PHI 103 RS T1Logical Arguments Matrix PDF

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Logical Arguments Matrix Name: Jacqueline Sandoval Part 1. Instructions: Complete the matrix below by answering the following: 1. Whether the argument is valid or invalid. 2. If the argument is valid, identify the argument type. 3. If the argument is invalid, identify the argument type and explain why the argument is invalid. Please use an original example, do not copy from the course materials, or any other sources.

Argument EXAMPLE: (1) If Joe is eligible to be president, he is 35 or older. (2) Joe is 35 or older. _____ (3) Joe is eligible to be president.

Valid?

INVALID

Type of argument or explanation This is an example of affirming the consequent. Being 35 or older is a necessary, but not sufficient condition for being president. He must also be a natural born U.S. citizen and not a felon.

INVALID

This is an example of an invalid (MT) Modus Tollens because the second premise says he “needs” glasses. Him being nearsighted does not mean he specifically needs a prescription for glasses.

INVALID

This is an example of an invalid (MT) Modus Tollens because it commits the mistake of affirming the consequent.

VALID

This is (MP) Modus Ponus

(1) If Jack is severely nearsighted, then he needs glasses. (2) Jack does not need glasses. _____ (3) Jack is not severely nearsighted.

(1) If Jill plays football in the NFL, then she is a professional athlete. (2) Jill does not play football in the NFL. _____ (3) Jill is not a professional athlete.

(1) If Marie is in Paris under the Eiffel

Tower, then she is in France. (2) Marie is in Paris under the Eiffel © 2020 Grand Canyon University. All Rights Reserved.

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Tower. _____

(3) Marie is in France.

Part 2. Instructions: First, write out the argument’s form in symbolic notation (do not use words, only symbols, see the textbook and overview for illustrations). Then, create examples of the following kinds of valid arguments: hypothetical syllogism, disjunctive syllogism, and constructive dilemma. Construct two examples for each type of argument. Please use an original example, do not copy from the course materials, or any other sources.

TYPE EXAMPLE: Modus Ponens

Symbolic Notation P Q P ————

YOUR EXAMPLE #1

YOUR EXAMPLE #2

If my pizza is Chicago-style, then it will have layers of crust and sauce. My pizza is Chicago-style. Therefore, my pizza has layers of curst and sauce.

If Ryan owns a beagle, then his pet is a dog. Ryan owns a beagle. Therefore, his pet is a dog.

If I pass my class with the highest test grade then I will get $100 dollars from my parents.

If I go to sleep early I will be able to wake up before class starts

Q Hypothetical Syllogism

P→Q Q→R ———— ∴P →R

If I get $100 dollars from my parents then I will be excited Therefore, if I get the highest test grade then I will be excited

Disjunctive Syllogism

PvQ ¬Q ———— ∴P PvQ

If I am late for my class then I will miss the teachers announcements Therefore, if I go to sleep early I will be able to wake up before class starts

I will go to the mall or I will go to the movies

I will be absent or I will go to P.E

I do not want to go to the movies

I do not go to P.E Therefore, I will be absent

Therefore, I will go to the mall

¬P ———— ∴Q © 2020 Grand Canyon University. All Rights Reserved.

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ConstructiV e Dilemma

P→Q, R→S PvR ————— Q v S.

If I am watching Netflix I am happy, If I am reading a book then I am bored.

If Stephanie listens to rain she will dance, If Stephanie listens to Mariah Carey she will jump.

I am either watching Netflix or I am reading a book.

Stephanie will listen to either rain or Mariah Carey

Therefore, I am happy or bored.

Therefore, Stephanie will either dance or jump.

© 2020 Grand Canyon University. All Rights Reserved.

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