Sample Exam1 Essay Answers

1. The difference between inductive and deductive arguments.

In order to explain the difference between inductive and deductive arguments, we first need to clarify what we understand by the term "argument". In everyday situations, when two people have an argument, it means they disagree about something; in this case "argument" means "dispute". In logic, however, an argument consists of a set of statements or claims that offer reasons to accept another, final claim. The claims that express the reasons for accepting the final claim are the premises; the claim they mean to support is the conclusion. We use this kind of arguments to express how we reached a position on certain matters, and to persuade others to accept our point of view. Arguments in this sense occur in everyday situations too, e.g., "You shouldn’t drink so much coffee; your blood pressure is already too high." As a matter of fact, if only we would offer more good arguments, we might end up having fewer arguments.

This brings us to the subject of what constitutes a good argument. As I pointed out above, an argument in logic consists of one or more premises and a conclusion. If the premises offer good reasons to accept the conclusion --in other words if they support the conclusion, we say that the argument has good logic. If the premises fail to support the conclusion, i.e., the conclusion does not follow, the argument has bad logic. However, having good logic does not necessarily make the argument good; it only means that the conclusion follows from the premises, and that if the premises are true or reasonable to believe, the conclusion will be true or very likely. In other words, good logic is necessary, but not sufficient for a good argument; in order to determine whether an argument is good or bad, we also need to check if the premises are true or reasonable to believe, and if the statements are clear. If all this is the case, we can say we have a good argument. If we have a good argument that is deductive we call it sound. This takes us to the difference between deductive and inductive arguments.

In a deductive argument, the arguer claims that the conclusion must be true if, and only if, the premises are true. If the premises support the conclusion, we call it a valid argument: e.g.,

1. Cats have whiskers.

2. Animals with whiskers are mammals.

C. Cats are mammals.

This is a deductive argument that is valid and has true premises . We call this a sound argument.

A deductive argument can also have good logic even if the premises are false. This is still a valid argument, but it is not sound. Here is an example.

1. All birds can fly.

2. A penguin is a bird.

C. A penguin can fly.

This is a valid argument, but a penguin clearly cannot fly. The premise "all birds can fly" is false.

If a deductive argument has bad or incorrect logic -- the premises do not support the conclusion even if the premises are true, we call the argument invalid. E.g.,

1. All humans are mammals.

2. My cat is a mammal.

C. My cat is a human.

1. When I take a shower, I get wet.

2. I’m wet.

C.I must have taken a shower.

Both conclusions are false: my cat, clearly, is not a human, and I could have just fallen in the pool, or even stepped out in the rain. Both arguments commit the fallacy of affirming the consequent. These examples show that truth value of the premises is irrelevant for the validity of an argument and that validity relies solely on the logical form.

However, as we have already pointed out, when a deductive argument has good logic but false premises, or true premises but bad logic, the argument is flawed and we should reject its conclusion. It is unsound. If a deductive argument is clear, valid and has all true premises, we have a sound argument and we have every reason to accept its conclusion.

In an inductive argument, the arguer claims that the conclusion is highly likely if the premises are true. If a inductive argument has good logic, we call it a strong argument. If a inductive argument has bad or incorrect logic we say the argument is weak.

Here are a few examples:

1. Most students at a community college live within a 20 mile radius of the campus.

2. WVC is a community college.

3. Abby is a student at WVC.

4. She must live within a 20 mile radius of WVC.

This conclusion is very plausible because the premises are relevant to the conclusion. We may say that this argument is likely.

1. Marc and Tom are both students at WVC.

2. Marc is tall and so is Tom.

3. Marc and Tom are both 20 years old.

4. Marc majors in math, and so does Tom.

5. Marc is on the basketball team.

6. Tom must be on the team, too.

This conclusion comes from nowhere. There are no premises that are relevant to our conclusion, except maybe that Marc and Tom are both tall. The argument says nothing about athletic abilities, which Marc more than probably has, since he is on the basketball team. However, that doesn’t mean that Tom is athletic and can play ball.

We can conclude that, in order for an inductive argument to be strong, it should have reasonable premises that are relevant to the conclusion.

