Information for quiz: based on material from Ch. 7. We will discuss part of section III today, and more of it during the first part of class Fri. Some things to do in preparation: p. 174, #1,2; p. 177, #1, 3; p. 187, #2, 3, 5; p. 194, #5; p. 201, #6. Possibly there will be a question about p. 194, #5. If so, a copy of the essay will be provided with the quiz.

 

 

I. Meaning and Definition

A. Arguments sometimes turn on meanings. Part of the job of analysis is to make meanings clear. It is up to you, as the person discussing an argument, to say as clearly as you can, what the various terms mean. In effect, if you use the words of another, than you are taking them on as yours. If you don't understand, then say so. And then talk about what the words might mean and how the argument works out given those various meanings. It’s especially important to get clear about the meanings of the controversial and confusing terms that play a central role in an argument.

 

B. A good definition states necessary and sufficient conditions for something. There are various ways we can write out definitions.

 

Uncle: brother of a parent

x is the uncle of y =df. x is a brother of a parent of y.

 

Suppose we were considering an argument about lying and it became important to understand what lying is, what counts as a lie.

 

Lie: A false statement.

x is a lie =df. x is a false statement

 

Even better

 

S lied in saying p =df (i) S said p, (ii) p is false

 

The definition implies the corresponding “if and only if sentence”:

 

S lied in saying p iff S said p and p is false.

 

And this implies the two conditionals:

 

If S lied in saying p, then S said p and p is false

If S said p and p is false, then S lied in saying p

 

And these are to be understood as asserting the corresponding generalizations:

 

All cases in which a person lies in saying something are cases in which the person says that thing and it is false.

 

All cases in which a person says something and it is false are cases in which the person lies in saying that thing.

 

The latter says that the stated conditions are sufficient for lying. The former says that they are necessary - it isn’t a lie without those conditions.

 

C. You object to a proposed definition by giving a counterexample. This is an example showing either that the stated conditions are not necessary or that they are not sufficient. In this case, it is clear that the conditions are not sufficient: an honest mistake is not a lie. Actual examples are best. Highly realistic examples are good. Sometimes unusual, but possible, cases help make a point vivid. What’s best is that it be clear cut: anyone who understands the words should agree that the conditions are satisfied but it is not a lie.

            Often, a definition can be fixed up. If the stated conditions are not sufficient, adding another condition may yield something sufficient. Maybe:

 

S lied in saying p =df (i) S said p, (ii) p is false, and (iii) S intended to deceive others by saying p.

 

This avoids the honest mistake objection.

            But it may be that these conditions are not all necessary. Suppose I heard on the radio that Boston beat NY. I know that you would be very happy about this. In an effort to deceive, and disappoint, you I say that NY best Boston. Finally, suppose that in fact the radio got it wrong. So what I said was actually true. Conditions (i) and (iii) are satisfied, but not (ii). I think I did lie. So I’d say

 

S lied in saying p =df (i) S said p, (ii) S intended to deceive others by saying p.

 

This last objection is not so clear cut.

 

D. Dictionary definitions are often objectionably circular. Thus, my dictionary defines ‘censorship’ as the actions of a censor. Not very helpful! 

 

II. Ambiguity, Vagueness, Imprecision, Incompleteness, and Obscurity

A. We’ll consider five ways in which words or sentences can be indefinite and examine how they affect arguments.

1. A word or sentence is ambiguous when it has more than one potential meaning. Eg., “I went to the bank.” Context often helps us understand which meaning a speaker intends. The text separates out various kinds of ambiguity.

Dictionary.com gives lots of meanings for “lie” - in addition to meanings having to do with lying down, it also says this:

 

   1. A false statement deliberately presented as being true; a falsehood.

   2. Something meant to deceive or give a wrong impression.

 

I take it that it is saying the word has these two different meanings, corresponding to our second and third definitions.

