against all of them that they are all wrong and to not learn from any of them. There can be only one truth but there may be many falsehoods. Out of 30 different answers from 30 different scholars only one may be right i.e. 1/30 chance of picking the right one to learn from. This leaves 29/30 false beliefs one could acquire. Trying to find the one true belief out of 30 scholars is an impossibility with no prior knowledge of the subject. This leaves us with what we do know for certain and that is 29/30 have to be wrong. Also, it is a possibility that even 30/30 could be wrong since we have no way to judge the validity of the 30 different truths. I think this satisfactorily demonstrates the difference between unreasonable risk and reasonable risk. While writing this I’ve thought about its application to religion. It could be said that it is entirely unreasonable to believe in any religion because there are many, many different religions each with its own truth. The person trying to decide which religion to believe in has no prior knowledge of the truth of any of them. This is why in order to believe in a religion one is said to have faith. To a mathematician this mean, you are taking your chances. By my calculations those are probably something like 1?/2600 the question mark meaning that with no prior knowledge to judge even the one religion that is supposedly right could really be wrong. So lets make it something like 0/2601. That is as good as saying the truth, if such a thing even exists, hasn’t been found yet. Which makes the agnostics right, so far. Good luck, in your own searches for truth. Until next post, keep thinking on this.