One of the most practical lessons in Introductory Logic is Lesson 32, “Establishing Conclusions.” Here you are no longer analyzing someone else’s arguments; you are now writing your own. The hardest part of this lesson is developing an argument for a conclusion while being allowed to use any valid form. In the video for this lesson, I encourage you to find a middle term that connects to the major and minor terms in the conclusion. Let me suggest another way to continue this process.
If you understood hypothetical syllogisms well in the lesson prior, you may use them to help you develop a valid argument. For example, in Exercise 35, question 2, you are asked to establish this conclusion (straight out of Calvin and Hobbes):
Ask yourself why bats aren’t bugs. You might say, “Because mammals are not bugs.” Turn that into a hypothetical statement, and complete the modus ponens:
If a creature is a mammal then its not a bug.
Bats are mammals. Therefore, bats aren’t bugs.
This easily converts into the required EAE-2.
No bugs are mammals.
All bats are mammals.
∴ No bats are bugs.
For an example in which the form is not given, consider question 6, where you are asked to establish this conclusion:
Whoever turns away from Christ cannot be His disciple.
Ask yourself why this is. You may say, “Because only followers of Christ are His disciples.” Good. Now let’s turn that into a hypothetical statement. Keeping the “only” in mind (which switches the terms), it should be translated, “If one is Christ’s disciple, then one follows Christ.” Then complete the modus tollens:
If one is Christ’s disciple then one follows Christ.
Whoever turns away from Christ does not follow Him.
Therefore, whoever turns away from Christ cannot be His disciple.
This can be converted into an AEE-2 syllogism for the assignment.
What about if the conclusion is particular? Consider this example:
Some killing is not murder
What is some killing that is not murder? Well, legal executions are not murder. Turn this into a hypothetical statement, and try the modus ponens:
If it’s a legal execution then it’s not a murder.
Some killings are legal executions.
Therefore, some killing is not murder.
Note that, if the conclusion is affirmative, try using modus ponens. If the conclusion is negative, and your hypothetical is negative, then again use modus ponens. But if the conclusion is negative and your hypothetical statement is affirmative, try using modus tollens.
Arguments in real life do not need to be in categorical form, and it is easier to think of modus ponens and modus tollens arguments in real-time. This may help you develop arguments to establish conclusions in real life more quickly.