I. Ambiguity = Equivocation = 2 terms with distinct
meanings
A. Examples:
bank = place to put money
bank = side of a river
hit = a blow
hit = a very successfuol event (the play was a hit)
B. Ambiguity can be determined with a dictionary.
II. Vagueness = there are borderline cases (NOT the same as Ambiguity)
A. Examples
Tall (is 5'11" tall?) (What is the comparison group: humans?
females? giraffes?)
Heavy ( is a 180 lb. male heavy?)
Blue (is aquamarine really blue?)
B. Some have argued that all terms are vague to a degree.
III. Evaluating Arguments that contain ambiguous terms
A. Ambiguity does not mean invalidity. You must test each argument separately to see.
B. Example 1.
man1 = human
man2 = male human
This argument form is deductively valid:
Not C
If A then B
If B then C
So not A
nothing1 = no object
nothing2 = no space
IV. Arguments that contain vague terms can be valid.
During daylight, normal people can see well enough to read outdoors.
It is now noon.
_____________
Now normal people can see well enough to read outdoors.
A. The argument is valid provided noon is considered to be a time during daylight. But that interpretation is no problem at all.
B. If it has said "It is now dusk" it would have been a different matter since dusk is not a clear case of daylight.
C. But here noon is not a borderline case, so the argument is
fine.
V. How to check whether two terms have the same meaning.
A. NOT by showing the terms pick out the same things.
Example:
1. has a 4-chambered heart.
2. has a kidney
It is a biological fact that 1. and 2. pick out the same animals, but 1. and 2. do NOT mean the same thing.
B. The Correct Test (Like a counterexample)
Ask whether it is POSSIBLE for the two terms to apply to different things. If it does they can't mean the same thing.
The following argument is invalid. This helps us see that 1. and 2. have different meanings.
All mammals have 4-chambered hearts.
All mammals have kidneys.
I. Conditionals are sentences of the form:
A is the antecedent
B is the consequent
If A then B If B then A are DIFFERENT
If Hammy is a dog then Hammy is a mammal.
If Hammy is a mammal then Hammy is a dog.
B. Conditionals can be true even when their antecedents and consequents are false.
If the moon is made of cheese then it is edible.
C. Conditionals do NOT say the antecedent entails (provides a valid argument for) the consequent.
The moon is made of cheese.
The moon is edible.
This argument is invalid.
D. Conditionals do not (necessarily) say the antecedent precedes the consequent in time.
If you are a doctor then you went to med. school.
Note: being a doctor comes after med. school.
II. How to detect conditionals in text.
Antecedent Indicators: If, Provided that, When
If A then B = B if A
Provided A, B = B, provided A = If A
then B
When A, B = B, when A = If A then B
Consequent Indicators: Then, Only if, Results in, Causes
A only if B = Only if B, A = If A then B
I will help only if you pay me.
If I will help then you will pay me.
NOT! If you pay me then I will help.
A results in B = If A then B
A causes B = If A then B
III. Necessary and Sufficient Conditions
A. A is sufficient for B = If A then B
Sufficient conditions are antecedents.
B. A is necessary for B = If B then A
Necessary conditions are consequents.
To be a doctor, it is necessary to go to med. school.
If you are a doctor then you went to med. school.
NOT:
If you went to med. school then you are a doctor.
IV. Biconditionals
A is a necessary and sufficient condition for B
= If A then B and if B then A
= A if and only if B
= A iff B
V. Unless (= If not)
A unless B
= A if not B
= If not B then A
NOT = If B then not A
Buy a million shares unless I call before noon.
NOT = If I call before noon then do not buy
a million shares.
not A unless B
= not A if not B
= if not B then not A
= If A then B
NOT = If B then A
You can't come in unless you are wearing shoes.
NOT = If you are wearing shoe you can come in.
Does A unless B entail If B then not A?
I think NOT! There are clear exceptions.
VI. 'All' and 'Only'
It is useful to convert the expressions 'All A are B' and 'Only A re B' into conditionals as follows:
All Cadillacs have airbags = If you are a Cadillac then you have an airbag.
Only Cadillacs have airbags = Only IF you are a Cadillac
do you haved an airbag.
= You have an airbag only if you are a Cadillac.
= If you have an airbag then you are a Cadillac.
(Note 'only if' indicates the consequent, so 'Cadillac' is in the consequent.)