 

2. Ambiguity differs from vagueness. A word is vague when it has indefinite boundary conditions - there simply is no correct answer to the question of whether it applies in some cases. E.g., “tall”, “intelligent”, “wealthy”. This indefiniteness is not a matter of our simply not knowing enough about the thing. You could know someone’s exact height and it still, if the person is on the borderline, it is just indeterminate whether the person is tall. Vagueness extends also to non-comparative terms: “chair”.

Vagueness and ambiguity differ from one another. A word with two non vague meanings is ambiguous. A vague word need not be ambiguous, since it might have only one (vague) meaning. But a word can be both vague and ambiguous. Perhaps “tall” is both vague and ambiguous. It is used in both “tall person” and “tall story”. These are different meanings (ambiguity). Each meaning is vague.

 

3. Ambiguity and vagueness both differ from imprecision. An example of the latter: “over 20 years old.” This applies to a wide range of things. The word “imprecise” is less than ideal here. The word does have a precise boundary, although it is open-ended on one end. But other imprecise terms are definite on both ends - “between 20 and 120 years old”. Perhaps it would be better to say that these words have a wide range of application.

 

4. Some sentences (not individual words) are incomplete. Two sorts of incompleteness: implicit relativity and missing quantifiers. We’ve already discussed the latter. The word “big” illustrates the former. Dumbo may be a big animal but a small elephant. So the sentence “Dumbo is big” is incomplete.

 

5. Finally, some words and phrases are obscure. I think the word “subjective” is like this. Notice that this differs from vagueness. Vague terms can be quite clear (in a sense), but just have indefinite boundary conditions. Obscure words just don’t say anything clear at all. Lots of jargon is like this. Obscurity is in itself a problem - you just can’t evaluate an argument if you can’t understand it.

 

B. Context

Context does a great deal to help us deal with some of these matters. Almost everything is ambiguous. (Check out a dictionary.) We often know the intended completion of a sentence. E.g., if we are looking at the elephants at the zoo and come upon baby Dumbo and say “Dumbo is small” the intended completion is obvious. Note also how quantifiers work. If I say at the beginning of class, “Everyone is here now”, only a wise guy would point out that there are lots of people (e.g., Michael Jackson) not here.

 

C. Connection to Arguments

Try to revise reconstructed arguments to eliminate obscurity. The other features are not in themselves as problematic. Where there is ambiguity, you have to be careful to consider the most suitable interpretation of the premises. Where there is vagueness, you have to see if the argument exploits that vagueness in an unacceptable way. We’ll look at some examples soon. Imprecision isn’t a problem at all. Just evaluate the argument. Where there is incompleteness, it’s up to you to fill out the missing element to get a clear argument, which can then be evaluated.

 

A key idea: these features of language always matter for argument analysis, in that we have to clear about what an argument says if we are to evaluate it competently. But the mere presence of an ambiguous or vague word does not show an argument to be defective. It must be that the argument somehow exploits those features, that it goes wrong in some way because of them. We’ll look later at how that works.

 

III. Definitions and Arguments

 

Exercise 4, p. 192 - Cults

1. In the first ¶ on p. 193, the author, Pico Iyer, writes, “A cult, in other words, is a religion and isn’t one, depending on who’s looking.” How does he arrive at this conclusion? What is his point when he says this?

It’s very hard to say. Maybe because people will disagree about what’s false? Another possible reason: the definition includes the words “considered to be false.” Well, different people will consider different things to be false. So,

 

D1. X is a cult =df. x is a religion some people consider to be false.

 

But this has the result that all religions are cults, given that each religion is considered false by someone or other. It’s hard to accept that this is what he means. Maybe he meant to say that a religion both is and is not a cult. Perhaps some variation on (D1) is supposed to imply this. Maybe he thinks that a thing is a cult “for a person”. But it’s very hard to understand what that means. In any case, my guess is that he thinks that the dictionary definition he’s mentioned is no good. He doesn’t actually believe this conclusion, i.e., that a religion both is and is not a cult.

