Ethics Courses

Dr. Callahan

PHILOSOPHICAL METHOD:

LOGIC ASSIGNMENT

1. To defend a philosophical position (or a solution to a philosophical problem) is to give reasons for holding that position. When we talk about giving reasons in philosophy, we are talking about offering arguments for (or against) a certain position or view. The readings we shall study in this course will present certain philosophical views or positions on questions of moral importance. In order to understand what these positions are and whether they ought to be accepted, we shall need to be able to identify and evaluate the arguments our authors give for their positions.

2. An argument is a group of statements or propositions in which one statement, the conclusion, is claimed to follow from the others, which are the premises. The examples of arguments that follow all have two premises and a conclusion. But don't let this mislead you -- arguments usually have more than two premises. Two-premise arguments are offered here as examples just for the sake of simplicity and clarity.

Therefore______________________________________________

(ii) MODUS PONENS: LOGICAL FORM:

Therefore________________________________________________

3. It is important to realize that 'premise' and 'conclusion' are relative terms. That is, a statement that is a conclusion in one argument may serve as a premise in another and vice versa. For example:

4. Arguments are evaluated on the bases of their logical structures and the truth values (or probable truth values or reasonableness) of their premises. The two concepts used to evaluate arguments are validity and soundness.

5. Validity is a property of arguments ( not statements -- thus, validity is not a property of premises or conclusions). Whether an argument is valid is a function of its structure or form alone. An argument is said to be valid when its premises and conclusion are so related by its structure or form that if all of the premises are true, the conclusion must be true. That is, if an argument is valid in form and all of its premises are true, it would be impossible for the conclusion to be false. Or, again, an argument is valid when, if its premises were true, its conclusion would have to be true. Thus, a valid argument with all true premises necessarily has a true conclusion. An argument is valid, then, in virtue of its form or structure alone. Recall the example of an argument at (i) above. That argument has this form:

C is B

This structure tells us that everything that belongs to class (group) A also belongs to class B; C belongs to class A; therefore, C belongs to class B. If it is true that everything that belongs to A also belongs to B (i.e., that there is no A that is not also B), and if it is true that C is A, then C is necessarily B (since C is A and there is no A that is not also B). This, then, is an example of a valid argument -- if its premises are true, its conclusion is necessarily true. This is why valid argument forms are truth-preserving; valid arguments preserve the truth of their premises in their conclusions. That is, if their premises are true, valid argument forms preserve that truth in their conclusions.

6. Soundness is also a property of arguments ( not statements). An argument is sound when (a) its form is valid and (b) its premises are all true. Since this is how soundness is defined, an argument can be unsound for one of two reasons -- (a) its form is invalid or (b) it has at least one false premise. Notice that a valid argument can have a false conclusion (if at least one of its premises is false). But a sound argument (by definition) never has a false conclusion, since (by definition) a sound argument is (a) valid and (b) has all true premises.

(iv)


All dogs are cats. (All A is B)

Lassie is a dog. (C is A)

__________

Lassie is a cat. (C is B)

Argument (iv) is valid in form (see our previous example), but it is unsound because its first premise is false.

(vi)


7. In this course, we shall be interested in sound arguments, or (minimally) arguments that are always valid in form and that have premises that can be well defended. We shall be looking for soundness in arguments in the readings, in lecture and discussion, and in the arguments you put forward in support of your own views on the issues we'll examine.

8. It is important to realize that the fact that an argument is unsound (either because it is invalid in form or has at least one false or highly questionable premise) does not entail that the argument's conclusion is false. Recall Argument (v) above -- that argument is unsound, but its conclusion is true. And the same is true of the following argument, which has the same structure as Arguments (v) and (vi) and has a false premise:

9. Most of the arguments we'll be reading, considering, and developing in this course will not be presented in the straightforward forms of those presented above as examples. Your own arguments (you'll see!) will be developed in ordinary prose, and you often will have to extract the arguments of our authors (and your instructor) from ordinary prose. A central aim of this course is to have you do this development and extraction of arguments with relative ease and consistent success.

