We've been talking about fallacies that result from the use of expressions that
are vague. In other words, that signify something
without precise boundaries. Now I want to talk about a different kind
of fallacy, fallacies that result from the use of
expressions that are not necessarily vague but ambigious.
To say that an expression is ambigious is to say that it has different meanings,
and there are 2 kinds of ambiguity that I want to distinguish.
We'll call them semantic ambiguity and syntactic ambiguity.
Let me start off by talking about semantic ambiguity.
Semantic ambiguity is a kind of ambiguity that results when a single word means
more than one thing. Consider the word bank.
If I say Jill went down to the bank, I could mean two different things.
I could mean Jill went down to the financial institution, or I could mean
Jill went down to the edge of the river, because the word bank in English can mean
either of those two things. It can mean a financial institution, or
it can mean the edge of the river. Another example is if I say John became a
cardinal. The word cardinal, in English, can be
used to mean different things. It can be used to mean, rank in the
Catholic hierarchy, just below the rank of pope,
or it can be used to mean a baseball team that plays for St.
Louis, or it can be used to mean a particular
kind of bird, a red bird. So when I say John became a Cardinal, I
could mean he was promoted to the rank of Cardinal from the rank of Archbishop,
or I could mean that he was recruited to play for the St.
Louis Cardinals. Or I could mean that he was magically
turned from a person into a red bird. I've just given you some examples of
words that are semantically ambiguous, that have multiple meanings,
words like cardinal or bank. Another example of such a word is the
word odd. Odd could mean strange, and it could also
mean indivisible by two. An odd number is a number that's not
divisible by two. Now here's an example of how the
ambiguity in the word odd, the semantic ambiguity of odd, can give rise to a
fallacy. Consider this argument.
Premise 1, 6 is an odd number of legs for a horse.
Most horses have four. Premise two.
Odd numbers are not divisible by two. Therefore, conclusion, six is not
divisible by two. Now,
that conclusion is obviously false, but is this argument valid? I mean, if 6
is an odd number, and odd numbers are not divisible by 2, doesn't it follow that 6
is not divisible by 2? The only way to explain what's wrong with
this argument is to point to the ambiguity in the word odd. When the word
odd appears in premise 1, it means, strange.
6 is a strange number of like for a horse to have.
It's not a normal number of legs for a horse to have.
But, when the word odd appears in premise 2, it has a different meaning.
It means indivisible by 2. And so of course, it's true, just by the
definition of odd in this second meaning, that odd numbers are not divisible by 2.
So, premise one is true, given the correct understanding of odd.
Premise two is true given the correct understanding of odd for premise two But
the argument is not valid because the meaning of odd in this premise is
different from the meaning of odd in that premise.
That's how the ambiguity in the word odd can give rise to a fallacy,
can give rise to bad reasoning that might appear to be valid.
In the examples of symantic ambiguity that we've looked at so far, examples
concerning the word odd, or cardinal, or bank, you have a single word in English
that has completely different meanings. But there are other examples of symantic
ambiguity where a single word can mean 2 different categories, and one of those
categories is broader than the other and includes the other.
Let me give you an example of what I'm talking about to illustrate.
Consider the word drug. Sometimes when we use the word drug,
we're referring to any kind of drug whatsoever, legal or illegal, licit or
illicit. But other times when we use the word
drug, we're only referring to illegal or illicit drugs. So in the example that I
just gave, one category that's signified by the word drug is broader than, and
includes, the other category that's signified by the word drug.
Because illicit drugs. are a subcategory of the broader category
of all drugs. So that's a kind of semantic ambiguity,
and that kind of semantic ambiguity can also give rise to fallacies.
Consider this example. Premise 1, our company.
you might say to a perspective employee, our company cannot hire drug users.
Premise 2, Walter, you might find out, takes
aspirin. Premise 3.
Aspirin is a drug. And now from those 3 premises,
it might look like you can validly conclude, our company cannot hire Walter.
Now, that argument might look valid, because if Walter takes aspirin and
aspirin is a drug, then it looks like Walter is a drug user.
