Chapters 8-12 Flashcards
What is Categorical Logic?
A system of logic based on the relations of inclusion and exclusion among classes (“categories”). This branch of logic specifies the logical relationships among claims that can be expressed in the forms: “All ___ are ___,” “No __ are __,” “Some ___ are ____,” and “Some ___ are not ____.”
Categorical Logic was developed by _______ in the ____ century B.C.E.
Aristotle in the fourth century B.C.E. it is also known as Aristolian or traditional logic
Truth-Functional logic and Categorical logic are useful in
clarifying and analyzing deductive arguments.
Do these claims mean the same thing? 1. Everybody who is ineligible for Physics 1A must take Physical Science 1. 2. No students who are required to take physical science 1 are eligible for physics 1A.
NO
What is a Categorical Claim?
Any standard-form categorical claim or any claim that means the same as some standard-form categorical claim.
A Categorical Claim says something about
classes or categories of things.
A ____________ is a claim that results from putting names or descriptions of classes into the blanks of the following structures: A: All ___ are ___. E: No ___ are ___. I: Some ___ are ___. O: Some ___ are not ___.
Standard-Form Categorical Claim
In the example: Some Muslims are not Sunnis what type of claim is being used?
O-Claim
In the example: All Presbyterians are Christians what type of claim is being used?
A-Claim
In the example: Some Christians are Arabs what claim is being used?
I-Claim
In the example: No Muslims are Christians what claim is being used?
E-Claim
A: All ___ are ___. The phrases that go in the blanks are called?
terms
A: All ___ are ___. The one that goes into the second blank is called the
predicate term
A: All ___ are ___. The one that goes into the first blank is called the
subject term
A: All S are P stands for
A-Claim: All ___ are ___. S stands for subject term and P stands for predicate term.
Only ___ and ___ will work as terms.
nouns and noun phrases
“All fire engines are red” is this an example of a standard form categorical claim?
No because red is an adjective not a noun or noun phrase.
How do you check if something is a standard-form categorical claim?
Switch the S and P. For example with the sentence “All fire engines are red” to check you would switch it to “All red are fire engines” since it does not make sense it is not a standard-form categorical claim.
“All red vehicles are fire engines” is this a standard-form categorical claim?
Yes even though it is false it makes sense.
What claim does this represent?
A-Claim
All S are P
What claim does this represent?
E-Claim
No S are P
What claim does this represent?
I-Claim
Some S are P
What claim does this represent?
O-Claim
Some S are not P
Notice in the diagram for the A-Claim that area that would contain any members of the S class that were not members of the P class is _____ which means _______.
colored which means that is empty.
This diagram represents the claim that “All S are P” since
there is no S left that isn’t P
In the diagram for E-Claim the area where S and P overlap is ___
Empty; any S that s also a P has been eliminated. Hence “No S are P”
I-Claim Some S are P
At least one S is P and the X in the middle shows that
at least one thing inhabits this area
O-Claim Some S are not P
X in the area of the S circle that is outside the P circle representing
the existence of at least one S that is not a P
