—

“Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are ‘da’ and ‘ja’, in some order. You do not know which word means which.”

Here’s a few clarifications about the puzzle.

1. It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).

2. What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)

3. Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.

4. Random will answer ‘da’ or ‘ja’ when asked any yes-no question.

—

The first approach I took here was to find a god that I could be certain is not Random which would make that god either True or False.  This is quite difficult though because you do not know what ‘da’ or ‘ja’ means.  All you know is that each of them either means yes or no.

To get to the appropriate answer then, I thought about forming the question using logical connectives such as:

“Does ja mean no if and only if you are true if and only if B is random?” (p ≡ q ≡ r)

p = ja means no

q = you (the god) is true

r = B is random

As you can see from above I used a biconditional to construct my question.  A logical biconditional is a logical operator that connects two statements to assert the statement p if and only if q (or p ≡ q).  The different between a biconditional and a material conditional (if-then statements) is only seen when the hypothesis (p) is false and the consequent (q) is true.  In the case of the material condition that statement is true, but in the biconditional that result is false.  Here is a truth table to show this:

.

.

.

You could actually formulate many different questions to found out which god is for certain not random.  The similarity between all these different questions that involve biconditionals is that there are three statements being made and we are asking if an odd number of the following statements are true.

This approach can be a bit difficult if someone doesn’t have a background in basic formal logic.  Another way to solve the puzzle is by using counterfactuals.  A counterfactual is a “if-then” statement that indicated what would be the case if its antecedent were true.  If you are using counterfactuals, the goal is to formulate a yes/no question (Q) for either True or False that asks the following: If I asked you Q, would you say ‘ja’?

By doing so, you get an answer to the question that results in the answer ‘ja’ if the truthful answer to Q is yes, and ‘da’ if the truthful answer to Q is no.

You might be asking, “Why can we assume that the answer would be ‘ja’ if the truthful answer to Q is yes and ‘da’ if the truthful answer to Q is no?”  The simple is that this question covers every situation possible and leaves no unanswered questions in figuring out which god is True, False, and Random.  There are eight possible situations within two different circumstances in this puzzle and this question covers all of them.  Let’s look at them.

Let’s assume the answer ‘ja’ means yes and ‘da’ means no.

1. True is asked Q and answers with ‘ja’.  Since she can only tell the truth, the truthful answer to Q is ‘ja’ which means yes.
2. True is asked Q and answers with ‘da’.  Since she can only tell the truth, the truthful answer to Q is ‘da’ which means no.
3. False is asked Q and answers with ‘ja’. Since she can only tell lies, it follows that if you asked her Q she would instead answer ‘da’.  Because she’s lying, the truthful answer to Q is ‘ja’ which means yes.
4. False is asked Q and answers with ‘da’. Since she can only tell lies, it follows that if you asked her Q she would instead answer ‘ja’.  Because she’s lying, the truthful answer to Q is ‘da’ which means no.

Now let’s assume the answer ‘ja’ means no and ‘da’ means yes.

1. True is asked Q and answers with ‘ja’.  Since she can only tell the truth, the truthful answer to Q is ‘da’ which means yes.
2. True is asked Q and answers with ‘da’.  Since she can only tell the truth, the truthful answer to Q is ‘ja’ which means no.
3. False is asked Q and answers with ‘ja’. Since she can only tell lies, it follows that if you asked her Q she would instead answer ‘ja’.  Because she’s lying, the truthful answer to Q is ‘da’ which means yes.
4. False is asked Q and answers with ‘da’. Since she can only tell lies, it follows that if you asked her Q she would instead answer ‘da’.  Because she’s lying, the truthful answer to Q is ‘ja’ which means no.

As you can see, this makes the puzzle relatively simple.  From this we can finally attack the puzzle and ask the three gods our three questions. (These three steps were taken from Brian Rabern and Landon Rabern’s solution to the logic puzzle which can be found at the bottom of this article.  My solution to the puzzle was quite similar to theirs, but they have written a clear explanation of their solution that is more eloquently written than I could ever conjure up.)

