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
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:
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)
Identify the rules that prove the statements you created in #2 false.
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)
Identify the rules that prove the standard-form statements you created for #4 TRUE.
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).
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”)
Problem #2
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?
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)
Identify the rule that proves the standard-form statement you created for #2 FALSE.
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.)
Explain why the truth values of the standard-form statements you created for #4 are LOGICALLY UNDETERMINED.
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.)
What is the truth value of the final statement you created for #6?
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.
Explain how the Venn diagram shows the statement you created for number 1 to be true.
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.
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.)
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
Answer the following question with a single standard-form categorical statement: What kind of animal is a good indoor pet?
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).
Symbolize the argument you created by reducing the categories to terms (be sure to indicate which letters symbolize which categories).
What kind of proposition (A, E, I, O) is the premise proposition of the immediate inference you created in #2?
What kind of proposition (A, E, I, O) is the conclusion proposition of the immediate inference you created in #2?
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.
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.)
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
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):
Youtube
Sports
Sexual harassment
Politics
Gun control
Celebrities
Marijuana
Alcohol
Music
Morality
Gardening
Technology
College
What kind of statement (A, E, I, O) is the premise statement of the immediate inference you created in #1?
What kind of statement (A, E, I, O) is the conclusion statement of the immediate inference you created in #1?
Symbolize the argument you created by reducing the categories to terms (be sure to indicate which letters symbolize which categories).
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.
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)
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?
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.)
What is the truth value of the proposition you created for #8?