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.
Examples of (valid) arguments:
(i) A CATEGORICAL SYLLOGISM - LOGICAL FORM
premise 1: All humans are mortal. = All A is B
premise 2: George Bush is human. = C is A
Therefore______________________________________________
conclusion: George Bush is mortal. = C is B
(ii) MODUS PONENS: LOGICAL FORM:
premise 1: If it is raining, the streets are wet. = If p, then q
premise 2: It is raining. = p
Therefore________________________________________________
conclusion: The streets are wet. = q
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:
(iii) All mortals will die.
Madonna is mortal.
_____________________
Madonna will die.
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:
All A is B
C is A
________
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.
(v)
All dogs are mortal. (All A is B)
Lassie is mortal. (C is B)
_________
Lassie is a dog. (C is A)
Argument (v) has true premises, but it is unsound because its form is not valid. That is, we can plug true premises into the form of Argument (v) and derive an obviously false conclusion.Consider the following argument, which has the same form as (v) and which also has true premises, but which has a false conclusion:
(vi)
All UK students are mortal. (All A is B)
Brad Pitt is mortal. (C is B)
_________________
Brad Pitt is a UK student. (C is A)
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:
(vii)
All heads of state are famous men. (All A is B)
George Bush is a famous man. (C is B)
_____________________
George Bush is a head of state. (C is A)
Even though this argument "goes wrong" in two ways (it is invalid in form and the first premise is false because some heads of state are women), it has a true conclusion. Finding that an argument is unsound, then, only allows one to say that a bad argument has been given for a certain conclusion. That is, unless the conclusion is obviously false, it may be true. All we know is that one cannot soundly argue for the conclusion on the basis of the particular argument offered, and that no one needs to accept the conclusion on the basis of that argument.
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:
Don't believe them -- they're teenagers (or Democrats, or Christians, or gays, or men, or women, or . . .)
Argument (viii) is a condensed argument that rests on suppressed (or hidden, inexplicit) assumptions which serve as premises, and is a shortened version of the valid 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
(a) In your first argument, use true premises and derive a true conclusion.
(b) In your second argument, use at least one false premise and derive a true conclusion.
(c) In your third argument, use true premises and
derive a false conclusion.
(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.
If p, then q
p
____________
q
(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.
If p, then q
q
____________
p
(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.
(a) Fetuses are innocent human beings -- they should not be killed.
(b) It's alright for Mary to lie to protect David -- she's his lawyer.
(c) The Republicans ought to be in power -- my father says so.
(d) The Democrats ought to be in power -- my mother says so.
(e) Knowing she has cancer will greatly upset Mrs. Green, so Dr. Blue shouldn't tell her about it.
(f) General Electric's managers aren't morally blameworthy for trying to fix prices; they were only trying to maximize profits for their shareholders.
(g) Euthanasia, whether requested or not, takes an innocent human life, thus no doctor or nurse should assist with it.
(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 --
All A is B
C is A
_________
C is B
(a) All Wranglers are Jeeps. (T)
Sherry's car is a Wrangler. (T)
_______________________
Sherry's car is a Jeep. (T)
(b) All dogs are canine. (T)
Lassie is a dog. (T)
___________________
Lassie is canine. (T)
___________________________________________________________________________
(2) Three examples, invalid form --
All A is B
C is B
______________
C is A
(a) True premises, derive true conclusion:
All Queens of England are women. (T)
Queen Elizabeth is a woman. (T)
____________________
Queen Elizabeth is a Queen of England. (T)
(b) At least one false premise, derive true conclusion:
All U.S. presidents have been African American.
(F)
George Bush is African American. (F)
_________________________
George Bush is a U.S. president. (T)
(c) True premises, derive a false conclusion:
All automobiles are complex objects. (T)
Alison's computer is a complex object. (T)
_____________________
Alison's computer is an automobile. (F)
___________________________________________________________________________
(3) Valid structure, make two sound arguments (add true premises) --
If p, then q
p
__________________
q
(a) If Bush won, Gore lost. (T)
Bush won. (T)
_______________________
Gore lost. (T)
(b) If UK is in Lexington, it's not in Chicago. (T)
UK is in Lexington. (T)
___________________
UK isn't in Chicago. (T)
___________________________________________________________________________
(4) Prove that this form is invalid ---
If p, then q
q
_______________
p
Give two examples to prove it is invalid
(i.e., put in true premises and derive a false conclusion):
(a) If his starter is broken, Chip's car won't start. (T)
Chip's car won't start. (T)
_______________________
Chip's starter is broken. (F)
In fact, Chip's starter is just fine -- his car won't start because its battery is dead.
