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Assignment

For this argument construction assignment, you will use your knowledge of categorical logic.  It is extremely important that you read the instructions for each individual problem very, very carefully and that you do exactly what you are asked to do.  It is also extremely important that you show your work for each step of each problem.  

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Argument Construction #3: Propositional Logic

Assignment

For this argument construction assignment, you will use your knowledge of propositional logic to generate arguments and test their validity.  It is extremely important that you read the instructions for each individual problem very, very carefully and that you do exactly what you are asked to do.  It is also extremely important that you show your work for each step of each problem.  You may type your responses to each question or you may handwrite your responses.  If you handwrite, print legibly. 

Be certain you  SHOW YOUR WORK  for each part of the problem.  

NOTE: A “ordinary language” argument uses actual words; a “symbolized argument” uses letters and operators.

Argument #1: CHOOSE EITHER OPTION A OR OPTION B BUT NOT BOTH

OPTION A

The film Freaky Friday relies on us accepting a controversial idea: the essence of our personality (our “me-ness”) is nonphysical and, thus, is not bound by our physical bodies. “I” can exist in the body of someone else and see the world as “me” from the vantage point of this other person’s body. My “self” or “mind” or “spirit” can inhabit the body of another without my memories, my thoughts, my preferences….all the things that make me “me”….ceasing to exist. “I” remain intact even though “I” am no longer in my body with my brain. This belief is common to religions that hold that when we die, we continue to exist as ourselves in some manner—that is, that our “souls” are reincarnated into another body or go to some spiritual plane like heaven. The contrary belief is that we are nothing but physical bodies and that whatever qualities you have that you associate with your personality and sense of self are merely the byproducts of your physical brain. There is no nonphysical you. Moreover, since your personality exists only as a physical phenomenon, it is not impossible that someday we can do a complete map of your neural network, translate that map to computer code, upload that code to a computer, and allow you to experience your “you-ness” forever….although all of your experiences and relationships would be in a computer world. Until this technology exists, though, people will cease existing in any way once their physical bodies die.

1. Construct a VALID ordinary-language argument that

 a. Has the form Modus Ponens

            AND

 b. Answers the following question:

Do you exist only as a physical thing or is some aspect of the essence of your “self” nonphysical?

OPTION B

Consider ideas like “justice” and “fairness” and “morality” and “beauty”….and all the other abstract ideas. These terms don’t refer to anything that we can perceive with our senses—that is, I can see examples of people enacting justice; I can hear people make claims about what is moral and immoral; I can feel (or taste) a statue or hear a song that someone says is beautiful. But I can never perceive with my eyes, ears, nose, tongue, or fingers “justice” or “morality” itself because these things do not have physical properties that would allow my physical senses access. So this raises a question: are these things actually exist as anything other than individual and cultural creations? Can I say any of these things is “real” in the same way I can say dogs and cats and students and carrots are real?

1. Construct a VALID ordinary-language argument that

 a. Has the form Modus Ponens

            AND

 b. Answers the following question:

Are ideas like justice, fairness, morality, and beauty purely individual and cultural creations, or do they exist in some way independently of people and cultures?

For questions 2-4, refer to the argument you created for Option A or Option B above.

2. Arrange the argument on a single line and construct an ORDINARY truth table (i.e. using L=2n) for the argument (be sure to indicate which letters represent which statements that make up the ordinary-language argument).

3. Justify the soundness of the argument by explaining why you believe the premises are BOTH true. (this means that you explain why you think the premises of your argument are TRUE statements; DO NOT explain why the argument is valid or why the conclusion is true. Explain why you believe the premise is a true statement.)

3. To which premise(s) of the argument is someone most likely to object, and what are likely to be the objections to this premise(s)? In other words, which premise(s) do you think someone could legitimately claim is false?

Argument #2

1. Construct a VALID ordinary-language argument that

 a. Has the form Modus Tollens

AND

 b. Answers the following question: Has social media (like Facebook, Twitter, etc.) made life better?

