The Liar Paradox and Other Puzzles: Games Logicians Play Dr. Sara L. Uckelman s.l.uckelman@durham.ac.uk Undergraduate Open Day 22 March 2017 Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 1 / 10
What is logic? Logic is a little tweeting bird chirping in the meadow. Logic is a wreath of pretty flowers which smell bad. https://www.youtube.com/watch?v=wlMegqgGORY Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 2 / 10
What is logic? Logic is the science of correct argumentation. Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 3 / 10
What is logic? Logic is the science of correct argumentation. What is an argument? What is a correct argument? Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 3 / 10
What is logic? Logic is the science of correct argumentation. What is an argument? ◮ Any ordered collection of one or more declarative statements, the last of which is called the conclusion and the rest of which are called premises. What is a correct argument? Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 3 / 10
What is logic? Logic is the science of correct argumentation. What is an argument? ◮ Any ordered collection of one or more declarative statements, the last of which is called the conclusion and the rest of which are called premises. What is a correct argument? ◮ An argument is good if it provides good epistemological grounds for the conclusion. Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 3 / 10
What is logic? Logic is the science of correct argumentation. What is an argument? ◮ Any ordered collection of one or more declarative statements, the last of which is called the conclusion and the rest of which are called premises. What is a correct argument? ◮ An argument is good if it provides good epistemological grounds for the conclusion. ◮ An argument is valid if it is impossible for the premises to be true when the conclusion is false. Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 3 / 10
The liar paradox Is the man who says he tells nothing but lies telling the truth? Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 4 / 10
The liar paradox Is the man who says he tells nothing but lies telling the truth? Principle of bivalence: Every sentence is true or false. That includes the sentence “This sentence is false” (1). Suppose (1) is true. Then what is says is the case, namely, that (1) is false. So on the assumption that it is true, we are able to prove it is in fact false. Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 4 / 10
The liar paradox Is the man who says he tells nothing but lies telling the truth? Principle of bivalence: Every sentence is true or false. That includes the sentence “This sentence is false” (1). Suppose (1) is true. Then what is says is the case, namely, that (1) is false. So on the assumption that it is true, we are able to prove it is in fact false. Not so fast. . . Principle of non-contradiction: No sentence is both true and false. That includes the sentence (1) “This sentence is false”. We proved above that (1) is false. That means that what it says is not the case, namely, that (1) is false. But then, it is true that “This sentence is false”. Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 4 / 10
The liar and the truthteller You are standing in front of two doors, one of which leads to certain death and the other of which leads to a life of endless happiness. You do not know which is which. In front of the doors are two guards. One of them always lies, one of them always tells the truth. You do not know which is which. You may ask one guard one question to help you determine which door to open. What question do you ask? Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 5 / 10
The liar and the truthteller Answer: “Which door would the other guard says leads to happiness?” Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 6 / 10
The liar and the truthteller Answer: “Which door would the other guard says leads to happiness?” If you’ve asked the liar, he will indicate the door leading to death, because the other guard would tell the truth and point to the door leading to happiness. If you’ve asked the truthteller, he will indicate the door leading to death, because the other guard would lie about which leads to happiness, and point to the door leading to death. Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 6 / 10
More to logic than paradoxes Deductive logics: The logic of propositional connectives: and, or, not, if. . . then. The logic of quantification and predication: all, every, some, there is The logic of modalities: necessity, possibility, knowledge, belief, action, agency, obligation, time. . . Non-deductive logics: Inductive logic Abductive logic Non-monotonic logic Probabilistic logic Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 7 / 10
Connections to. . . . . . philosophy of language . . . philosophy of mathematics . . . metaphysics . . . epistemology . . . ethics . . . economics and much more! Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 8 / 10
A bit more seriously. . . Why study logic? Central part of the analytic tradition in philosophy. Great for interdisciplinary work. Employers look for analytical skills. Hugely rewarding in its own right. Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 9 / 10
What can you study at Durham? 1st year: Introduction to Logic 2nd year: Logic, Language, & Reality 3rd year: Formal & Philosophical Logic 3rd year: Possibility to write a logic-based thesis. Dr. Sara L. Uckelman The Liar Paradox and Other Puzzles 22 Mar 2017 10 / 10
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