(b) If Kate's alarm goes off at six, she'll be on time for the trip. (T)
Kate is on time for the trip. (T)
__________________________
Kate's alarm goes off at six. (F)
In fact, Kate forgot to set the alarm, but her roommate's snoring woke her up at 5:45 and she had plenty of time to get ready.
___________________________________________________________________________
(5) Supply the missing/suppressed/assumed premises [SP] and say whether the argument seems sound. Give reasons for your judgments on soundness.
(a) It is wrong to kill an innocent human being. [SP] (?)
Fetuses are innocent human beings. (?)
_______________________
It is wrong to kill fetuses. (?)
Problem: There is an ambiguity in the first two premises -- two senses of 'human being' are involved. Premise 1 is generally acceptable if we understand 'human being' to mean 'person' (i.e., a moral being with the full range of moral rights). But if we put this meaning of 'human being' into premise 2, that premise is open to serious question. Premise 2 is only obviously true if we take 'human being' to mean something like 'of the biological species homo sapiens'. In order to make both premises obviously acceptable, then, we must substitute quite different meanings for 'human being' in the first two premises, with premise 1 taking 'human being' in the moral sense as 'person,' in premise 2 taking 'human being' in the biological sense. But now, 'human being' is a different term in premise 1 and premise 2, and we get the following structure, which fails to entail the conclusion offered:
All A is B
C is D
________________
C is B
This conclusion simply does not follow from the premises. So, we have a complicated problem in this first argument. Either we keep the moral meaning for 'human being' throughout the argument and accept that the argument is not obviously sound because premise 2 is questionable; or we keep the biological meaning of 'human being' throughout the argument and accept that the argument is not obviously sound because premise 1 is questionable; or we substitute two meanings for 'human being' in the premises, thereby making each premise alone uncontroversially acceptable, but thereby also rendering the argument invalid, and therefore unsound. So, this argument seems to be unsound no matter how we try to patch it up. The only hope for redeeming this argument would be a prior argument justifying the moral use of 'human being' in premise 2 or the biological use of 'human being' in premise 1.
______________________________________
(b) It is morally permissible for lawyers to lie to protect their clients. [SP] (?)
Mary is David's lawyer. (T)
_____________________
It is morally permissible (alright) for Mary to lie to protect David. (?)
Problem: First premise here is seriously questionable, thus we can't accept this argument as sound. We would need a prior argument to justify the first premise.
_____________________________________
(c) Whatever my father says is correct. [SP] (?)
My father says the Republicans ought to be in power. (T)
____________________
The Republicans ought to be in power. (?)
Problem: Fathers can make mistakes on such matters, so we cannot accept
the first premise as true, thus we cannot conclude that the argument is
sound.
_____________________________________
(d) Whatever my mother says is correct. [SP] (?)
My mother says the Democrats ought to be in power. (T)
________________________
The Democrats ought to be in power. (?)
Problem: Mothers can make mistakes on such matters, so we cannot accept the first premise as true, thus we cannot conclude that the argument is sound. Same problem as in (c).
_____________________________________
(e) Doctors should not tell their clients things that will upset them. [SP] (?)
Telling Mrs. Green she has cancer will greatly upset her. (T)
________________________
Dr. Blue should not tell her. (?)
Problem: Same as in (b) -- we need further
argument to justify premise 1. Without further argument, this is a highly
questionable premise, and we can't conclude that the argument is sound.
__________________________________
(f) It is morally permissible for corporations to try to fix prices to maximize their shareholder profits. [SP] (?)
GE's managers tried to fix profits to maximize their shareholder profits (T)
___________________
GE's managers are not morally blameworthy for
trying to fix prices. (?)
Problem: Same as in (b) and (e) -- the first premise is seriously questionable and cannot be accepted without further argument.
_____________________________________
(g) No doctor or nurse should assist in taking an innocent human life. [SP] (?)
Euthanasia, whether requested or not, takes an innocent human life. (T)
______________________
No doctor or nurse should assist in euthanasia.
(?)
Problem: Same as in (b), (e), and (f) -- first premise cannot simply be
assumed, we need a prior argument defending it. Thus, it is not clear that
this argument should be accepted as sound.
_____________________________________
(h) Those who make more money are smarter than those who make less. [SP]
(F) .
In general, white men make more money than women and black men. (T)
___________________
In general, white men are smarter than women
and black men. (F)
Problem: The first premise and conclusion are patently false, so this argument is clearly unsound.
___________________________________________________________________________
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.