2. Arrange the argument on a single line and construct an INDIRECT truth table (i.e. a one-line truth table) for the argument (be sure to indicate which letters represent which statements that make up the ordinary-language argument).  Indicate clearly where a contradiction occurs that proves the argument valid.

3. Justify the soundness of the argument by explaining why you believe the premises are BOTH true. (this means that you explain why you think the premises of your argument are TRUE statements; DO NOT explain why the argument is valid or why the conclusion is true. Explain why you believe the premise is a true statement).

4. To which premise(s) of the argument is someone most likely to object, and what are likely to be the objections to this premise(s)? In other words, which premise(s) do you think someone could legitimately claim is false?

Argument #3

1. Create a VALID ordinary-language argument that

 a. Has the form Modus Ponens (MP), Modus Tollens (MT), OR Pure Hypothetical Syllogism (HS)

 AND

b. Answers the following question:  Are you plugged into the Matrix? (If you haven’t seen the film The Matrix, you can answer this question instead: Are you dreaming or hallucinating right now?)

2. Identify the form of the argument you constructed in #1.

3. Arrange the argument on a single line and construct an INDIRECT truth table (i.e. a one-line truth table) for the argument (be sure to indicate which letters represent which statements that make up the ordinary-language argument).  Indicate clearly where a contradiction occurs that proves the argument valid.

4.  Justify the soundness of the argument by explaining why you believe the premises are BOTH true. (this means that you explain why you think the premises of your argument are TRUE statements; DO NOT explain why the argument is valid or why the conclusion is true. Explain why you believe the premise is a true statement). 

5. To which premise(s) of the argument is someone most likely to object, and what are likely to be the objections to this premise(s)? In other words, which premise(s) do you think someone could legitimately claim is false?

Argument #4

1. Create a VALID ordinary-language argument that

 a. Has the form modus ponens, modus tollens, disjunctive syllogism, or pure hypothetical syllogism.

 AND

b.Addresses an issue related to any ONE of the following topics:

      Politics

      Sports

      Music

      College

      Technology

      Philosophy

      (other topic of your choice)

2. Identify the form of the argument you created in #1.

3. What is the question your argument addresses? Think carefully here.

4. Arrange the argument on a single line and construct an INDIRECT truth table for the argument (be sure to indicate which letters represent which statements that make up the ordinary-language argument).  Indicate clearly where a contradiction occurs that proves the argument valid.

5.  Justify the soundness of the argument by explaining why you believe the premises are BOTH true. (this means that you explain why you think the premises of your argument are TRUE statements; DO NOT explain why the argument is valid or why the conclusion is true. Explain why you believe the premise is a true statement). 

6. To which premise(s) of the argument is someone most likely to object, and what are likely to be the objections to this premise(s)? In other words, which premise(s) do you think someone could legitimately claim is false? 

Argument #5

1. Create an INVALID ordinary-language argument with exactly two propositions that answers the following question: Is logic class the most superrific class ever?

2. Arrange the argument on a single line and construct an ORDINARY truth table (i.e. using L=2n) for the argument (be sure to indicate which letters represent which statements that make up the ordinary-language argument).

3. Identify the line of the truth table that shows the argument to be invalid.

4. Modify the FORM of the argument you created so that the argument is valid.

5. Arrange the modified argument on a single line and construct an INDIRECT truth table (i.e. a one-line truth table) for the argument (be sure to indicate which letters represent which statements that make up the ordinary-language argument).  Indicate clearly where a contradiction occurs that proves the argument valid.

Argument Construction #1: Immediate Inferences

Assignment

For this argument construction assignment, you will use your knowledge of categorical logic. It is extremely important that you read the instructions for each individual problem very, very carefully and that you do exactly what you are asked to do. It is also extremely important that you show your work for each step of each problem.

