logic infusion demo

8/6/2019 Logic Infusion Demo

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Daily Overhead Assignment

Logic InfusionGreetings!

You have purchased one of Pathos Learning’s Daily Overhead Assignmentseries entitled “Logic Infusion.” This Logic Infusion unit is actually meant toperform as a complete unit, not just as a daily warm-up activity. It isdesigned to teach logic in terms of symbols representing categories.

Since all knowledge is about categorizing information, with human thoughtbeing the process of accessing and applying such categories, the teachingof logic can be one of the most important tools a teacher can introduce intoa classroom. As a teacher of logic, you are not only teaching students agreat way to analyze arguments and an excellent means of experiencinglanguage visually as an organization of interrelated ideas. You are alsoteaching students how to think, to understand the relationships betweenconcepts in a statement. What could be more rewarding for you or your students?

This unit includes overhead notes and Daily Overhead Assignmentactivities for 36 weeks (explained below). It also includes practiceactivities and tests categorized by each type of syllogistic statement.

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A Synopsis of the Unit

DAILY OVERHEAD ASSIGNMENTS

Essentially, as explained in the overhead notes, three-part syllogistic arguments are

typically diagrammed in two ways. Probably the easier and more limited of the twomethods is the Eulerian method first developed by Leonard Euler in the 18 th century.The second method was an improvement on Euler’s with the advent of the Venndiagram, invented by John Venn in the 19th and 20th centuries. Students typically seemto understand Euler’s method quicker than Venn’s but both are quite accessible by eventhe below-average student, with some practice. Euler is often used to introduce Vennsince many of the basic concepts are the same. See the notes on each for completedescriptions of how they work.

Daily Overhead Assignments need not be done only once per day, or necessarily everyday. The teacher should gauge these to the needs and abilities of the students in the

classroom. Advanced students should be able to learn the techniques in Venn andEuler relatively quickly with plenty of practice and may become bored with too muchstretching out of the material.

The Daily Overhead Assignment sections also work well as quizzes in themselves.Regardless, to use them you should of course cover up each answer on the right-handside until the student has had a chance to work the problem out. Call students up to theboard; have them volunteer; let them make games out of symbolic logic! Thepossibilities are endless.

TYPES OF STATEMENTS AND THE WORKSHEETS

As the notes reflect, there are essentially four types of logical statements that can bediagrammed. We have named them Types A, B, C, and D. Eulerian diagramming isreally limited to working with types A, B and C while all four types can be worked withVenn. Also, while Eulerian diagramming gets jumbled when a student attempts todiagram more than two premises, the Venn method easily allows the diagramming of multiple premises beyond two in the same diagram. Ultimately, then, if you plan toteach only one method, Venn may be the better bet. If you students are well belowaverage in language skills, however, you may consider starting with Euler and seeinghow far they are capable of moving up towards Venn. This is of course completely up

to the teacher. Again, all exercises and tests were written to work with both methods—except the “Type D” exercises and tests. These can only be worked using the Vennmethod.

Thanks again and good luck!



NOTES ON DIAGRAMMING SYLLOGISMS

A syllogism is a three-part argument with two premises and aconclusion.

A premise gives a statement that should be generally accepted astrue.

A conclusion is a truth derived from the acceptance of the twopremises.

Example:

All teachers are human beings(and ) Mr. Everett is a teacher (therefore) Mr. Everett is a human being

Premises

conclusion

We can diagram the syllogism to see if the conclusion really is ac-ceptable based on the premises. If we accept the TRUTH of thepremises and all three statements exist in the same diagram (areVALID in other words) then we must accept the truth of the conclu-sion.

The syllogism and the diagram started with Aristotle in the 2ndcentury b.c. as a means of creating and validating a deductive ar-gument. Euler simply made a few adjustments.

1



Here is one way of diagramming a syllogism (created by LeonardEuler in the 18th century):

humanbeings teachers

teachersMr. Everett

Premise 1: Premise 2:All teachers are human beings Mr. Everett is a teacher.

Since teachers are inside the category of human beings and Mr. Everett is

inside the category of teachers, Mr. Everett must also exist inside the

category of human beings. Thus, the syllogism is VALID.

Here are the human beings

two statements

combined in teachersone

Diagram: Mr. Everett

The circles are actually spheres. Each one exists inside the other. Think

of them as balloons inside of balloons.

**Remember, you only diagram the premises, not the conclusion. Once

you’ve diagrammed the premises, you simply sit back and look to see if

the diagram matches the conclusion. If it does, it’s valid. Otherwise, it’s

invalid.2



Symbolic Logic Practice(with Positive and Negative Terms)

Part I: SYLLOGISMSDirections: 1) assign the terms, 2) diagram the syllogism, 3) declare whether the conclusionis valid or invalid based on the premises.

1. All computers compute stuff,and broken calculators do not compute stuff.Thus, broken calculators are not computers.

2 Steve does not like going to the movies.But Steve is Amish.Thus, the Amish do not like going to the movies.

3. Motorcycles are faster than cars.

Also, things that are faster than cars are not as fast as jets.Therefore, motorcycles are not as fast as jets.