1. Ask god B, “If I asked you ‘Is A Random?’, would you say ‘ja’?”. If B answers ‘ja’, then either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is indeed Random. Either way, C is not Random. If B answers ‘da’, then either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is not Random. Either way, A is not Random.
2. Go to the god who was identified as not being Random by the previous question (either A or C), and ask him: “If I asked you ‘Are you True?’, would you say ‘ja’?”. Since he is not Random, an answer of ‘ja’ indicates that he is True and an answer of ‘da’ indicates that he is False.
3. Ask the same god the question: “If I asked you ‘Is B Random?’, would you say ‘ja’?”. If the answer is ‘ja’ then B is Random; if the answer is ‘da’ then the god you have not yet spoken to is Random. The remaining god can be identified by elimination

Thus, you have supposedly solved the hardest logic puzzle ever.  I believe you can formulate Q in a number of ways in the same fashion that can successfully cover all eight possible situations within the two different circumstances of ‘ja’ and ‘da’.  The goal is to nevertheless

—

For those who found this puzzle relatively easy, there are ways to make this puzzle a bit more difficult.  Try to solve the puzzle in two questions or less.  It’s entirely possible to do so and people have done it before!

Are there harder ones?  Of course there are.  Unfortunately the new puzzle will be posted in the next issue of the online edition of Prometheus.

—

If you want to look at a different take to the logic puzzle, please look at George Boolos’s solution here.

If you have any questions about my solution, please check out Brian and Landon Rabern’s solution here.

If you have specific questions not answered in any of these philosopher’s solutions or a different solution to the puzzle that you want to be verified, please feel free to e-mail me at editors@prometheus-journal.com.  I always look forward to reader’s e-mails.

Editor-in-Chief

Cuong Q. Nguyen

Prometheus is a peer-reviewed international undergraduate journal of philosophy providing a forum for scholarly discussion among undergraduates on both early and modern philosophy.  The print journal emphasizes discussions on a broad range of philosophical topics emphasizing thoughtful analysis and creative solutions to early and modern philosophical problems and puzzles prevalent in the field today.

We extend our sincerest gratitude to the members of Prometheus for their hard work and dedication, the philosophy graduate students for their continued support, our submitters for their insightful and illuminating papers, and our graduate advisor Matthew Holtzman for his continued guidance and wisdom throughout the process.

Prometheus is distributed throughout Homewood Campus and philosophy departments across the nation.  Printed issues of Prometheus are also available online on our website.

Editorial enquiries and enquiries concerning subscriptions and journal copies should be e-mailed to editors@prometheus-journal.com or should be sent to:

Prometheus

Department of Philosophy

Johns Hopkins University

2850 North Charles Street

Room 1202C

Baltimore, MD 21218

Editors-in-Chief

Cuong Q. Nguyen & Shane Steinert-Threlkeld

Graduate Philosophy student Alexander James will be presenting a short talk and leading a discussion on “The philosopher within: Wittgenstein’s critical
reflection on the beginnings of philosophy.”

Coffee and snacks provided.

All are encouraged to attend.

For more information, see:
http://prometheus-journal.com/events/seminar/

“Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are ‘da’ and ‘ja’, in some order. You do not know which word means which.”

Here’s a few clarifications about the puzzle.

1. It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).

2. What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)

3. Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.

4. Random will answer ‘da’ or ‘ja’ when asked any yes-no question.

So after five months of on-and-off work on the problem, I think I’ve finally solved it.  But it wouldn’t be fun just to tell you my answer and how I solved it.  In all honestly, I’m more interested IF YOU can solve it and, if so, how quickly.

I’m positive there’s someone out there who can solve it faster than I.  If you think you have an answer to the puzzle, feel free to post in the comments section your solution.  At the release of the next issue, I’ll put up my solution to the puzzle and compare it to the solution given by philosopher George Boolos.