10. Missing premises. As you read for this course (and as you read for other courses and do ordinary reading, e.g., of newspapers), you'll often find that authors do not make all of their premises explicit. This is, philosophically speaking, a bad habit, and one which you should avoid making in arguing for your own positions (in class and out of class). Still, it does go on, and one sometimes needs to tease out and clarify missing premises that are assumed in an argument. Consider the following argument:


(ix)

You should not believe unreliable people.

Teenagers (or Democrats, or Christians, or gays, or . . .) are unreliable people.

"They" are teenagers (or . . .)

________________________

You should not believe them.

Although this argument is valid in form, how would you comment on the soundness of this argument, filled out with 'Christians,' 'gays,' 'men,' 'women,' etc.?

11. There is much more that can be said about logic and arguments, and some of it will emerge as the course goes along. But this should be enough to get us started. (If you are interested in logic, there are whole courses in it offered by the Philosophy Department; or there are fine "teach yourself" books around.)

EXERCISES TO BE PREPARED FOR CLASS

Please do the following exercises on a separate sheet. You won't be required to hand them in; but if, after going over them in class, you'd like them looked at, feel free to hand them in. BE SURE TO DO THE EXERCISES -- THERE MAY BE A LOGIC QUESTION ON THE MIDTERM (see the Supplemental Study Questions), AND DOING THE EXERCISES WILL PREPARE YOU FOR ANY SUCH QUESTION.

(1) Use the following valid argument form to create two arguments of your own. Use true premises in both arguments, and make sure you consistently substitute the same terms for A, B, and C within each argument. You will be creating two sound arguments.

All A is B

C is A

___________

C is B

(2) To see how unreliable invalid arguments are, use the following in valid argument form to create three arguments.

All A is B

C is B
________________

C is A

(3) Use the following valid argument form to create two sound arguments. Say exactly what you need to add to this form to create sound arguments.

(4) The following argument form is invalid. In order to prove that it is invalid, create two arguments with obviously true premises that lead to an obviously false conclusion.

(5) Supply the missing premises for the following arguments, and say for each argument as filled out, whether it seems sound and why this is your judgment.

(h) Since white men generally make more money than women and black men, white men generally are smarter than women and black men.




SAMPLE ANSWERS TO THE LOGIC EXERCISES TO COMPARE WITH YOUR OWN

(1) Two examples, valid structure, true premises --

___________________________________________________________________________

(2) Three examples, invalid form --

___________________________________________________________________________
(3) Valid structure, make two sound arguments (add true premises) --

___________________________________________________________________________

(4) Prove that this form is invalid ---

(5) Supply the missing/suppressed/assumed premises [SP] and say whether the argument seems sound. Give reasons for your judgments on soundness.

______________________________________

_____________________________________

_____________________________________

___________________________________________________________________________
Each of the above arguments can be put into a valid form. But once put into a valid form, each contains at least one seriously questionable or false premise. Thus, none of these arguments is obviously sound and some are obviously unsound. Much of our concern in this course will be with questioning the acceptability of premises in arguments. As you read the selections assigned, extract the arguments being offered by our authors, and ask yourself whether those arguments contain any seriously questionable premises. And, as you construct arguments for your own positions on the moral problems and cases we discuss, ask yourself if your positions are leaning on any questionable premises. If they are, push deeper and think through any prior arguments that might be needed to justify your premises. As we shall see, the kinds of problems and cases we'll be discussing in this course don't lend themselves to easy resolution, and there will often be disagreements among us on how a given problem or case should be resolved. However, we'll also find that some arguments for some conclusions are really very bad arguments. Much of what we do in the course will have to do with recognizing bad arguments and finding the most plausible arguments for various positions. A large part of the task in this course, then, will involve having you develop careful, plausible arguments for the positions you think are correct on the problems and cases we'll confront.