4. No keys work in this door,and all keys work in the other door.Consequently, this door is not the other door.

5 Wearing Ties is appropriate in this office.However, wearing ties is not casual dress.

Thus, casual dress is not appropriate in this office.

Part II: SYLLOGISMS FROM SENTENCESDirections: 1) Write out the following sentence into syllogism form. Pay attention to transi-tions that signal conclusions and premises. 2) Assign the terms, 3) diagram the syllogism,and 4) declare whether it is valid or invalid.

6. People who like sandwiches like fast food, and people who like fast food do notlike stew. Thus, people who like stew do not like sandwiches.

7. Since all A’s are B’s, no B’s are C’s because no A’s are C’s.

8. No donuts are fat-free because the Bear Claw is a donut and the Bear Claw is notfat-free.

9. All D’s are J’s and no J’s are K’s; thus, no K’s are D’s.

10. All teachers were once students because all students become teachers and noone who was once a student is a student.



Symbolic Logic Practice II(with Positive and Negative Terms)

Part I: SYLLOGISMSDirections: 1) assign the terms, 2) diagram the syllogism, 3) declare whether the conclusionis valid or invalid based on the premises.

1. No students who play an instrument are underachievers,Tom is not an underachiever.Thus, Tom plays an instrument.

2 People who smoke have an increased health risk.Juanita does not smoke.Thus, Juanita does not have an increased health risk.

3. A good neighbor maintains his yard.

Jim is a good neighbor.Therefore, Jim maintains his yard.

4. No one who eats lettuce dislikes salads,Janie dislikes salads.Consequently, Janie does not eat lettuce.

5 People who fear flying have a phobia.However, Elizabeth does not fear flying.

Thus, Elizabeth does not have a phobia.

Part II: EnthymemesDirections: 1) Write out the following sentence into syllogism form, adding the unspokenpremise that makes it valid. 2) Diagram it to prove its validity.

6. Bodybuilders are healthy because they do not eat unhealthily.

7. Since I don’t eat meat, I am a vegetarian.

8. I don’t hug trees, so I am not an environmentalist.

9. Republicans support free enterprise; thus, Sam is not a republican.

10. I don’t like leeches because they are slimy.



Symbolic Logic Exam(On Positive and Negative Terms)

PART IDirections: 1) assign the terms, 2) diagram the syllogism, 3) declare whether the conclusionis valid or invalid based on the premises.

Diagram Here

1. All A’s are B’s,and no A’s are C’s.Thus, no C’s are B’s

2. No A’s are C’s.Also, no B’s are A’s.Therefore, no B’s are C’s

3. All dogs have fleasJojo is not a dog.Thus, Jojo does not have fleas.

4. No seniors are freshmen,And all freshmen are adolescents.Thus, no adolescents are seniors.

5. All chairs are made for sitting on.Also, no tables are for sitting on.Thus, no tables are chairs.

Part IIDirections: 1) Write out the following sentence into syllogism form. Pay attention to transi-

tions that signal conclusions and premises. 2) Assign the terms, 3) diagram the syllogism,and 4) declare whether it is valid or invalid.

6. All junk food is unhealthy, but apples are not junk food, so apples are not unhealthy.

7. No computers are infallable because things thatare infallable are perfect and computers aren’t perfect.

8. Since I am a poet, I am not illiterate because no poets are illiterate.



Symbolic Logic Exam(On Positive and Negative Terms)

PART IIIDirections: 1) Decide what implied premise exists that makes each syllogism valid and writeit on the line. 2) Diagram the argument to prove its validity.

Diagram Here

9. No A’s are B’s _________________ No B’s are C’s

10. All dogs have fur _________________ No snakes are dogs.

11. No geniuses have low IQ.’s

_________________ No rocket scientists have low I.Q.’s

PART IVDirections: 1) Create three of your own syllogisms with negative terms that are valid.

2) Diagram them to prove their validity.

12.

13.

14.



KEY for Type B practice and tests

“Symbolic Logic Practice (with Positive and Negative Terms)”

1. valid 2. invalid 3. valid 4. valid 5. invalid

6. valid 7. invalid 8. invalid 9. valid 10. invalid

Symbolic Logic Practice II (with Positive and Negative Terms)”

1. invalid 2. invalid 3. valid 4. valid 5. invalid

6. People who eat unhealthily are not healty (and vice versa).

7. (impossible to have a type A conclusion with a Type B premise)

8. Environmentalists hug trees.

9. Sam does not support free enterprise.10. I don’t like slimy things.

“Symbolic Logic Exam: Positive and Negative Terms”

1. valid 2. invalid (4 terms) 3. valid

4. invalid 5. valid 6. valid

“Symbolic Logic Exam: On Positive and Negative Terms”

Part I: 1. invalid 2. invalid 3. invalid 4. invalid 5. valid

Part II: 6. invalid 7. valid 8. valid

Part III: 9. All C’s are A’s

10. No snakes have fur.

11. All rocket scientists are geniuses.

Part IV: (Answers will vary.)

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