Reasoning & Problem Solving
Lecture 7
Clear Thinking and Clear Writing
By David Kelsey
Vagueness
•
A vague statement is one whose meaning is indistinct, imprecise or
lacks details.
•
Degrees: Vagueness isn’t all or nothing. It comes in degrees.
– Apartment example
Clarifying vagueness
•
Desirable vagueness: sometimes vagueness is actually desirable.
–
•
Being Romantic
Clarify: If we come across a vague statement we can simply try to clarify the
lack of detail or indistinct-ness.
–
Job example
Vagueness
and Propositions
•
A vague statement
– it is unclear what proposition the sentence asserts at all.
– It could be any one of a number of propositions
Ambiguous Claims
•
•
•
An ambiguous claim is one that is subject to more than one interpretation.
Claim x
 
– P1
P2
–
Jessica rents her house
Semantic Ambiguity
•
A sentence that is semantically
ambiguous is one which contains
an ambiguous word or phrase.
•
For example:
– Jessica is cold.
•
Fixing the ambiguous word
Syntactic Ambiguity
•
A sentence is syntactically
ambiguous when it is ambiguous
because of its grammar or the way it
has been structured or put together.
–
Susan saw the farmer with
binoculars.
–
You will need a birth certificate or a
driver’s license and other photo id.
•
When you have come across a
semantic ambiguity you can simply
alter the grammar
•
Or you might need to re-write the
claim altogether.
Grouping Ambiguity
•
Grouping ambiguity:
– unclear whether some word in the sentence is referring to a group or an
individual.
– Secretaries and Physicians
– Lawnmowers and dirt bikes
Composition and Division
•
The fallacy of Division:
•
The fallacy of Composition:
–
When we think that what is true of a
group of things taken collectively is
automatically true of the same
things taken individually.
–
When we think that what holds for a
group of things individually holds
automatically for the entire collective
group.
–
The Giants example:
–
The Patriots example:
Stipulating Definitions
•
Stipulating definitions:
– Terms are used that we don’t fully understand.
– A term used is unusual or unfamiliar.
– A brand new word
– A familiar word is being used in a new way
Precising Definitions
•
Precising definitions:
–
Used to reduce vagueness or to eliminate ambiguity.
–
Some examples:
• Justice:
• Permissible:
Definitions:
by Example & by synonym
•
Definition by example:
–
•
We define a term by example when we point to, name or describe one or more
examples of something to which the defined term applies.
Definition by synonym:
–
We define a term by synonym when we give another word or phrase that means the
same thing as the term being defined.
–
Bachelors example
Analytical Definitions:
their form
•
An Analytical definition is composed of a definiendum and a definiens.
–
–
•
The definiendum:
The definiens:
Form: the form of a definition is this:
–
X =df _____
•
–
Which is the definiendum and which is the definiens?
For example,
• Knowledge =df true belief
Necessary and
sufficient conditions
•
We can think of a definition as a set of necessary and sufficient
conditions.
–
•
X is a necessary condition of Y if and only if (or iff) we cannot have Y without
also having X.
–
•
The definiens is a set of necessary and sufficient conditions for the definiendum.
Oxygen and Combustion
X is a sufficient condition of Y iff X is all that is needed to get Y.
–
Being born in the US and citizenship
Necessary and
Sufficient Conditions #2
•
X is both a necessary and sufficient condition of Y iff both
–
–
•
1) we cannot have Y without also having X &
2) X is all that is needed to get Y.
Knowledge is JTB
Correct Definitions
•
For a definition to be adequate the definiendum and definiens must be
co-extensive.
•
For the defiendum and definiens of any definition to be co-extensive it
must be the case that:
– 1)
– 2)
– What is the extension of a concept?
Co-extensiveness:
An example
•
So if your definition of KNOWLEDGE as TRUE BELIEF is correct then:
–
Everything in the extension of KNOWLEDGE is in the extension of TRUE BELIEF and
vice versa.
Testing definitions
•
To determine if a definition is adequate:
–
–
determine if its definiendum and definiens are co-extensive.
Is there any item in the extension of one that isn’t in the extension of the other?
–
Example: Knowledge is true belief
• All Knowledge is true belief.
• All true belief is knowledge.
• Universal generalizations and counterexamples
Counterexamples
•
A counterexample: a case that violates a universal generalization.
•
If we define knowledge as true belief we just need one counterexample to show
this definition inadequate.
–
–
We need to find a case of knowledge that isn’t what?
Or a case of true belief that isn’t what?
–
A counterexample:
•
The Belief Game:
Counterexamples #2
•
Love: Say I define Love as a deep seated feeling composed of compassion &
care which one can have for another human being.
–
•
Can anyone find a counterexample to this definition?
We are looking for either:
–
–
a case of love that isn’t ____________
a case of having this feeling for another human which isn’t ______________
–
Any thoughts?