Exam 1 Flashcards
Logic
The study of methods for evaluating whether the premises of an argument adequately support its conclusion
Argument
A set of statements where some of the statements are intended to support another
Statement
A declarative sentence that is either true or false
Premise
The statements offered in support of an argument
Conclusion
The claim to be supported in an argument
Deductive Argument
Where the premises are intended to guarantee the conclusion
Inductive Argument?
Where the premises are intended to make the conclusion probable, without guaranteeing it
Valid Argument?
A deductive argument in which the premises succeed in guaranteeing the conclusion
Invalid Argument
A deductive argument in which the premises fail in guaranteeing the conclusion
Sound Argument
A valid argument in which all of the premises are true
(valid + all premises true = sound)
Unsound Argument
An invalid argument or has at least one false premise
(invalid = unsound or valid with at least one false premise = unsound)
Argument Form
A pattern of reasoning
Substitution Instance
An argument form that results from uniformly replacing the variables in that form with statements
Valid Argument Form
Every substitution instance is a valid argument
Formally Valid Argument
An argument that is valid in virtue of its form
(an argument can be valid w/o being formally valid)
Negation
The denial of a statement
Conditional Statement
An if, then statement
(ex: If A, then B)
Antecedent
The first part or if-clause of a conditional statement
(antecedent is sufficient for consequent)
Consequent
The second part or then-clause of a conditional statement
(consequent is necessary for antecedent)
Disjunction
An either-or statement
(ex: Either A or B)
Disjunct
The parts of a disjunction statement
Modus Ponens (valid argument form)
- if A, then B
- A
- So, B
Modus Tollens (valid argument form)
- if A, then B
- Not B
- So, Not A
Hypothetical Syllogism (valid argument form)
- if A, then B
- if B, then C
- So, if A, then C
Disjunctive Syllogism (valid argument form)
- Either A or B
- Not A
- So, B
or
- Either A or B
- Not B
- So, A
Constructive Dilemma (valid argument form)
- Either A or B
- if A, then C
- if B, then D
- So, Either C or D
Famous Forms Method
Step 1: label each statement in the argument with a capital letter
Step 2: rewrite the argument replacing each statement with the letters
Step 3: check to see if the pattern of reasoning is taken from one of the famous forms. If it is, the argument is valid
Invalid Argument Form
An argument that has some invalid substitution instances
Counterexample
A substitution instance in which the premises are true and the conclusion is false
(this helps us show that an argument is an invalid argument form)
Good Counterexample
A substitution instance in which the premises are well-known truths and the conclusion is a well-known falsehood
(the counterexample proves that the form is invalid)
Fallacy of Denying the Antecedent
- if A, then B
- Not A
- So, Not B
(opposite of Modus Tollens and an invalid argument form)
Fallacy of Affirming the Consequent
- if A, then B
- B
- So, A
(opposite of Modus Ponens and an invalid argument form)
Categorical Statement
A statement that relates two classes or categories, where a class is a set or collection of things
(signaled by “all”, “some”, or “no”)
The Counterexample Method
Step 1: Use capital letters to stand for statements or terms
Step 2: Find statements to terms that are known to be true for the premises and a well-known falsehood for the conclusion and replace them with the letters
Step 3: if succeeded the argument should be invalid
Strong Argument
When it is probable (but not necessary) that, if the premises are true, then the conclusion is true
Weak Argument
When it is NOT probable that, if the premises are true, the the conclusion is true.
Cogent Argument
A strong argument in which all premises are true
Uncogent Argument
An argument that is either weak or strong with at least one false premise