And if our company cannot hire drug users, then our company cannot hire
Walter. But even though that argument might look
valid, it's not,
and here's why. When premise 3 says that aspirin is a
drug, it's using the word drug to mean the broad category of drugs,
the category that includes not just illegal or illicit drugs, but all drugs.
But when premise 1 says, our company cannot hire drug users, presumably the
word drug in that premise is being used to mean the narrower category of drugs,
the category of illegal, or illicit drugs.
So, even though this argument might look valid, it really is invalid, because the
word drug in premise 1 means something different than, and something narrower
than, the word drug in premise 3. The fallacious argument that we just
considered helps us to appreciate how widespread semantic ambiguity is in our
language. For instance, consider a variation of
that fallacious argument. Suppose I say, premise 1,
our company cannot hire drug users. Premise 2,
Walter uses marijuana as a wall decoration.
Now, from those 2 premises, it might seem that we can validly conclude our company
cannot hire Walter. But again, this argument is invalid,
and it's invalid because the meaning of use.
In this premise, is the narrower than the meaning of use in this premise.
Here in premise 1, where I say, our company cannot hire drug users, what I
mean is our company cannot hire people who use drugs in the way that they're
designed to be used. So for instance, people who use marijuana
to get high or who use amphetamines to achieve a rush.
But in premise 2, I'm using the verb use in a much more unspecific way when I say
Walter uses marijuana as a wall decoration.
Well, he is using it, but he's not using it in the way that
it's designed to be used. He's using it in some other way.
So, while it might be true that Walter uses marijuana as a wall decoration,
that doesn't make him a drug user in the specific sense of use as is shown in
premise 1. So he's not a drug user just by virtue of
using marijuana as a wall decoration. So the verb to use here means something
more specific, more narrow than what it means here.
And so this argument, contrary to initial appearances,
is not valid. This is another example of a fallacy that
results from semantic ambiguity. And to see just how widespread semantic
ambiguity is, at least in the English language, notice that every single word
in this sentence is semantically ambiguous.
I've just shown you how the word user is semantically ambiguous and the word drug
is semantically ambiguous, but so too is the word hire.
When you hire someone, do you hire them as a full-time employee, or does hiring a
contractor count as hiring them? Cannot. What do you mean when you say our company
cannot hire drug users? They're legally prohibited from doing so? It's physically
impossible for them to do so? It's morally impermissible for them to do
so? Cannot can mean different things.
Company. What is a company? Is it a corporation,
or is it the people that we're hanging out with,
the people whose company we keep? And finally our, what do I mean by our?
Our is a first person plural pronoun, but does the first person plural extend
just to me and a few other people, or does it extend much more widely than
that? All of these words, every single one of them, is semantically ambiguous.
And so, each one of them can give rise to the kind of fallacy that we've described
so far. Let's call that kind of fallacy a fallacy
of equivocation. Now that we've looked at fallacies of
equivocation that arise from semantic ambiguity.
Let's look at fallacies of equivocation that arise from a different kind of
ambiguity, a kind of ambiguity that we'll call
syntactic ambiguity. Sometimes it's called amphiboly.
Now the second kind of ambiguity, syntactic ambiguity,
isn't an ambiguity in the meaning of any particular word.
Rather, it's an ambiguity in the grammar of a whole phrase or sentence.
Let me give you an example of what I'm talking about.
Consider the sign that was common in the United States during World War II, that
said Save Soap and Waste Paper. Now what does that sign mean? Well, one
way of understanding it is as saying that we should save soap but we should waste
paper. Now that is one way of understanding the
sign, but it's probably not what the sign was supposed to mean.
There's no reason why anyone would make a sign telling you to waste paper during
wartime. So that's one interpretation of the sign,
but it's not a very likely interpretation.
A much likelier interpretation of the sign is that it's telling you to save
soap, and also to save waste paper, paper that you've already used and that you
were going to throw away. The sign is telling you not to throw it
away, but to save it, because presumably that waste paper can be turned into
something useful. So that's another way of interpreting the
sign. It's telling you to save waste paper,
but what's different between those two interpretations? The first
interpretation, where the sign tells you to waste paper, and the second
interpretation where the sign tells you to save waste paper.