 

2. Iyer considers a series of possible definitions of “cult”. One possibility is that a cult is defined as a “small congregation.” What point does he make about this definition?

 

D2. x is a religion =df x is a religion with a small congregation.

 

Followers of Emerson or Whitman are said to provide counterexamples to this. I think: they satisfy the condition but are not cults. The stated condition is not sufficient.

 

3. The next definition he considers includes the idea that cults lack an ancient scripture. What point does he make about this idea?

 

D3. x is a cult =df. x is a religion lacking ancient scriptures.

 

Zoroastrians are supposed to be a counterexample to this. (According to my dictionary, they are a “Persian religion prior to Mohammedianism”). Presumably, he thinks that they are a cult, but have an ancient scripture. So, the condition is not necessary. Notice the rhetorical question here, “Why does an internet index call it a cult?” Presumably, he thinks that it in fact is one.

 

4. Another suggestion is to define “cult” as “unorthodox religion.” What does Iyer say about this definition?

 

D4. x is a cult =df x is an unorthodox religion

 

Followers of Jesus, Budda, or Muhammed (in their day) are supposed to be counterexamples to D4. Why? I guess he thinks they aren’t cults. But maybe they were.

 

D4a. x is a cult at time t =df x is an unorthodox religion at time t.

 

A moral to be drawn from (D4a) is that whether or not a group counts as a cult can change over time. The religions mentioned were cults in earlier times.

 

Iyer seems to think that there is no clear definition of “cult”. That may not be right. A reasonably good definition of a cult is: a small, unorthodox religion. This allows that some religions once were cults but no longer are. And a religion that is not a cult can become one. One could argue, with some plausibility, that there is more to it than that - not only unorthodoxy is required, but perhaps some sort of extremism. Maybe there’s also an element of a leader who is followed fanatically. It looks like we can do reasonably well in defining what a cult is: a small, unorthodox religion, which is extremist and has a leader who is followed fanatically.

 

Iyer’s discussion, and what we’ve just done, illustrates the way you can assess definitions by looking for counterexamples.

 

B. Exercise 5 - Volunteer Work [The points here do not correspond exactly to the questions on the quiz.]

1. In ¶6 the author, Lynn Stirer says that President Clinton “wants to force young people to do something that should be, by its very definition, voluntary.” What is the thing that, by definition, should be voluntary?

Presumably, community service. Maybe she has the following definition in mind:

 

But this definition is wrong. The voluntariness requirement is a mistake. Counter example: people convicted of crimes are sometimes required to do community service. It is not voluntary. This condition is not necessary for community service.

 

Another possibility is that she means to say that volunteer service is what is, by definition, voluntary. That is obviously correct.

 

3. In ¶3 Stirer says that she stood against the program under discussion “on principle.” What was the principle she stood on? In the third paragraph she describes the requirement as “involuntary servitude.” So, maybe it is:

 

S. Students should not be subjected to involuntary servitude.

 

The idea that students should object to “involuntary servitude” is fairly strange. Students are required to do all sorts of things in order to graduate. It isn’t any more “involuntary servitude” to require community service than to require physical education, math or a foreign language. Maybe you can come up with some important difference between math and community service so that only the latter counts as “servitude.” But I don’t know what that would be.

 

3. Assess the principle:

 

 S1. Students should not be required to do volunteer work.

 

If a person is a volunteer only if the person engages in an activity without coercion, then the idea of required volunteer work is incoherent. (The phrase is an oxymoron.) So, she’s right about (S1). But there is nothing incoherent about the idea of required community service. If the requirement were simply described as community service, then there would be nothing to complain about along these lines.

 

4. What considerations does Stirer offer against the principle:

 

 S2. Students should not be required to do community service.

 

There is no clear principle that supports this. Of course, it is still possible that it is a bad idea to require community service. Perhaps Steirer’s real point is that it is better for community service to be volunteer work rather than a requirement. However, there is almost nothing said in defense of this. The closest to an argument comes in the middle, when she says the requirement destroys rather than elevates the American spirit of volunteerism. But this point gets no defense other than pointing out that some students didn’t take their work seriously. This hardly shows that it’s a bad idea to require it.