IMPORTANT: YOU SHOULD ASSUME THE ARISTOTELIAN STANDPOINT AND USE THE TRADITIONAL SQUARE OF OPPOSITION FOR EACH PROBLEM (THIS IS VERY IMPORTANT WHEN CREATING YOUR VENN DIAGRAMS).

ALSO IMPORTANT: You may type your responses to each question using the electronic version of this form or you may handwrite your responses on this form. If you handwrite, print legibly.

Problem #1

  1. What is the standard-form, ordinary-language translation (this means you use real words like the ones you’re reading here, not symbols) of the following statement:

There’s no such thing as a logic student who’s not a rascal.

All logic students are rascal’s.

  1. Assume the standard-form statement you created for #1 above is FALSE , and then use the rules of conversion, obversion, contraposition, contraries, subcontraries, subalternation, or contradiction to create two other standard-form statements that are also necessarily FALSE . (NOTE: you may need to use more than one rule to create a false statement)

No logic students are non-rascals. (obversion)

All non-rascals are non-logic students. (contraposition)

  1. Identify the rules that prove the statements you created in #2 false.

Obversion, Contraposition

  1. Assume the standard-form statement you created for #1 above is FALSE , and then use the rules of conversion, obversion, contraposition, contraries, subcontraries, subalternation, or contradiction to create two other standard-form statements that are necessarily TRUE. (NOTE: you may need to use more than one rule to create a true statement)

Some logic students are rascals – Some rascals are logic students.

  1. Identify the rules that prove the standard-form statements you created for #4 TRUE .

Conversion

  1. Create a labeled Venn diagram that shows the standard-form statement you created for #1 above” to be FALSE (be sure to label your circles—and remember: your Venn diagram should show the statement to be FALSE ).

LS R

“All logic students are rascals.”

  1. Explain how the Venn diagram shows the standard-form statement you created for #1 is FALSE . (Think here about how you’d explain to a class mate how your diagram shows the statement to be false—that is, “Well, see, if you look here, you’ll see blady blah… and that means bleedy blah… because blowdy blah”)

By shading in circle 1, you are referring to all logic students. And by the circled X in circle 2, you are saying if any, at least ONE must be there. Because, referring to all can be 1 or more persons.

Problem #2

  1. Answer ONE of the following question with a TRUE standard-form categorical proposition:

What kind of college student is always successful?

OR

What kind of college student is never successful?

All good college students are successful.

  1. Assume the standard-form statement you created for #1 above is TRUE , and then use the rules of conversion, obversion, contraposition, contraries, subcontraries, subalternation, or contradiction to create one other standard-form statement that is necessarily FALSE. (NOTE: you may need to use more than one rule to create a false statement)
  2. Identify the rule that proves the standard-form statement you created for #2 FALSE .

Contraries

  1. Assume the standard-form statement you created for #1 above is TRUE , and then use the rules of conversion, obversion, contraposition, contraries, subcontraries, subalternation, or contradiction to create two other standard-form statements that have LOGICALLY UNDETERMINED truth values. (NOTE: remember: you create logically undetermined statements by using rules in ways you’re not allowed to—for example, illicit conversion. You may need to use more than one rule to create an undetermined statement.)
  2. Explain why the truth values of the standard-form statements you created for #4 are LOGICALLY UNDETERMINED .
  3. In order, if you obvert, then subalternate, then convert, and then contrapose the standard-form statement you created for #1 what statement results? (“ in order” means that you first obvert, then using the new sentence you created subalternate, then using that new statement, convert, and so on. Show every step and identify each operation.)
  4. What is the truth value of the final statement you created for #6?
  5. Create a labeled Venn diagram for the statement you created as your answer to number 1. Be sure to label your Venn diagram using the method described by Hurley.
  6. Explain how the Venn diagram shows the statement you created for number 1 to be true.
  7. Using the statement you created for #1 above, apply the rule of conversion, obversion, contraposition, contraries, subcontraries, subalternation, or contradiction to create a valid standard-form categorical immediate inference. What results should be something like “All A are B. Therefore, Some A are B.” Or something like that.
  8. Justify the soundness of the immediate inference by explaining why you believe the premise to be true. (this means that you explain why you think the premise of your immediate inference is a TRUE statement; DO NOT explain why the argument is valid or why the conclusion is true. Explain why you believe the premise is a true statement.)
  9. What reasons would someone offer for rejecting the premise of your immediate inference? In other words, what might cause them to believe your premise is FALSE ?

