1. Ambiguity arises from words or phrases having multiple meanings, while vagueness arises from unclear cases of application of a term. 2. Arguments can equivocate by relying on ambiguous terms, while Sorites arguments illustrate problems that can arise from vagueness. 3. It is important to distinguish using language to talk about the world versus using language to talk about language itself (use versus mention). Failing to do so can lead to errors in arguments.

1. Language Part I
Ambiguity, Vagueness, and
Use/Mention

2. Ambiguity
• A word, phrase or sentence is ambiguous if it has
multiple, distinct meanings.
• Examples:
– Bat1-a handled stick for striking a ball
– Bat2-a flying nocturnal mammal
– Credit1-an ability to acquire something prior to
expected payment
– Credit2-an acknowledgment of positive contribution

3. Two Kinds of Ambiguity
• Term ambiguity arises from the possible meaning of a word
or term. The examples on the last slide are examples of
term ambiguity.
• Structural ambiguity arises from arrangement of a clause or
sentence. This is often called amphiboly. Here’s an
example:
- Jerry presented the bill with an incendiary introduction.
A handy (but fallible) rule is: if you can rearrange the
sentence and eliminate the ambiguity then it was an
amphiboly not a term ambiguity.
Contrast: (1) Jerry, with an incendiary introduction, presented
the bill. (2) The bill with the incendiary introduction, Jerry
presented.

4. Equivocation
• An argument equivocates when it relies on an
ambiguous word or phrase for its seemingly
good form.
• For example,
1. Nothing is better than a month in Tahiti.
2. A half-day at Frankenmuth is better than
nothing.
3. So, a half-day at Frankenmuth is better than a
month in Tahiti.

5. 1st Example Continued
• If you don’t think the premises are true, insert your
dream vacation spot in premise one and your least
favorite but still visitable vacation spot in premise two.
• The argument has this form:
1. B > C
2. A > B
3. So, A > C
If the premises of an argument like this are true then the
conclusion must be true! So, it has good form (or it
seems to).
So, the argument proves a conclusion that you should
think is absurd.

6. Another Example
1. Under the current tax code, Buffet’s secretary
pays higher taxes than he does.
2. It’s unfair for a secretary to pay more money for
tax than the world’s third richest man.
3. The current tax code is unfair.
‘Pays higher taxes’ can mean ‘pay a higher
percentage of income for tax’ or ‘pay more
money for tax’. Premise one is true only in the
first sense the argument has good form only if
premise one is understood in the second sense.

7. Vagueness
• A term is vague when it
has unclear cases of
application.
• For example, ‘bald’ is
vague because it is
difficult to say whether
this guy is bald.
• Can you say why these
terms are vague? Red,
thin, mansion, rich.

8. Sorites Argument
1. A person worth forty billion dollars is rich.
2. If a person is rich then losing a penny won’t
make a difference to her (she’ll still be rich).
3. So, a person worth $39, 999, 999, 999.99 is rich.
2. If a person is rich then losing a penny won’t make
a difference to her (she’ll still be rich).
4. So, a person worth $39, 999, 999, 999.98 is rich.
…
…
399,999,999,987. So, a person worth 13¢ is rich.

9. The problem
• It’s difficult to say exactly what the problem is
with the Sorites argument; but it’s clear that the
problem arises because of vagueness (of ‘rich’ in
the last example).
• While this should motivate caution in relying on
vague terms in argument, it’s important to note
that a term’s being vague does not imply its being
meaningless or useless. It might not be clear
whether a person worth 750K is rich, but a
person worth forty billion is definitely rich and a
person worth eleven cents is definitely not.

10. Use and Mention
• We can use language to talk about the world or we can
use language to talk about language.
• Contrast these two sentences:
1. Montana has seven cities with more than 20,000
people.
2. ‘Montana’ has seven letters.
The first is about the fourth largest U.S. state and the
second is about the name of that state. The first uses
the name ‘Montana’ to talk about the state and the
second mentions the name ‘Montana.’
In print, quote marks clear up the ambiguity. Out loud we
use context to clear up the ambiguity.

11. More Examples
Right:
John goes by the name ‘Jack.’
There are no vowels in ‘thpppt.’
Joe said ‘I will pay.’
Wrong:
Gary has four letters and starts with G.
(‘Gary’ has four letters and starts with ‘G.’)
USPS has more letters than UPS.
(Unless ‘letters’ means ‘notes in envelopes’ it should be:
‘USPS’ has more letters than ‘UPS.’)

12. An argument relying on a
Use/Mention error
1. Romney said “I heard Obama say ‘I love big
government’.”
2. You can’t quote someone else without saying
what he said.
3. So, Romney said ‘I love big government.’
4. So Romney claims to love big government.

13. Two Problems
• These arguments relying on unclear language are
not new problems an argument can have. There
are still just two: bad form and false premises.
• In most cases of tricky language, the problem is
bad form. For example, the argument on slide
four only appears to have good form. ‘Nothing’
has different meanings in premises one and two
(if those premises are true); so it would be wrong
to say the argument has the form on slide five.