Reasonable people should believe the conclusions of sound arguments because a sound argument is an argument that is clear, i.e., free from ambiguity or vagueness,has good logic and true premises. Since we know that if an argument has good logic its conclusion MUST be true if all the premises are true, it is obvious that the conclusion of a sound argument is true. Therefore, it is obvious that any reasonable being should accept the conclusion of a sound argument. We can actually prove this by putting our reasoning in a standard valid deductive argument form. Our argument becomes immediately clear if we arrange the claims so that the premises precede the conclusion they want to support. Using this procedure, our argument becomes:

1. A sound argument has good logic and all true premises.

2. If an argument has good logic and all true premises, its conclusion MUST be true C A sound argument has a true conclusion. 1,2

Using variables and symbols, we recognize our argument as a form of Hypothetical Syllogism..

We will use the following variables: SA - sound argument

VA - an argument has good logic (valid arg.)

TP - all true premises

TC - true conclusion

1. SA --> VA.TP

2. VA.TP --> TC

C SA --> TC (1,2) q.e.d.

If we want to critically analyze any argument, we first have to try to put it in standard form. This means we have to identify the premises and the conclusion, or conclusions in the case of complex arguments. After careful reading, and without worrying too much about obvious vagueness of the statements, I came up with the following argument:

1. Whatever people say, they’re just expressing their personal opinions. PS--> OP

2. Opinions are subjective. OP-->S

3. Nobody can be objective. (1, 2) (Whatever people say is subjective.) PS-->S
(Unstated premise: People are either subjective or objective. S v OB )

4. Knowledge requires objectivity. K-->OB

5. Therefore, there is really no such thing as (objective) knowledge. (3,4) not K

6. Honest opinions are equally correct. (5) OP-->C

(If there is no objective standard, then any opinion is as good as another.)

7. Also, we all live in our own private little worlds. PR

8. No private reality is more real than anyone else’s.

9. Therefore, all private realities are equally real. (equivalent to 8) PR-->R

10.There is no such thing as objective reality. (7,8,9) not OR

This looks like a deductive argument because the arguer claims that the premises support the conclusion, i.e., if the premises are true, the conclusion must follow. In order to check the validity, I have already represented each premise by variables to the right, but I will come back to this later. First we have to check the clarity of the statements and make sure we know what they mean.

In putting the argument in standard form, I have discarded some of the statements because they are objectionably vague and, therefore, only succeed in complicating the argument needlessly. I identified the following statements as irrelevant to the argument:

a) Every person’s set of personal experiences is unique. This is obviously true, but it is also very vague and I don’t see how it furthers the argument. The arguer should specify what she means by the term "unique." Does she mean unique in the sense of "only from the point where I am standing," at that particular time of day, and therefore, different every single time? Does she mean "unlike any other set of experiences I might have" or "unlike anyone else’s experiences?" This is confusing. However, if she would state: "Every person’s experiences are subjective," it would be relevant for the argument against objectivity, and I would include it in the standard form.

b) Every person comes from somewhere. So? What does that mean? Does it mean I cannot be objective because I come from Belgium, and my friend cannot be objective because she comes from Japan? What about Americans? Do they have more chances of being objective because their ancestors come from all over the world? Or does "somewhere" mean something different? Please clarify.

c) There is no "view from nowhere." Same problem. Does this mean there is no such thing as "nowhere," so there cannot be a view from there? Or does "nowhere" exist, but is there simply no view from "there?" Of course, it’s difficult for anyone to have a view from "nowhere," if we all come from "somewhere," unless there happened to be someone there, "nowhere" who also has a view from there. It’s all a little confusing; we need better definitions.

After this first step in the clarity check of the statements, there still remain some very ambiguous terms in the argument. The arguer most notably equivocates the words, objective and subjective, but also opinion and knowledge, when she claims that all opinions are subjective, and that we cannot possibly have knowledge because knowledge requires objectivity, and we cannot be objective. Moreover, she claims there is not even an objective reality. Let’s examine this problem more closely.

