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: –When we think that what is true of a group of things taken collectively is automatically true of the same things taken individually. –The Giants example: The fallacy of Composition: –When we think that what holds for a group of things individually holds automatically for the entire collective group. –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. –The definiens is a set of necessary and sufficient conditions for the definiendum. X is a necessary condition of Y if and only if (or iff) we cannot have Y without also having X. –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?