PHIL 2303, Introduction to Symbolic Logic Why Study Logic? PHIL 2303, Introduction to Symbolic Logic

What is Logic good for? How can we understand ‘good’ or ‘utility’ or ‘value’? Intrinsic value: for its own sake Instrumental value: valued for its capacity to assist in the the production of some other valuable thing.

Instrumental Value of Logic Virtually every science or skill employs some logic. Logical inference enables you to solve puzzles and discover unknowns. Many actions and beliefs ought to be guided by logical reasoning.

Intrinsic Value of Logic Reason is normatively logical Logic sets the standards of correct reasoning Logic is the study of virtuous reasoning. Since human beings ought to be rational (in many things), they ought to be logical. Logic provides an objective standard for evaluating reasoning.

We need logic … like a knife needs a whetstone. We are rational creatures (or at least we ought to be). And reason is ought to be logical. So, we ought to be logical (even though we’re not).

Logic is a corrective We are frequently irrational: Consider the case of two candies: a Lindt chocolate truffle and a Hershey’s kiss. When the truffle costs $.15 and the kiss costs $.01 73% buy the truffle and 27% buy the kiss. When the truffle costs $.14 and the kiss is free 69% buy the kiss and 31% buy the truffle. Source: Ariely, Predictably Irrational (2008)

We can be fooled by priming Consider the case of Tom W, who is a graduate student at UT-Austin, what is he studying? Suppose I tell you some more about Tom: intelligent, but lacks creativity; enjoys detail and tidiness; has an interest in science fiction; is introverted and keeps to himself. Arrange the following list of possible areas of study in the order from which is most probably Tom W’s area to which is least probably his area of study.

List of areas of study Business administration Computer science Engineering Humanities and education Law Medicine Library science Physical and life sciences Social sciences and social work Source: Kahneman, Thinking Fast and Slow (2011)

Does your list look like this? Humanities and education Social sciences and social work Physical and Life Sciences Business Administration Engineering Medicine Law Computer science Library science

Base rate and probability The second list is based on the proportion of students in each of those programs as a percentage of total graduate students at UT-Austin (this is the “base rate”). Regardless of Tom W’s particular personality, the probability that he is in any particular program ought to be close to the base rate. The statistically logical answer is different from the intuitive answer.

Going with our gut The human brain is dominated by hidden, parallel, multi-directional, largely automatic actions. The part of our brain that is responsible for conscious, rational thought is comparatively small. Logic can help restrain the errors that our irrational and unconscious brain can lead us into.

Some more fallacies of reasoning, in case you’re not convinced yet.

What are the chances that two people in this class share a birthday? If the class has 23 students or more, the probability is better than 50%! This is called the “birthday paradox.” Its solution requires some fairly lengthy computations.

Consider Linda Linda is 31, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with gender issues and social justice. She participated in anti-war demonstrations. Which of the following two statements is more likely true of Linda today? Linda works at a bank. Linda works at a bank and is a women’s rights activist.

The conjunction fallacy If you said that the second statement is more likely true than the first, you responded illogically. Consider it this way: The set of people who work at a bank MUST be larger than the set of people who work at a bank AND are women’s rights activists. So, every instance that makes the second statement is true is also an instance that makes the first statement true. So, it has to be more likely that the first statement is true than the second statement is true.

The Monty Hall Problem In the game show “Let’s Make a Deal,” contestants were offered a choice of three doors. Behind one of them was a great prize; behind the other two a goat.

Do you switch? After the contestant has made a selection, Monty Hall would reveal what was behind one of the other doors—always the goat, never the great prize. And then he would ask, “Do you want to stay or switch?” Which choice offers the greatest probability of wining? Stay, or switch?

You should always switch Switching will get you the prize at a ratio of 2 : 1 Consider the following: When you make the initial selection, the probability you chose the prize is 1/3 When Monty Hall reveals what’s behind one of the doors, nothing changes your initial choice. But now there are only two doors and the probability that the prize is behind each door has to add to 1. 1/3 + 2/3 = 1 So, the probability that the prize is behind the door you originally selected is 1/3 and the probability that it’s behind the other door is 2/3.

In many ways, we are poor reasoners. Logic can help sharpen and improve our reasoning.