Elementary Logic

Elementary Logic PHIL 105-302 Intersession 2013 MTWHF 10:00 – 12:00 ASA0118C Steven A. Miller Day 2

Implication “There’s beer in the fridge.” When said to a visiting friend? When said to a customer? When speaking to an alcoholic partner?

Implication Jon: We’re going out for drinks tonight. Frank: If we’re doing that, let’s go to Sidetracks or The Cellar. Jon: I’m banned from Sidetracks! What’s the conclusion? What’s implied?

Implication The principle of charity: “in formulating implicit statements, give the arguer the benefit of the doubt; try to make the argument as strong as possible while remaining faithful to the arguer’s thought” (S, 12). In general, try to be a friendly and helpful reader.

Implication “If you were a real American, you wouldn’t oppose (the military / paying taxes / gun control / other issue of the day).” Is it an argument? What’s the implied conclusion?

Implication The Cubs are the best C-named MLB team. We know this because the Cardinals are the worst MLB team, and the worst cannot be the best.

Implication 1) The Cubs are the best C-named MLB team. 2) The Cardinals are the worst MLB team. 3) The worst cannot be the best. What’s the argument’s conclusion?

Implication 1) The Cubs are the best C-named MLB team. 2) The Cardinals are the worst MLB team. 3) The worst cannot be the best. What’s missing / implied to complete it?

Implication 1) The Cubs are the best C-named MLB team. 2) The Cardinals are the worst MLB team. 3) The worst cannot be the best. 4) There are only two C-named MLB teams: the Cubs and the Cardinals.

Implication In standard form: 1) There are only two C-named MLB teams: the Cubs and the Cardinals. 2) The Cardinals are the worst MLB team. 3) The worst cannot be the best. 4) [Therefore,] The Cubs are the best C- named MLB team.

Use / mention Michelle Obama is the First Lady. Michelle Obama has two daughters. Michelle Obama has thirteen letters.

Use / mention Michelle Obama has thirteen letters. “Michelle Obama” has thirteen letters.

Use / mention The first letter of Jingle Bells is “D.” The first letter of “Jingle Bells” is “D.” The first letter of the words to “Jingle Bells” is “D.”

Formal / informal These cookies cost twenty-five cents each. I have a dollar. I can buy four of them. 1.00 / x = y x = .25 1.00 / .25 = y 4 = y

Formal / informal Informal logic: If it’s dark, then it’s night. It’s dark. Therefore, it’s night. Formal logic: D ⊃ N D ∴ N

Formal / informal D ⊃ N D ∴ N If I’m disappointed, then I’m nervous. I’m disappointed. And so I’m nervous.

Seventh Inning Stretch (“Take Me Out to the Ballgame, …”)

Argument evaluation What makes an argument good? 1) true premises 2) conclusion at least probable, given 1 3) premises are related to the conclusion 4) the conclusion can’t be undermined

Argument evaluation 1) true premises In many cases, this is obvious: “Carbondale is south of Chicago.” “Carbondale is north of Chicago.” But in others, it’s more problematic: “There is a treasure chest buried 500 feet below where I stand.” This truth of this latter kind is indeterminate.

Argument evaluation 1) true premises For our purposes, we’ll treat the latter kind of sentence, the indeterminate ones, as true. Or, more properly, we’ll see what happens if they were to be true.

Argument evaluation 2) conclusion at least possible, given 1. The concern here is that the argument is valid, which means that there is a particular kind of relationship between the premise(s) and conclusion.

Argument evaluation Two kinds of argument: deductive and inductive 1) deductive argument – an argument in which the conclusion follows necessarily from the premises

Argument evaluation deductive validity – 1) The conclusion necessarily follows from the premises. 2) If the premises are true, the conclusion must also be true. 3) It is impossible for the premises to be true and the conclusion to be false.

Argument evaluation If it’s dark, then it’s night. It’s dark. Therefore, it’s night. This argument is deductively valid: If its premises are true, its conclusion cannot be false.

Argument evaluation Bill drove to work. Therefore, Bill must be over the age of 16. Not necessarily valid: impossibility is not legal or practical but rather logical. It is conceivable that Bill could be under 16 and driving to work, and so it is possible.

Argument evaluation Bill drove to work. Anyone who drives to work must be over the age of 16. Therefore, Bill must be over the age of 16. Valid.

Argument evaluation A deductive argument is valid when it is impossible (in the strongest sense) for the premises to all be true and the conclusion to be false.

Argument evaluation 2) inductive argument – an argument in which the conclusion is likely to follow from the premises

Argument evaluation 91% of Polish people are Catholic. Pitor is a Polish person. We can conclude that Pitor is Catholic. This argument is inductive: If its premises are true, its conclusion may still be false.

Deductive or Inductive? 1) Historians know of no civilizations that worshiped lizards. 2) So, humans never worshiped lizards. Inductive.

Deductive or Inductive? 1) No cats are purple. 2) Sashabear is a cat. 3) So, Sashabear is not purple. Deductive.

Deductive or Inductive? 1) The sidewalk is wet. 2) Usually, the sidewalk gets wet from rain. 3) It must have rained. Inductive.

Argument evaluation What makes an argument good? 1) true premises 2) conclusion at least probable, given 1 3) premises are related to the conclusion 4) the conclusion can’t be undermined

Elementary Logic