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Categorical Arguments, Claims, and Venn Diagrams
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Sign In!
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Review
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Group Abstractions!
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Categorical Arguments
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Types of Categorical Claims
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Diagramming the claims
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For next time: Read Chapter 8 pages 257-263
Review
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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
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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
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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
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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
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“Everybody who is ineligible for Physics 1A must take Physical
Science 1”
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All students who are ineligible for Physics 1A are
students who must take Physical Science 1
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All As are Bs
“No students who are required to take Physical Science 1 are
eligible for Physics 1A”
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No students who must take Physical Science 1 are
students who can take Physics 1A
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No Bs are Cs
To see why these claims are different we can diagram them
Warming up even more
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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:
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“There are frogs wherever there are snakes”
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“Not every lizard is a salamander”
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“Some aardvarks are not mammals”
Subject and Predicate Terms
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Every Categorical Claim has the following basic form:
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Indicator [group] indicator [group]
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All As are/are not Bs
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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
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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:
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1. A-Claim: All As are Bs [A = All]
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2. E-Claim: No As are Bs [E = Excludes]
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3. I-Claim: Some As are Bs [at least one A is a B]
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4. O-Claim: Some As are not Bs [ at least one A is not a B]
Affirmative and Negative Claims
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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
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Let's diagram each of these different claim types:
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A-Claim: All As are Bs
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ex- All zombies are undead
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E-Claim: No As are Bs
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ex- No living humans are zombies
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I-Claim: Some As are Bs
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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
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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
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“Minors are not eligible”
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“Some veeblefetzers are carbostats”
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“Idiots would support the measure, but no one else
would”
“Coffee is a stimulant, since coffee contains caffeine”
Working Backwards
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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
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In groups of 3-4, what
Categorical Claim is
implied by this
diagram?
Are there any other
claims implied by the
diagram?
Group Exercises!
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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)
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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
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Read Chapter 8 pages 257-263
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Quiz!