Argument
A group of statements of which one (the conclusion) is claimed to follow from the others (the premises)
Statement
A sentence that is either true or false
Premise
The information intended to provide support for a conclusion
Conclusion
The statement that is claimed to follow from the premises of an argument
Logic
The study of reasoning
Truth Value
Every statement is either true or false; these two possibilities are called truth values
Proposition
The information content imparted by a statement, or, simply put, its meaning
Inference
A term used by logicians to refer to the reasoning process that is expressed by an argument
Conclusion indicator
Words and phrases that indicate the presence of a conclusion
Premise indicator
Words and phrases that help us recognize arguments by indicating the presence of premises
Inference claim
If a passage expresses a reasoning process--that the conclusion follows from the premises--then we say that it makes an inferential claim
Explanations
Provides reasons for why or how an event occurred. By themselves, explanations are not arguments; however, they can form part of an argument.
Deductive argument
An argument in which it is claimed that the conclusion follows necessarily from the premises. In other words, it is claimed that under the assumption that the premises are true it is impossible for the conclusion to be false
Inductive argument
An argument in which it is claimed that the premises make the conclusion probable. In other words, it is claimed that under the assumption that the premises are true, it is improbable for the conclusion to be false.
Enthymemes
Arguments with missing premises, missing conclusions, or both
Principle for charity
We should choose the reconstructed argument that gives the benefit of the doubt to the person
Rhetorical language
When we speak or write for dramatic or exaggerated effect; that is, the language we employ may be implying things that are not explicitly said
Rhetorical question
When a statement is disguised in the form of a questions
Rhetorical conditional
A conditional statement that is used to imply an argument
Rhetorical disjunction
A disjunction that is used to disguise a statement or an implied argument
Disjunction
A compound statement that has two distinct statements (called disjuncts) connected by the wedge symbol
Conditional
In ordinary language, the word "if" typically precedes the antecedent of a conditional. The horseshoe symbol is used to translate a conditional statement
Biconditional
A compound statement consisting of two conditionals--one indicated by the word "if" and the other indicated by the phrase "only if." The triple bar symbol is used to translate a biconditional statement
Well-formed formulas
Compound statement forms that are grammatically correct
Main operator
The operator that has in its range the largest component or components in a compound statement
Truth function
The truth value of a truth-functional compound proposition is determined by the truth values of its components and the definitions of the logical operators involved. Any truth-functional compound proposition that can be determined in this manner is said t
statement variable
A statement variable can stand for any statement, simple or complex
Statement form
A pattern of statement variables and logical operators
Inclusive disjunction
Where both disjuncts can be true at the same time
Exclusive disjunction
Where both disjuncts cannot be true at the same time
Contingent statements
statements that are neither necessarily true nor necessarily false
Noncontingent statements
Statements such that the truth values in the main operator column do not depend on the truth values of the component
Tautology
A statement that is necessarily true
Self-contradiction
A statement that is necessarily false
Logically equivolent
Two truth-functional statements may appear different but have identical truth tables. When this occurs, they are logically equivolent
Contradictory statements
Two statements that have opposite truth values on every line of their respective truth tables
Consistent statements
Two or more statements that have at least one line on their respective truth tables where the main operators are true
Inconsistent statements
Two or more statements that do not have even one line on their respective truth tables where the main operators are true (but they can be false) at the same time
Cogent argument
When the argument is strong and the premises are true
Categorical syllogism
A syllogism constructed entirely of categorical propositions
Strong inductive argument
An argument such that if the premises are assumed to be true, then the conclusion is probably true
Valid deductive argument
An argument in which, assuming the premises are true, it is impossible for the conclusion to be false.
Sound argument
When logical analysis shows that a deductive argument is valid, and when truth value analysis of the premises shows that they are all true, it is a sound argument.