 

The point illustrated by this example is that confusion about words gets in the way of being clear about issues. If we frame the issue as being about required community service, then she has no good objection to the policy. At most, there are the points that some students lie about it and don’t take it seriously. That’s not a very strong objection. [More on this sort of thing later in the semester.] If we frame the issue as being about required volunteer work, then she’s right to object that this is incoherent - the point about it being voluntary by definition is right - but then the objection does not provide any reason at all to complain about required community service work.

Had the issue been framed clearly, without using the word ‘voluntary’, it wouldn’t have even seemed as if she had a point. Had the issue been stated clearly, the Times wouldn’t have published this article.

 

 

V. Ambiguity and Arguments

A. Mill’s Proof of Utilitarianism

See text. [This is a slightly different presentation of the material there.] In a very famous passage from his book, Utilitarianism, J. S. Mill writes:

There is considerable controversy about the proper interpretation of this passage. Mill is defending the view that actions are right when they promote the general happiness. And one of his ideas is that we each desire our own happiness. And this is supposed to support the idea that collectively we desire the general happiness. [The are problems with this inference as well, and it is doubtful that Mill was just making the mistake suggested by what I said.] The quoted passage plays some role in his discussion of that thesis. An uncharitable interpretation of Mill has him asserting the similarity of the following arguments:

 

1. x is seen.
2. x is visible.

 

1. x is heard.
2. x is audible.

 

1. x is desired.
2. x is desirable.

 

In our terms, all of these arguments are ill-formed. It is easy to make them valid. Add: Anything seen is visible. That is unproblematic. But to the last we add a premise, making the argument:

 

And this is problematic. Two definitions of “desirable”

 

(D1) x is desirable =df x is capable of being desired.
(D2) x is desirable =df. x is worthy of being desired.

 

It’s probably very rare that we use ‘desirable’ in the (D1) sense. But it is a potential meaning of the term. (“Some people do desire pain. So, pain is desirable.”)

So, suppose we want to prove in the way Mill suggests that something is desirable. Suppose that the thing in question is “living for ever” or “the general happiness” (which is what Mill wanted to prove). There are three versions of the argument - use (D1) throughout, use (D2) throughout, switch meanings.

(i) One version of the argument is deductively sound - use (D1) throughout. (2) is true. So is (1). Unfortunately, the conclusion isn’t the one Mill wanted. He wanted the conclusion in the (D2) sense.

(ii) Use (D2) throughout. The argument is valid but (2) is plainly false.

(iii) If the (D1) sense is used in (2) and the (D2) sense in the conclusion, the argument is ill-formed.

It helps to see all this by substituting the different definitions into the statement of the argument.

So: the argument discussed here plays upon an ambiguity. There is no sound argument for the intended conclusion. Note well, again: it is far from clear that Mill was confused about any of this.

B. Another Example

The decision to have an abortion is an important personal decision. But if a decision is a personal one, then no one else should interfere. Therefore, no one should interfere with a woman's decision to have an abortion.

1. All important personal decision for a person are decisions that the person should be allowed to make and carry out without interference. [EP]
2. A woman's decision about having an abortion is an important personal decision for her. [EP]
3. A woman should be allowed to make and carry out a decision about having an abortion without interference. (1), (2).

 

What does 'i.p.d.' mean?

D1. x is an important personal decision for S =df. x is a decision that will affect S's life in significant ways.
D2. x is an important personal decision for S =df. x is decision about matters that are significant and affect only S.

(D1) emphasizes the “importance” of the decision and makes it personal because it affects the person. Marriage, where to live, etc. are i.p.d.s, in this sense.