What's different between those two interpretations is that they each provide
a different grammar for the sentence. The first interpretation, Save Soap and
Waste Paper understands the verb to save as applying only to soap,
whereas the second interpretation, Save Soap and Waste Paper, interprets the verb
to save as applying not just to soap, but also to waste paper.
It's not that the verb to save means something different in the two
interpretations. The verb to save means exactly the same
thing in the two interpretations. It's just that in the first
interpretation, save is applied only to soap,
and in the second interpretation, save is applied both to soap and to waste paper.
That's the difference between the two interpretations.
So it's a difference not in the meaning of the word save, it's a difference in
the grammar that's assigned to the sentence by the two interpretations.
So that's an example of syntactic ambiguity.
Here's another example of syntactic ambiguity.
Consider the sentence first uttered by Paul Benacerraf, as far as I know.
Only Sons Marry Only Daughters. Now what does that sentence mean? Well,
there are two ways of understanding what it means, at least two ways.
One is that male children who are only children who have no siblings marry
female children who are only children, who have no siblings.
That's one way of understanding what it means.
Another way of understanding what it means is that the only people who marry
daughters are sons and the only people who marry sons are daughters.
Those are two different interpretations of that sentence, but they don't differ
in the meaning that they assign to the word son or daughter or marry.
They differ in the grammar that they assign to the sentence, Only Sons Marry
Only Daughters. On the first interpretation, only sons
should be understood as a single phrase referring to a certain class of boys and
only daughters should be understood as a single phrase referring to a certain
class of girls. In the second interpretation, only,
should be understood as applying to what follows it.
Only sons marry only daughters, and only daughters marry only sons.
So, the two interpretations differ, not in the meaning that they assign to any
particular word, but in the grammar that they assign to the whole sentence.
Those are some examples of syntactic ambiguitiy, and there are plenty of
others. And, now I want to show how syntactic
ambiguity can result in fallacy just as semantic ambiguity can.
Here's an example of how a fallacy of equivocation can result from syntactic
ambiguity. Consider this argument.
Premise 1, this is a headline I remember seeing
once. Police cannot stop gambling.
Premise 2, if you cannot stop gambling, you should
seek therapy. Now it might appear that from those two
premises, you could validly conclude police should seek therapy,
but in fact, that argument is not valid. That argument is a fallacy of
equivocation, because in premise 2, when premise 2 says you can cannot stop
gambling, what that means is if you cannot stop yourself from gambling, then
you should seek therapy. Alright, there's no reason why you should
seek therapy just because you are incapable of stopping other people from
gambling. If I want to stop other people from
gambling, but I am unable to do so, that's no reason for me to seek therapy.
So premise 2 says if you cannot stop yourself from gambling, then you should
seek therapy. But when premise 1 said police cannot
stop gambling, did that premise mean the police could not stop themselves from
gambling? I doubt it. I think it meant that the police cannot
stop other people from gambling. Police cannot stop the practice of
gambling from taking place in our society.
So I think the phrase, cannot stop gambling, has a different interpretation
in premise 1 than it does in premise 2. And now notice, even though it's a
different interpretation for that phrase, the difference in interpretation is not
the result of any semantic ambiguity. The word gambling means the same thing in
the two interpretations, the word stop means the same thing in the two
interpretations, and the word cannot means the same thing in the two
interpretations. What differs in the two interpretations
is not the meaning of any particular word that's used in that phrase,
but it's the grammar of the phrase. Who is it who cannot be stopped from
gambling, according to the phrase? Is it the police themselves, or is it someone
else? So, premise 1 should be understood to mean that the police can't stop others
from gambling. Premise 2, that phrase should be used to
mean that if you cannot stop yourself from gambling, then you should seek
therapy. And so the conclusion the police should
seek therapy does not follow validly from those two premises.
This argument is an example of a fallacy of equivocation that results from
syntactic ambiguity.