On the ordinary view, "subjective" means according to someone’s beliefs, feelings, opinions, experiences. On this view "subjective" is the complete opposite of "objective", meaning that something is factual, certain, quantifiable. On top of that, we often contend that everything has to be either subjective or objective. If this is so, how can we claim that some things are objective if all we know is that we had an experience of it? In other words, how does my experience of pleasure differ from my experience of seeing the ocean? The first one is certainly subjective because only I can experience my pleasure. On the other hand, I also have a very personal experience when I’m looking at the ocean, different from anybody else’s. So this experience is also subjective. If all our experiences are "subjective," everything we experience is just an opinion, and nothing exists independently of our mind. The problem is that we associate "subjectivity" with all our experiences. Philosophers solve this problem by distinguishing two kinds of subjectivity: metaphysical subjectivity, and epistemological subjectivity. Metaphysical subjectivity exists only as experienced by someone: e.g., "My neck is sore." This does not imply that the pain is not real, only that nobody else experiences that pain. Epistemologically subjective claims, on the other hand, are claims for which there are no public methods available to decide whether the claim is true or false: e.g., "Orange juice with calcium tastes better than orange juice without." This is clearly not about knowledge; it is simply a matter of opinion.

We can, in the same way, distinguish between metaphysical objectivity, and epistemological objectivity. Metaphysical objectivity exists independently of my experience. So I can, indeed, claim that the ocean exists in a metaphysically objective way because its mode of being is public. Epistemologically objective claims are claims for which publicly available methods exist to determine whether the claim is true or false. In this case knowledge is possible. It is not just a matter of opinion: e.g., Alison’s claim "I just turned 28, yesterday" is epistemologically objective, even if in reality she turned 36. "Objective" does not mean the claim is true; it only refers to the fact that we can verify the truth or falsity of a claim.

Now that we know the distinction between metaphysical and epistemological subjectivity, and metaphysical and epistemological objectivity, we still have to refute the presupposition that everything is either subjective or objective. Let me go back to the claim: "My neck is sore." One morning, my youngest daughter woke up with just that complaint. Although I felt empathy for her --I have frequently had a sore neck myself , I could not feel her pain, and I thought a little massage would make her feel better. However, she could not stand being touched at her neck and she could not lift her head. I finally succeeded in getting her dressed, and took her to the doctor. He told me that this was a pretty common symptom of a growth spurt, and that she would need three to four days to recover. He recommended ice packs, rest, and pain relievers. This little story illustrates that something metaphysically subjective can very well be epistemologically objective. Therefore, the presupposition that everything must be either subjective or objective is false.

We can now return to the argument against objective reality and examine it in light of our findings. The arguer basically claims that there are only personal opinions, and that opinions are subjective; therefore, there is no objective truth. She even claims that there is no objective reality; there are only private, subjective worlds. It is obvious that the arguer equivocates the terms "subjective" and "objective." She uses them indiscriminately in the metaphysical and epistemological meanings. As we have demonstrated, it is not because my experience of the ocean is personal that the ocean does not objectively exist. The same goes for the claim about "our own private little worlds." It is not because we experience the world privately that the world does not objectively exist. As for the claim that "there is no such thing as knowledge," we have pointed out that knowledge is possible because there are epistemologically objective claims for which we have publicly available methods to decide about the truth value. Moreover, we have stated that personal opinions cannot express knowledge precisely because there are no public methods available for determining their truth value. We can, therefore, claim that the assertion that there are only "personal opinions" is false.

The last problem of clarity I want to point out is the mistake of the arguer to assert that because opinions are subjective, nothing can be objective. This is the misconception that something has to be either objective or subjective. We have clearly refuted this, above, with our story about the sore neck.

The remaining steps in our critical analysis are: logic check and facts check.

Let’s look at the standard form using the variables to check the logic of the argument.

1. PS-->OP

2. OP-->S

3.PS-->S 1,2 This is a Hypothetical Syllogism, which is a valid form.

S v OB <--> (not S -->OB) Unstated premise and definition of implication.

not (not S)

so not OB From 3 and the unstated premise. Disjunctive Syllogism is valid

4.K-->OB

5. not K From not OB (3) and 4 This is Modus Tollens, a valid form. .

9.PR-->SR

7.PR

SR valid Modus Ponens.

SR v OR <--> (not SR --> OR) Unstated premise and definition of implication.

not(not SR)

10. not OR 7, unstated premise. Disjunctive Syllogism, valid.