Is there a prize?  Of course, you win the honor of solving the hardest logic puzzle ever with your own wit! I encourage everyone to join in on the fun and definitely look forward to your solutions.

NOTE: I know there are solutions online but, please, don’t ruin the fun for yourself and everyone else by looking up the answer.  You can do it by yourself.  Trust your own abilities!

[ UPDATE: You can find my solution and other solutions to the puzzle here. ]

Cuong Q. Nguyen

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Cover image: “introspection” by ~final-testament

Some numbers:

 
• 50 submissions
• 37 undergraduate philosophers
• 5 countries: USA, England, Scotland, Canada, Australia

 

For our first submission cycle, our expectations have been far exceeded. We’d like to thank everyone who has helped us make this possible.

These submissions, however, represent not a successful end, but a very promising start to producing a high quality academic journal.  Only now does the real intensive work begin.  The papers will go through a rather intense review process where they will meet multiple pairs of eyes and pass through many review cycles.

To everyone who submitted a paper, we will keep you posted on its (their) progress through the review process. We plan to have the final product finished before the end of April.

The talk will take place in Maryland 202 at 8PM on Wednesday February 18, 2009.

Q&A session to follow.

Coffee and snacks will be provided.

The first seminar will be delivered by James Gilmore on Februrary 18th at 8PM in Maryland 202.  For more details about the seminar, please see:

http://prometheus-journal.com/events/seminar/

Details about future locations, abstracts of the talks, and any other information will continue to be updated on that page, so keep checking back.

We look forward to hosting this wonderful series and hope to see you there.

When we took on the daunting challenge of creating an undergraduate philosophy journal here at Hopkins, we imagined but also sometimes doubted the success that we have had thus far.  Prometheus has been a labor of love, a vision largely realized between the hours of 12 and 5am.

Beyond the long list of thank yous extended above, we must primarily thank the never-dying ember alive within all of us who seek ansers to life’s most difficult questions.

In search of these answers, Prometheus has a few ideas, in addition to our print journal at the end of the year, that are currently in the planning stage but should become a reality in this coming semester:

1. Seminar on meta-philosophy. We will sponsor, pending approval of the JHU Philosophy department, a graduate-student-run seminar on meta-philosophy. Held bi-weekly, these seminars will consist of a 30-40 minute presentation followed by an open Q&A forum concerning issues in the practice of philosophy.
2. Undergraduate conference. We plan to host a day-long undergraduate philosophy conference, open to any undergraduates who can provide travel expenses. Our schedule is still tentative, so please let us know if you have any ideas for events you would like to see. The main foundation of the conference will be the presentation of undergraduate philosophy papers.

To make these great visions happens, we will need all the help we can get.  If there is any way you can and would like to help, please feel free to contact us (info on Staff and Contact pages).

Thanks again for the successful beginnings of a great publication. Here’s to an even more successful future.

Happy Holidays.

Shane Steinert-Threlkeld and Cuong Q. Nguyen

Editors-in-Chief, Prometheus

What is a Good Life?

When asked, ‘What do you want from life?’, or ‘What is a good life?’, many respond with the age-old slogan, ‘All that really matters is that you’re happy’. Does this slogan capture all that is relevant to a good life?

Imagine that in the future, scientists and engineers develop an ‘experience machine’. People can program into the machine whatever experiences they want to undergo, and hook themselves up to this machine such that once inside, the experiences are indistinguishable from reality. Subjects can choose to live out their entire lives in the machine, experiencing whatever joys and achievements their hearts desire just like it were really happening.  Once in the machine the person is ignorant of the fact that they are really just lying in a vat or on a table having their brains manipulated according to the plan they had previously invented.

A machine like this seems sufficient to ensure a person’s happiness, but would a life in the experience machine be a good life?  Assuming that the machine is without flaws, would you agree to be hooked up to the machine and live out your dreams? Why or why not?