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Lecture 4 Notes

Forms of Arguments
The authors of your textbook identify a few of the many valid forms of arguments. The first is called “modus ponens” (page 58). The example they provide is:
(1) If it is snowing, then the roads are slippery.
(2) It is snowing.
———————
∴ (3) The roads are slippery. (from 1–2)
The form is:
(1) If A, then B.
(2) A
—————
∴ (3) B. (from 1–2)
The authors urge you not to confuse “modus ponens” with an unnamed but invalid form. It looks like this:
(1) If A, then B.
(2) not-A
—————
∴ (3) Not-B. (from 1–2)
Now, recall that if the form is invalid, then every instance where the form appears in an argument is invalid. So, for example (from the book), the following is invalid because it has the above form:
(1) If it is snowing, then the roads are slippery.
(2) It is not snowing.
———————
∴ (3) The roads are not slippery. (from 1–2)
In just a bit, I will provide an informal method to help you determine why the above argument is invalid yourself (without having to memorize valid and invalid forms). Intuitively, you might see it right away: It might have just stopped snowing, or ice might make the roads slippery. In just a case, the conclusion doesn’t follow from the premises, or more precisely (and I expect the precise answers for the quizzes and midterms): it is possible for the premises (1) and (2) to be true and the conclusion (3) false.
The text offers another example on page 58 that the authors call “process of elimination.” The example is:
(1) Either Joe or Jack or Jim or Jerry committed the murder.
(2) Joe didn’t do it.
(3) Jack didn’t do it.
(4) Jim didn’t do it.
————————-
∴ (5) Jerry committed the murder. (from 1–4)
You can probably see very quickly why such argument forms are valid. If not, read the author’s blurb. The form of the argument is this:
(1) Either A or B or C or D is X.
(2) A is not X.
(3) B is not X.
(4) C is not X.
——————–
∴ (5) D is X.
Don’t confuse the process of elimination with the following invalid form:
(1) Either A or B or C or D is X.
(2) A is X.
——————–
∴ (3) D is not X.
The example the authors use is this:
(1) Either Joe or Jack or Jim or Jerry committed the murder.
(2) Joe did it.
————————-
∴ (3) Jerry did not commit the murder. (from 1–4)
Intuitively, you might be able to see why the argument form is invalid—that is, it is possible for the premises to be true and the conclusion false (definition of invalidity). If you don’t, then don’t worry—I’m about to tell you how to figure it out.
——————-

1. To test for validity: easier to test for INvalidity.
Invalidity:  It is possible for the premises to be true and the conclusion false.
2. Isolate the form of the argument.
Convert sentence content into contentless symbols.
3. Look to see if I can invent a case in which the premises are in fact true, and the conclusion is false.
4. If I can find ONE example, then the argument form is invalid.
D. Soundness.
Must have these two properties:
a. argument is in valid form.
b. premises are true.
E. Tricky case.
Nigeria is in Africa.
Therefore, Nigeria is in Africa.
A = Nigeria is in Africa.
A
Therefore, A.
Is it valid?  Is it sound?  Is it a good argument?
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