We can conclude that the above premises support the conclusions, so the soundness of the argument will depend on clarity and truth value.

We can be short on the truth value of the facts since we already demonstrated that most of the premises are so ambiguous they end up being dubious or false. We have already concluded that it is not true that people only give opinions, and that the claim that knowledge does not exist is false. It is false that nobody can be objective, and it is certainly untrue that all honest opinions are equally correct. If I say: "I like milk chocolate better than white chocolate," there is no way to define the truth value of my statement. It is merely a matter of opinion. However, if a classical pianist claims: "Mozart is a better composer than Salieri," I figure this is a better opinion than that of a three year-old who says that "I love you; you love me" from Barney, the purple dinosaur, sounds better than Bach’s Brandenburg Concertos. We also demonstrated earlier that the claim: "There is no objective reality. We all live in our own private little worlds," is wrong.

To conclude, we can say that the greatest problems of this argument arise from the vagueness of the terms, which result in false or, at least, very dubious premises.

If we put the argument against abortion in standard form, we can simplify the statements to the following premises:

1. When a mother goes to the hospital to give birth, it’s pretty clear that she has a little person inside her.

2. The day before the delivery, it is still a little person.

3. And the day before that day, it is still a little person.

4. No matter how many days you count back, it’s still a little person.

5. Killing a person is wrong. (Unstated premise)

C. Therefore, killing it (the little person) at any point is wrong. I’m against abortion.

This argument against abortion concludes that abortion is wrong following the premises that (1) it is wrong to kill a person(unstated), and (2) a baby is a person, even before delivery, and at every stage of its evolution in the mother’s womb "no matter how many days you count back". The problem we have to deal with here is the problem of defining our concepts. In order to argue about abortion, we first state what the concepts mean, especially the concept "baby." However, few concepts come with an exact definition, meaning that it is possible to specify the connotation so that no doubt remains. E.g., the connotation of "square" is "equilateral and rectangular." Everything else is not "square." We call these concepts closed. Most concepts, though, are open, which means we cannot precisely specify their connotations, and it is sometimes hard to decide whether the concept applies or not. This is certainly the case with "baby." Does the concept only apply to the baby after delivery, or does it also apply to the foetus? It is easy to see how the use of an open concept raises problems in arguments about ethics, and it shows that we need to use argument by analogy in order to decide whether our concept applies in some cases or not. It certainly does not mean that the concept is useless because that would imply that there is no such thing as a baby, and that would be committing the fallacy of ad continuum, which is exactly what the above argument against abortion does, albeit the other way around. Let me explain.

The continuum fallacy argues that a debate is pointless because you cannot define your concepts clearly. It says you cannot draw the line exactly between what something is and is not; in other words, you cannot specify the difference between A and not-A. If you cannot point out the distinction between A and not-A, says a variant of the continuum fallacy, then, surely, there is no distinction between them. This is illustrated by the famous argument of the beard, which states that there is no difference between having a beard and not having a beard because we cannot draw the line precisely between the concept of a beard and "not-a-beard." Consequently, a man without a beard can never have one. The argument goes that if one whisker doesn’t give a man a beard, a second whisker won’t give him a beard either, nor will a third. Each whisker added still will not give the man a beard. So it doesn’t matter how many whiskers he has, he will never have a beard. So where do you draw the line between a beard and not-a-beard? The concept is moot, and we have no way to go with our argument, or so it seems. Our abortion opponent commits the same fallacy when he asserts that you cannot draw the line between a baby and not-a-baby. "No matter how many days you count back," he argues, a baby is always a baby. Hence, he seems to imply, you shouldn’t even discuss abortion because there is no such thing as "not-a-baby."

If we reverse the argument of the beard, we can point out the similarities with the argument against abortion even more clearly. What do you call a beard? Is it a full-grown beard that a man has had for at least a year, or can you say that a man who hasn’t shaved for a week has a beard? What about a man who hasn’t shaved for two days; does he have a beard? And what would you call the first few whiskers of an adolescent? Let’s compare this with the question, "what do you call a baby?" Is a baby a little person from the moment she is born? Or is she already a baby before the delivery? What would you call her when the mother is six moths pregnant, or what do you call a three month-old foetus? Is she already a baby immediately after conception? It is clear that we can go on and on, extending our definition "ad continuum" without a chance for a clear distinction between A and not-A, between a beard and a not-a-beard, between a baby and not-a-baby. If we follow this path, we will always fall into the trap of: what is, is no different from what is not, and we will never be able to put forth any reasonable argument.

