Critical Thinking – Categorical Syllogisms


E Mail #1

Hello Class,

I am sending everyone 4 e-mails. I am breaking them up so I don’t jumble a lot of information together. I want to help you study by breaking down the Exam. If anything I write seems incorrect, please let’s discuss it. I am giving you notes based on HOW I UNDERSTAND. I want to help, but I don’t want to confuse anyone, so if this helps you great. If it confuses you, study your own way, but make sure you study for this exam! I think the most important trick is to understand the Patterns. Once I saw the Patterns emerge today, everything seemed a little easier to do. I couldn’t understand any of this material until today. It really drove me crazy and made me anxious and depressed…so if I can overcome that, I think we all can!

If you have e-mails of anyone who missed todays class, I would forward them all of the 4 emails I am sending you, so they have the benefit of knowing what was discussed in the class today. Please pass this information along!

Class Four Recap

We found out the whole class, every team, failed the take home fallacy worksheet. She gave us the time to re-do the test, and earn 4 points (if we got all the fallacies correct this time). Anyone who wasn’t in class will have an opportunity to do the same thing on their take home test, in order to earn 75% on that take home test. I can discuss the take home test with anyone who needs to take it on the Fifth Class.

The class mainly missed these fallacies:

Appeal to Authority

Contrary to the Fact

False Dilemma

Hasty Generalization

False Analogy

Post hoc ergo propter hoc

Non-sequitur

Contrary to the Fact

We all did OK on Appeal to Ignorance (Ad ignorantium), Two Wrongs, Attacking the Person, Slippery slope, Appeal to Emotion,

Equivocation was the fallacy that was not used!

Anyone who missed class today will have a chance to earn up to 4 points only by getting all of the answers correct. I have just provided you all of the hints provided us in class. If anyone who wasn’t in class needs to discuss this, e-mail me to set up a time to call each other and we will talk about it over the phone.

If you earn all 4 points, it will only bring your grade on the Fallacy take home test up to a 75%

ABOUT THE EXAM

I’m highlighting things in Black that I am sure are on the FINAL EXAM.

The final exam is 25 questions, broken up into 3 segments.

1. Categorical Syllogisms

2. Hypothetical Syllogisms

3. Finish the sentence syllogism…..(categorical)

Here are some rules:

1. All valid syllogisms must have one affirmative premise.

2. Syllogisms are only valid if the conclusion has to be true based on the premise.

3. All valid syllogisms must have one universal premise-(ALL) Example: All people are homo-sapiens.

Deductive Reasoning: You have a Known set of facts. Truth. Validity-refers to structure (Do the premises prove the conclusion) Soundness & Acceptability.

CLASS,
I don’t know how soon I will send out the next two e-mails, it is going to take me some time to re-write my notes in an instructional manner. 
 
I do not know the order of the exam….but for purposes of breaking the 3 different subjects apart, I am calling this Part 1.
 
I’m highlighting things in Red that I am sure are on the FINAL EXAM.
 
Part 1 of EXAM:
From Chapter 9 pages 137-138 show other patterns that show up.
Categorical Syllogisms:
A categorical syllogism is a form of argument that contains statements) called categorical propositions) that either affirm or deny that a subject is a member of a certain class (category) or has a certain property.”
Determine valid or invalid-
 
Here is ONE basic pattern of a Categorical Syllogism: this will appear at least one time on the test in some way (either in pattern or direct example, I don’t know).
All X’s are Y’s
Z is an X
Therefore, Z is a Y
 
LEARN THE PATTERN
Pattern of Categorical Syllogisms
  1. Major Term: (This is usually found in the first line of the Categorical Syllogism, on the right hand side.) e.g. Our students are intelligent.  (MAJOR TERM)
  2. Find out what the MIDDLE TERM is. The middle term will duplicate itself in line ONE and line TWO.  Once you know what the Middle Term is, you can logically deduct what the major term is in the first line, and what the minor term is in the second line! e.g. Robert is one of our students.
 
Our students are intelligent.
Robert is one of our students.
 
*NOW WE KNOW STUDENTS IS THE MIDDLE TERM, SO THEREFORE WILL NOT BE IN THE CONCLUSION.
*The MAJOR TERM in line one has to be intelligent (found on the right of line one)
*The MINOR TERM always on line TWO is not students (Middle Term) so it must be Robert.
*The conclusion now must read with the
RULE
 
MINOR becomes the SUBJECT in the CONCLUSION.
MAJOR becomes the PREDICATE in the CONCLUSION.
 
EXAMPLE: Therefore, Robert (MINOR TERM NOW SUBJECT) is intelligent. (MAJOR TERM NOW THE PREDICATE)
 
ON THE TEST
            No geese are felines.
            Some birds are geese.
            Therefore, some birds are not felines.
 
Now break the syllogism down.
 
