Philosophical Methods Truth Tables - Logic Philosophical Methods

What do Logicians do? For many philosophical questions, philosophers tend to create arguments in which the premises are deeply-held intuitions. Philosophers use logic to uncover where people's intuitions differ. Philosophers evaluate both reasoning and content of arguments.

Enthymemes The President of the United States is powerful _______________________________ Trump is powerful What is implied here? Trump is the President of the United States Often one or more premises in an argument will be implied because some arguments depend on background knowledge that the author assumes the reader has.

Truth Tables Truth Tables are used to evaluate the validity of arguments more precisely. It is a table that allows us to keep track of all possibilities in a concise manner.

Here are the basics before we create some Truth Tables… Example: -Let P stand for: “The atomic number of hydrogen is 1.” -Let Q stand for: “The atomic number of helium is 2.” -Then “P and Q” means: “The atomic number of hydrogen is 1 and the atomic number of helium is 2.” Example (cont.) P Q __________ P and Q

Here’s a very simple Truth Table... Sooo…..if given this argument: P Q __________ P and Q The Truth Table would look like this: P Q P and Q T F

How do we fill this in, exactly? 1. In this example, the truth values in the first 2 columns are put into the table by running through all of the possibilities. 2. Column 3 – Here we fill in the truth value on each row by thinking about what “P and Q” means. 3. Intuitively, “and” means that both sentences joined by “and” are true. So, P and Q should be true only when “both” P and Q are true. 4. The argument is VALID! OK…Let’s look at this: (Have students help fill this in.)

Here’s another example… Fill-in the Truth Table Below P: Today is a weekday. Q: Tomorrow is a weekday. P ________ Not Q In English: Today is a weekday. Therefore, tomorrow is not a weekday. (All propositional argument premises must be written as affirmative atomic sentences.)

Let’s see if we were correct! P Q Not Q T F Intuitively, “not” tells us that “not Q” is true whenever Q is false and vice versa. There is a column in the truth table for Q even though it’s not a premise because we need it to work out all of the possibilities… so we know the values for “not Q”. Is the argument valid? The Premise (P) is true in rows one and two. The Conclusion is false on one of those rows. There is at least one case where the premise is true and the conclusion is false, so… The argument is INVALID!

What you can look forward to next! In the next PowerPoint, we will learn how to translate English into even more symbols! Stay tuned.