To support this analysis, I would like to present a few arguments by analogy to show that this particular argument against abortion is not a good one. The first argument goes as follows. Suppose Tom has removed all the plants from a small piece of his yard, and he has planted seeds because he wants to grow a beautiful flower garden. The next day, his neighbor’s dog comes running through and digs up the dirt in the process. Tom is furious, and complains to his neighbor, Gail."

--"Your dog has just destroyed my wonderful flower garden. I had worked so hard at it, and now I have to start all over again. Do you have any idea what new landscaping costs these days?"

--Gail replies: "I’m sorry if my dog ran through your yard, but how could he destroy anything if there was nothing there? It’s just a piece of dirt. I didn’t see any flowers."

--" What do you mean," retorts Tom, "there was nothing there? I had just planted seeds of the most beautiful flowers, some of them very difficult to grow, and now your dog dug up all of my plants and I have to redo my landscaping completely!"

--Gail: "Tom, I know you must be upset, but can we be reasonable? You’ve just planted the seeds; how can you possibly claim my dog destroyed a full-grown garden?"

--Tom: "You mean a garden is only a garden when you have a mature landscaping? You mean a flower is only a flower when it’s at the peak of its bloom? What about the day before the flower opens up? Nothing much has changed. It is still a flower; it is just not blooming yet. So what do you call it when it is still a bud, or before the bud has even formed? Surely, you talk about your flowers when the first sprouts appear? So where do you draw the line? I say you can’t, and for that reason, I say I had a beautifully landscaped garden, and your dog destroyed it completely. I say you should pay for new landscaping."

I would like to use one more argument by analogy to show that the continuum fallacy clearly leads to preposterous conclusions. Consider the case of Anne, who decides to sue the government over compensation for a house she’s never built. Anne owned a piece of land on which she was planning to build her dream house a few years from now. Because of redevelopment measures, the government has taken the land away from her, compensating her at fair market rates so that she can buy another piece of land of equal value. However, Anne does not consider this a fair deal; according to her, not only did she lose her land, she also lost her dream house. Indeed, Anne argues, "When I bought that land, I already had a precise idea of what kind of house I was going to build on it. As a matter of fact, I expressly bought that particular piece of land because it corresponded exactly to the plans I had for my dream house. I can point out where my kitchen would be, my bedroom, and my study; I can even show you the very spot where I would be lounging in my easy chair, overlooking the gorgeous valley from my deck outside of the living room. You see, as far as I’m concerned, my dreamhouse was there. And now I’ve lost everything. You cannot tell me I didn’t lose my house simply because it was not physically there. What do you mean by a house? Is it only a house when the construction is finished? What about the day before the roof goes up? It’s still a house, just not completely finished. And what would you call it before the walls are built, or when you lay the foundations? Don’t you call it your house when you have the blueprints? Where do you draw the line between what is a house and what is not a house? I say you can’t, and for that reason, no matter how far you go back in the construction phase, it’s still a house. Therefore, I say the government took my dream house without compensating me, and that’s wrong. I demand fair compensation."

I recognize that these examples are farfetched, but in order to demonstrate the continuum fallacy, we shouldn’t be afraid of highlighting the ridiculous conclusions that "follow" from this kind of argument.

I would like to conclude this analysis with an example from my personal experience because the continuum fallacy reminds me a little of an argument --in the sense of dispute-- I used to have with my older brother when we were kids. It was usually about reading a magazine, playing a game, even using the bathroom. He would say he was going to do something, and there I was, just before he could even get up, doing exactly what he was planning to do. He would get so mad and shout: "I said it first!" to which I would invariably reply: "But I thought of it first." I’m not proud of it, but in a funny way it illustrates a little how easily you can show the uselessness of a concept committing the continuum fallacy. Indeed, who has the right to do something first? The one who was there first, the one who said it first, or the one who thought of it first? Where do you draw the line?