LINE ONE: Since Geese is repeated in line one and line two, it must be the Middle Term.  So in line one the Major term is: Felines.
 
LINE TWO: Some birds are geese.  Geese is the middle term (appears in line one) so SOME BIRDS, must be the Minor Term: Some birds.
 
LINE THREE: To be VALID, it must have the Minor term as the Subject and the Major term as the predicate. Also watch the ALL & SOME!
 
Therefore, (minor term) some birds are NOT (to relate to the universal term in line one NO GEESE) felines (MAJOR TERM).
THIS EXAMPLE THEREFORE IS VALID
UNIVERSAL STATEMENTS IS ON THE TEST.  There has to be at least One universal statement seen when words like ALL OR NONE  is in the syllogism.
 
ON THE TEST
 
All zebras are striped animals.
No zebras are polar bears.
Therefore, no polar bears are striped animals.
 
Let’s walk through this:
The Middle term is Zebra’s but the universal term says ALL in the first line and NO in the second line!
The Major term is striped animals in line one because zebras is middle term.
The minor term is polar bears in line two because zebras is the middle term.
 
The conclusion must be written with the Minor term as the SUBJECT and the Major Term on the PREDICATE.
 
Therefore, (minor term) no polar bears are striped animals (major term).
So the problem is the universal statements are not matching up….. since NO goes with the minor term and ALL is in the major term, NO & ALL are opposite of each other, they are Negative, they do not match up….
THIS SYLLOGISM IS INVALID
 
EXAMPLE:
 
All clowns are funny individuals.
Some sad people are clowns.
Therefore, some sad people are funny individuals.
 
Let’s walk through this:
1.  CLOWNS repeats itself in line one and line two so it can not be in the conclusion, we know this is the MIDDLE TERM.
2.  In line one the MAJOR TERM must be FUNNY INDIVIDUALS.
3.  In the second line the MINOR TERM must be sad people.
So the last line must have the MINOR TERM as the SUBJECT, and the MAJOR TERM as the predicate, and watch the UNIVERSAL STATEMENTS ALL & SOME.
 
Therefore, some sad people (minor term) are funny individuals (major term.)
 
Look at it:  The minor term is the subject and in the right place, and the word SOME coincides with SOME in line two.  The Universal statements match.
THIS SYLLOGISM IS VALID
 
EXAMPLE:
Some sticky substances are yucky things.
All taffy is a sticky substance.
Therefore, some taffy is a yucky thing.               
 
Let’s walk through it:
MIDDLE TERM is sticky substance because it appears in line one and line two.  So therefore it can not appear in line 3.
Line one’s MAJOR TERM then must be yucky things.
Line two’s MINOR TERM then is taffy.
 
NOTICE: Universal statement ALL in line two.
Now:
Therefore, some taffy (MINOR TERM) is a yucky thing (MAJOR TERM).
The minor term is in the right place and the major term is in the right thing, BUT the Universal Statement doesn’t match.  In line two it says: ALL TAFFY, so when it says SOME TAFFY it doesn’t match! 
 
Therefore: INVALID
 
EXAMPLE
 
All items made of gold are expensive items.
Some rings are items made of gold.
Therefore, some rings are expensive items.
 
Let’s walk through it:
The MIDDLE TERM that appears in line one and line two is made of gold.
In Line One the Major term can be found on the right: expensive items.
In Line Two the Middle term must be: some rings.
 
Therefore, some rings (middle term becomes the subject) are expensive items (major term became the predicate). The UNIVERSAL TERM SOME matches. 
 
Therefore, some rings are expensive items.  THIS IS VALID!
 
Now, without any notes print out this portion and practice if these are valid or invalid by yourself! Circle one and go back over the answers above when you are done!  Practice, Practice, Practice!
 
All X’s are Y’s
Z is an X
Therefore, Z is a Y
 
VALID  OR   INVALID  
————————————–
Our students are intelligent.
Robert is one of our students.
Therefore, Robert is intelligent.
 
VALID OR INVALID
————————————-
 
No geese are felines.
Some birds are geese.
Therefore, some birds are not felines.
 
VALID OR INVALID
————————————
 
All zebras are striped animals.
No zebras are polar bears.
Therefore, no polar bears are striped animals.
 
VALID OR INVALID
———————————-
 
All clowns are funny individuals.
Some sad people are clowns.
Therefore, some sad people are funny individuals.
 
VALID OR INVALID
———————————-
 
Some sticky substances are yucky things.
All taffy is a sticky substance.
Therefore, some taffy is a yucky thing.               
 
VALID OR INVALID
———————————-
 
All items made of gold are expensive items.
Some rings are items made of gold.
Therefore, some rings are expensive items.
 
VALID OR INVALID
 
 
CLASS, IF YOU DON’T GET THESE RIGHT, KEEP PRACTICING UNTIL YOU ARE ONE HUNDRED PERCENT!
 

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