Problem #3

  1. Answer the following question with a single standard-form categorical statement: What kind of animal is a good indoor pet? (argument)

Some fish are good indoor pets

  1. Using the standard-form statement you created for #1 above, apply the rule of conversion, obversion, contraposition, contraries, subcontraries, subalternation, or contradiction to create a valid standard-form categorical immediate inference ( be sure to write BOTH the premise and the conclusion in ordinary language) .

Some fish are good pets

Therefore, some good pets are fish

  1. Symbolize the argument you created by reducing the categories to terms ( be sure to indicate which letters symbolize which categories).
  2. What kind of proposition (A, E, I, O) is the premise proposition of the immediate inference you created in #2?
  3. What kind of proposition (A, E, I, O) is the conclusion proposition of the immediate inference you created in #2?
  4. Prove the argument valid by illustrating it with a Venn diagram. Be sure to label the circles of your diagram in the manner described by Hurley.

Some fish are good indoor pets

  1. Explain why you believe the argument is sound. In other words, given that the form is valid, what reasons can you offer to prove the premise true? (this means that you explain why you think the premise of your immediate inference is a TRUE statement; DO NOT explain why the argument is valid or why the conclusion is true. Explain why you believe the premise is a true statement.)
  2. What reasons would someone offer for rejecting the premise of your immediate inference? In other words, what might cause them to believe your premise is FALSE ?

Problem #4

  1. Create a sound, ordinary-language, standard-form immediate inference that addresses ONE of the following topics (be sure to write both the premise and the conclusion in ordinary language):

Chase Camargo

Youtube

Sports

Sexual harassment

Politics

Gun control

Celebrities

Marijuana

Alcohol

Music

Morality

Gardening

Technology

College

“All people who garden are plant lover.”

Therefore, some people who garden are plant lovers.

(Don’t use)

  1. What kind of statement (A, E, I, O) is the premise statement of the immediate inference you created in #1?
  2. What kind of statement (A, E, I, O) is the conclusion statement of the immediate inference you created in #1?
  3. Symbolize the argument you created by reducing the categories to terms (be sure to indicate which letters symbolize which categories).
  4. Prove the argument valid by illustrating it with a Venn diagram. Be sure to label the circles of your diagram in the manner described by Hurley.
  5. Explain why you believe the argument is sound. In other words, given that the form is valid, what reasons can you offer to prove the premise true? (this means that you explain why you think the premise of your immediate inference is a TRUE statement)
  6. What reasons would someone offer for rejecting the premise of your immediate inference? In other words, what might cause them to believe your premise is FALSE ?
  7. In order, obvert, then contradict, then contrapose, and then subalternate the standard-form statement you created as a premise in #1. (“ in order” means that you first obvert, then using the new sentence you created subalternate, then using that new statement, convert, and so on. Show every step and identify each operation.)
  8. What is the truth value of the proposition you created for #8?

Argument Construction #2: Categorical Syllogisms

Assignment

For this argument construction assignment, you will use your knowledge of categorical logic.  It is extremely important that you read the instructions for each individual problem very, very carefully and that you do exactly what you are asked to do.  It is also extremely important that you show your work for each step of each problem.  

IMPORTANT: YOU SHOULD ASSUME THE ARISTOTELIAN STANDPOINT AND USE THE TRADITIONAL SQUARE OF OPPOSITION FOR EACH PROBLEM.

ALSO IMPORTANT: You may type your responses to each question using the electronic version of this form or you may handwrite your responses on this form.  If you handwrite, print legibly. 

