Philosophy Writing Assignment on the Liar Paradox

I have created this writing assignment for those students who have said that they don’t want 85% of their course grade to rest on a single exam. It is entirely optional. For details about the grading, see the latest version of the syllabus.

• You don’t need to consult outside sources for this assignment.

• If you do choose to consult outside sources, the normal rules about plagiarism apply. If you’re not sure about what constitutes plagiarism, consult this website.

• If you choose to complete this assignment, I recommend talking to me about it in office hours. (Or, if you are unable to attend my office hours, please email me to arrange a meeting at another time.)

• Please submit the assignment by email to me by the 17th of November. If you are completing the assignment, but will be unable to complete it by the normal deadline, please contact me in advance to arrange an extension.

• This is an individual assignment. While you may discuss the philosophical issues raised by the assignment with your classmates, the work you submit should be wholly your own. If I find that two students submit answers that are very similar (and I judge that the similarity could not be coincidental), I will penalize both students. For this reason, you should not share your answers with anyone. Indeed, you should take steps to ensure that your answers cannot be copied.

This assignment is about one of the oldest problems in philosophy, the Liar paradox. Before beginning this assignment, you should read Graham Priest’s article “Paradoxical Truth” from the New York Times, which introduces the problem. You should also watch my lecture on the principle of bivalence, if you haven’t already seen it.

In his article, Priest makes the extraordinary claim that some statements are simultaneously both true and false. Your task will be to explore this idea.

One (4 marks)
Here is one way of developing Priest’s idea. In standard (“classical”) logic, we assume that every statement is either true or false, but not both. According to the current proposal, there are three possibilities for each statement: Either the statement is true only, or it is false only, or it is both true and false. This makes our truth tables rather more complicated. Instead of having just two options for each square in the table (“T” and “F”) we now have three (“T”, “F” and “B”).

Fill in the truth tables for conjunction, disjunction, conditionals, and negation. Explain your choices carefully.

Two (4 marks)
Consider the natural deduction rules that we have studied in this course. Which of them are valid, given your new truth tables? Explain your answers. You should not consider the rules for the biconditional.
I recommend that you start with &I and &E, because these are rather more straightforward than some of the other rules.

Please note that there are no marks for just getting the correct answers here. The marks are for getting the correct answers and showing that they are correct.

Three (2 marks)
Do you think the resulting position is credible? (I’m not expecting an essay here, just a few sentences.)