 

(D2) emphasizes the “personality” of the decision by making it only about the decider and thus

Use (D1) throughout the argument. (2) is true but (1) is implausible. (D1) does not imply that the matter exclusively affects the decider. Lots of ipds, in this sense, affect others in important ways as well. No reason at all to think that no one else should get involved. E.g., the idea that no one else should interfere with my carrying out my decision about whom to marry is silly.

 

Use (D2) throughout. (1) is true but (2) is implausible. Others are affected by such decisions, so an abortion decision is not an ipd in this second sense. (Not just the fetus - the father is affected too, in many cases.)

 

If we switch meanings, making both premises true, then the argument is invalid.

 

We've used ambiguity as a way to help see how the meaning of words affects the evaluation of arguments. The general point - seeing what words mean and how this may affect evaluations - can be applied to arguments even where there is no ambiguity. Often, you have to say what a key word means, then analyze the argument given that meaning.

Notice what happened with the abortion example:

i) I did not commit myself to a right meaning of 'imp. pers. dec.'; I just said what happened to the arg. given various meanings. Thus, I avoided making questionable assertions about what it "really" means.

ii) I did not commit myself on abortion rights; I only addressed a specific argument. Good evaluation does not require proving the opposite conclusion.

iii) The best objections to the arg. did not require controversial claims. (a) Using one def., we objected to premise (1). It is surely true that some decisions imp. for oneself affect others and can legitimately be interfered with. (b) Using the other def., we objected to premise (2). It is surely true that an abortion decision affects some others besides the mother, even without thinking about its affects on the fetus. Moreover, that it affects the fetus is uncontroversial. Whether those affects should be considered is a different matter. The obj. here was not that some people think the fetus matters. That's an insubstantial objection.

iv) So, the point that emerged was there was no good version of the argument.

v) Maybe someone will come along and show us that there is a better version. Right. We just do the best we can.

The key point to understand about ambiguity and arguments is this: to point out the mere fact that an argument contains an ambiguous word or sentence is not make a good objection to the argument. There’s a good objection only if the argument turns on the ambiguity in the ways just illustrated. That is, ambiguity is a problem only when there is no interpretation of the argument that makes it a sound argument for its intended conclusion, and the main reason for thinking otherwise requires interpreting a key term in two different ways in the argument.

 

V. Arguments and Vagueness

We will deal with this briefly.

●          As already noted, vague words are words with indefinite boundary conditions. They admit of borderline cases.

●          Vagueness is a linguistic phenomenon. Words just don’t have precise boundary conditions in many cases. It isn’t that there are boundaries that we don’t know about. There just aren’t any.

●          It is not a defect of an argument that it contains a vague word. Suppose you want to argue for a policy such as having progressive tax rates. That means that wealthy people will pay higher taxes. But “wealthy” is vague. That’s no objection to the general idea.

●          Arguments about such matters can provoke objections along the lines of “Where do you draw the line between ...” But as formulated, these are insubstantial objections. Suppose one formulated a “should argument” for the conclusion just mentioned. It would have premises about a goal - collecting enough tax money-, a premise about a system in which wealthy people pay at a higher rate being successful at achieving that goal, and a premise saying that it’s the best way to do it. The vagueness of “wealthy” just does not undermine any of this. At most, it shows that some fairly arbitrary boundaries will be needed to implement a policy.

●          Some deeply problematic arguments do employ vague terms. Consider the principle

For any number of dollars, X, if a person with X dollars is wealthy, then a person with X dollars - 1 cent is also wealthy.

The idea is that one penny can’t make the difference. But consider the argument that makes repeated use of this premise, starting with a premise such as

A person with $1,000,000,000 is wealthy.

Eventually you get to the conclusion

A person with $0.00 is wealthy.

This is an unusual argument. It is valid. The premises seem to be true. But the conclusion surely is not. But it is very hard to say exactly what’s wrong with it. In the end, we seem to be committed to saying that, strictly speaking, the one cent can’t make a difference principle isn’t right. Consider also “The Early Vacation Principle” - missing one day of class won’t make a difference.