Chapter 1 - Basic Concepts Flashcards
What is an argument?
A set of statements: the conclusion and the premises. The conclusion is affirmed on the basis of the premises.
What is Logic?
Study of methods for evaluating whether the premises of an argument adequately support (or provide good evidence for) its conclusion.
(Study of methods for evaluating arguments.)
What is a valid argument?
It is necessary that if the premises are true, then the conclusion is true. (Premises completely support the argument.)
What is an invalid argument?
It is not necessary that if the premises are true, then the conclusion is true.
What is a sound argument?
It is valid, and all its premises are true.
What is an unsound argument?
It is either invalid or has at least one false premise.
What is deductive logic?
Concerns tests for validity and invalidity.
What is an argument form?
A pattern of reasoning - some valid, some not. The validity of an argument is guaranteed by its form - does not depend on its content.
What is a substitution instance of an argument form?
An argument that results from uniformly replacing letters in an argument form with terms (or statements). Must be uniform.
Modus Ponens
(mode of positing)
If A, then B.
A.
So, B.
Modus Tollens
(mode/way of removing)
If A, then B.
Not B.
So, Not A.
Denying the Antecedent
If A, then B.
Not A.
So, Not B.
Affirming the Consequent
If A, then B.
B.
So, A.
Hypothetical syllogism
If A, then B.
If, B then C.
So, if A, then C.
Disjunctive syllogism
Either A or B.
Not A.
So, B.
Constructive dilemma
Either A or B.
If A, then C.
If B, then D.
So, either C or D.
A term?
A word or phrase that stands for a class or set of things.
Counter example
A substitution instance whose premises are well-known truths and whose conclusion is a well-known falsehood.
Conditional statements
if-then statements. (Hypothetical in nature.)
“If” clause is the?
Antecedent
“Then” clause is the?
Consequent
Strong argument
Probable (not necessary) that if premises are true, then the conclusion is true.(Inductive)
Weak argument
It is not probably that if its premises are true, then its conclusion is true.(Inductive)
Cogent argument
It is strong and all its premises are true.(Inductive)
Uncogent argument
It is either (a) weak or (b) strong with at least one false premise.(Inductive)
Inductive logic
Methods of evaluating arguments for strength and weakness.
Using forms to test validity
- Identify component statements, labeling with capital letter.
- Rewrite using cap. letters.
- Identify famous forms & evaluate for validity. If no famous forms, construct counterexample.
Invalid arguments:
Strong arguments w/ all premises true are cogent.
Strong arguments w/ atleast 1 false premise is uncogent.
Weak arguments are all uncogent.
