Week 2 Prompt Option #4: Finding the Argument Form
One of the ways that we can determine whether a deductive argument is valid or not is based on its logical form. The first step in being able to make this determination is to be able to determine the logical form of the argument. This discussion allows you to get practice determining the logical form of various arguments. Once you get the hang of it, you might even find that discovering argument forms is fun.
Prepare: To prepare to respond to this question, read the required sections from Chapter 3 and Chapter 4, paying special attention to those sections that explain categorical argument forms (in Chapter 3) and propositional argument forms (in Chapter 4).
Reflect: Choose an argument from the list below. To find the argument’s form, leave in the logical terms in the argument and replace the other terms with variables. In the categorical examples, the logical terms are ‘all’, ‘no’, ‘some’, ‘only’, and ‘not’, and the variables are letters like A, B, and C.
Here is an example of finding the form of a categorical argument: Take the argument, “Some dogs are brown. Only brown things are mammals. Therefore, Some dogs are mammals.” What we do is replace the non-logical terms with variables (capital letters). We can use ‘D’ for dogs, ‘B’ for brown things, and ‘M’ for mammals. The result, in standard form, is that the argument has the form:
Some Ds are B.
Only B are M.
Therefore, Some D are M.
In the propositional examples, the logical terms are ‘and’, ‘or’, ‘not’, ‘if … then’, ‘only if’ and ‘if and only if’, and the variables, letters like P, Q, and R, represent the simplest component sentences. You may use the following simplified symbols: The symbol for ‘and’ is ‘&’, the symbol for ‘or’ is ‘v’, the symbol for ‘not’ is ‘~’, the symbol for ‘if … then …’ is ‘–>’, and the symbol for ‘if and only if’ is <–>’ (Don’t forget to use parentheses to clarify the grouping in complex statements).
Here is a propositional example: Take the argument, “If you don’t like cabbage, then you should eat the peas. You like the cabbage, so you should not eat the peas.” We’ll use the letter ‘C’ for the sentence “You like cabbage” and the letter ‘P’ for “You should eat the peas.” The result, in standard form, is:
~C –> P
Write: Choose an argument from the list below. Make sure not to pick one that someone else has used. Paste the argument at the beginning of your post, then use standard form to present its logical form, as with the examples above. Make sure to provide a key indicating what each letter symbolizes. Next, provide a brief discussion of whether the argument form is valid and why. If it is valid, try to explain why the conclusion must be true provided that the premises are. If it is not valid, try to explain how it would be possible for the premises to be true and the conclusion false.
- All dogs are mammals. No mammals are reptiles. Therefore, no dogs are reptiles.
- Some rabbits are white. Only white things are hungry. Therefore, all rabbits are hungry.
- Some humans are not tall. Only tall things are orange. So some humans are not orange.
- No snakes eat vegetables. All things that eat vegetables are rabbits. So no snakes are rabbits.
- All beegs are greebs. No greebs are dools. Therefore, no dools are beegs.
- Some beegs are not greebs. Some greebs are dools. Therefore, some beegs are dools.
- Some members of the club are not happy. Only honest people are happy. Therefore, some members of the club are dishonest.
- All politicians are crooks. No members of my church are not crooks. Therefore, no members of my club are politicians.
- Everyone who drives a Mercedes is rich. Someone who is eating at the soup kitchen drives a Mercedes. So someone who is rich is eating at the soup kitchen.
- Any basketball player is tall. No jockeys are tall. Therefore, no jockeys are basketball players.
- Some men are hungry. Only people hungry will enjoy this sandwich. Therefore, only men will enjoy this sandwich.
- Examples with more than two premises (called Sorites):
- Some dogs are lazy. No lazy things work hard. All things that work hard are useful. Therefore, no dogs are useful.
- All politicians are cronies. No cronies are members of this club. Only members of this club are required to pay dues. Therefore, no politicians are required to pay dues.
- Every mammal is warm blooded. No sharks are warm blooded. No whales are sharks. Therefore, all whales are mammals.
- Every rock star is talented. No talented people go to this school. Those who go to this school are smart. Therefore, no rock stars are smart.
- Every fish breathes underwater. Nothing that breathes underwater lives on land. All amphibians can live on land. Therefore, no fish are amphibians.
- If you are happy, then you know it. You are happy, so you know it.
- If you are tall and have talent, then you should try out for the team. You are tall. So you should try out for the team.
- You are either rich or you got a bargain. You are not rich. Therefore, you must have gotten a bargain.
- If Seinfeld was better than Frasier, then it would have been on the air longer. But Seinfeld was not on the air longer than Frasier. Therefore, Seinfeld was not better than Frasier.
- If you cause a crash, then you will have to pay money. You don’t have to pay money. Therefore, you must not have caused a crash.
- Either Mike is lazy or he was busy that day. Mike was busy all day. Therefore, he is not lazy.
- If you try out for the football team, then you will fail. If you try out for the football team and fail, then you will be depressed. Therefore, if you try out for the football team, you will be depressed.
- If you are a dog and you are playing outside, then you are happy. You are not happy. Therefore, you are not a dog.
- If you’re a monkey, then you like bananas. My friend climbs trees and likes bananas, so my friend is a monkey.
- If the maid is guilty, then the butler is innocent. The Buter was not present at the scene. In order to be guilty, the Butler would have had to be present at the scene (trick: this is actually a conditional statement). Therefore, the maid is guilty.
- Enthymemes: These ones are missing a premise or a conclusion. See if you can fill in the missing premise or conclusion as you find the logical form.
- Flipper is a mammal since he is a dolphin. (What is the missing premise?)
- Mike will either get rich or die trying. He will not get rich. (What is the conclusion?)
- If you are in love then you are happy. You are happy. (What is the conclusion?)
- If the Cowboys lose tomorrow, then I will lose a lot of money. If I lose a lot of money, then I will have to move into a tent. Therefore, I will be moving into a tent. (What is the missing premise?)