Argument #1

1. Construct a SOUND standard-form, ordinary-language (this means you use real words like the ones you’re reading now) categorical syllogism that provides an argument in response to the following question: Is spanking an effective form of discipline for children? (IMPORTANT: Your conclusion should DIRECTLY answer the question posed.)

2. Symbolize the argument you created by reducing the categories to terms (be sure to indicate which letters symbolize which categories).

3. What is the form (mood + figure) of the argument you constructed?

4. Prove the argument valid by illustrating it with a Venn diagram.  Be sure to label the circles of your diagram in the manner described by Hurley.

5. Justify the soundness of the categorical syllogism by explaining why you believe the premises are BOTH true. (this means that you explain why you think the premises of your syllogism are TRUE statements; DO NOT explain why the argument is valid or why the conclusion is true. Explain why you believe the premise is a true statement.)

6. To which premise(s) of the argument is someone most likely to object, and what are likely to be the objections to this premise(s)? In other words, which premise(s) do you think someone could legitimately claim is false?

Argument #2

1. Construct a SOUND, standard-form, ordinary language categorical syllogism that provides an argument in response to the following question: What is good (pick one) beer, beach, restaurant, bookstore, clothing store, hike, park, surf spot, mountain bike trail, movie, sledding spot) in Humboldt County?

2. Symbolize the argument you created by reducing the categories to terms (be sure to indicate which letters symbolize which categories).

3. What is the form (mood + figure) of the argument you constructed?

4. Prove the argument valid by illustrating it with a Venn diagram. Be sure to label the circles of your diagram in the manner described by Hurley.

5. Justify the soundness of the categorical syllogism by explaining why you believe the premises are BOTH true. (this means that you explain why you think the premises of your syllogism are TRUE statements; DO NOT explain why the argument is valid or why the conclusion is true. Explain why you believe the premise is a true statement.)

6. To which premise(s) of the argument is someone most likely to object, and what are likely to be the objections to this premise(s)? In other words, which premise(s) do you think someone could legitimately claim is false?

Argument #3

1. Construct a SOUND, standard-form ordinary-language categorical syllogism that provides an argument in response to the following question: Can pets be family members with humans?

2. Symbolize the argument you created by reducing the categories to terms (be sure to indicate which letters symbolize which categories).

3. What is the form of the argument you constructed?

4. Prove the argument valid by illustrating it with a Venn diagram. Be sure to label the circles of your diagram in the manner described by Hurley.

5. Justify the soundness of the categorical syllogism by explaining why you believe the premises are BOTH true. (this means that you explain why you think the premises of your syllogism are TRUE statements; DO NOT explain why the argument is valid or why the conclusion is true. Explain why you believe the premise is a true statement.)

6. To which premise(s) of the argument is someone most likely to object, and what are likely to be the objections to this premise(s)? In other words, which premise(s) do you think someone could legitimately claim is false?

Argument #4

1. Construct a SOUND standard-form, ordinary-language categorical syllogism that provides an argument in response to ONE of the following questions: 

Can computers think?

Do humans have souls?

Is non-reproductive incest between consenting adults wrong?

Is war ever morally justifiable?

Is Justin Beiber’s (or any other pop artist’s) latest song a “work of art?”

 Do bans on assault rifles make citizens safer?

2. Symbolize the argument you created by reducing the categories to terms (be sure to indicate which letters symbolize which categories).

3. What is the form (mood + figure) of the argument you constructed?

4. Prove the argument valid by illustrating it with a Venn diagram. Be sure to label the circles of your diagram in the manner described by Hurley.

5. Justify the soundness of the categorical syllogism by explaining why you believe the premises are BOTH true. (this means that you explain why you think the premises of your syllogism are TRUE statements; DO NOT explain why the argument is valid or why the conclusion is true. Explain why you believe the premise is a true statement.)

6. To which premise(s) of the argument is someone most likely to object, and what are likely to be the objections to this premise(s)? In other words, which premise(s) do you think someone could legitimately claim is false?

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