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Categorical Arguments, Claims, and Venn Diagrams Sign In! Review Group Abstractions! Categorical Arguments Types of Categorical Claims Diagramming the claims For next time: Read Chapter 8 pages 257-263
Review Last time we had begun to make the transition from informal logic to formal logic We did that by practicing and reviewing things we already knew: identifying claims and abstracting them We also were reacquainted with categorical claims and categorical arguments Let's take another quick look at categorical arguments
Review Categorical claims were claims that relate two different groups (categories) with one another When we translate sentences into categorical claims we must make sure to clarify the groups involved Ex: “All students pay fees” How would we translate this claim to make the groups clearer We also began to diagram some of these arguments using Venn Diagrams
A quick note about Venn Diagram We have been using Venn Diagrams all quarter to visualize the relationships between claims It's important to keep in mind what each overlap in a Venn Diagram is telling us when we attempt to use diagrams to prove validity The Image on the right demonstrates those relationships
Warm Up For each sentence, translate it into a categorical claim to make the groups clearer along with the relationship between the groups “Everybody who is ineligible for Physics 1A must take Physical Science 1” “No students who are required to take Physical Science 1 are eligible for Physics 1A” The two claims look similar but are in fact quite different
Warm Up “Everybody who is ineligible for Physics 1A must take Physical Science 1” All students who are ineligible for Physics 1A are students who must take Physical Science 1 All As are Bs “No students who are required to take Physical Science 1 are eligible for Physics 1A” No students who must take Physical Science 1 are students who can take Physics 1A No Bs are Cs To see why these claims are different we can diagram them
Warming up even more It's important that we practice these skills Translating claims into categorical claims (for now) and later into claims in sentential logic will need to become second nature Take a minute to practice the following claims. Make the groups as clear as possible: “There are frogs wherever there are snakes” “Not every lizard is a salamander” “Some aardvarks are not mammals”
Subject and Predicate Terms Every Categorical Claim has the following basic form: Indicator [group] indicator [group] All As are/are not Bs The first group in a categorical claim is typically called the subject term The second group in a categorical claim is typically called the predicate term Why do they have these names? A predicate is a property attributed to subjects in a sentence Ex- The child (subject) is tall (predicate)
The Four Categorical Claim Types Last time, we saw a lot of different indicators that we can use to express categorical claims All of those different kinds of categorical claims are reducible (i.e. can be translated into without changing the meaning of a claim) to one of four types of categorical claims: 1. A-Claim: All As are Bs[A = All] 2. E-Claim: No As are Bs[E = Excludes] 3. I-Claim: Some As are Bs [at least one A is a B] 4. O-Claim: Some As are not Bs [ at least one A is not a B]
Affirmative and Negative Claims A-Claims and I-Claims are sometimes called affirmative claims because they state a positive relationship between two groups Conversely, O-Claims and E-Claims are called negative claims because they state a negative relationship between two groups (the claim is negative because two groups are being excluded) We'll need these distinctions later but for now it's good to keep them in mind as we practice translating
Examples and Diagrams Let's diagram each of these different claim types: A-Claim: All As are Bs ex- All zombies are undead E-Claim: No As are Bs ex- No living humans are zombies I-Claim: Some As are Bs ex- Some undead beings are zombies. [At least one undead being is a zombie] O-Claim: Some undead beings are not zombies. [At least one undead being is not a zombie]
Practice makes perfect For each of the following: 1) figure out the subject and predicate terms 2) decide what the sentence is saying about the groups and then 3) translate the argument into standard categorical form; finally 4) diagram the claim “Minors are not eligible” “Some veeblefetzers are carbostats” “Idiots would support the measure, but no one else would” “Coffee is a stimulant, since coffee contains caffeine”
Working Backwards What categorical claims are implied by the Venn Diagram on the right? What conclusion(s) can you draw based on this diagram? Can you create a valid argument using the information here?
Group Exercises In groups of 3-4, what Categorical Claim is implied by this diagram? Are there any other claims implied by the diagram?
Group Exercises! Identify all of the categorical claims that are implied by the diagram on the right There may be many categorical claims, make sure to note whether they are A, E, I, or O claims
Group Exercises (last slide) Translate the claims below into standard categorical claim form THEN represent those claims with a single Venn Diagram “No members of the club are people who took the exam” “Some people who did not take the exam are members of the club” “None of the people who gave blood were tested, so everybody who gave blood must have been untested”
For next time Read Chapter 8 pages 257-263 Quiz!