Lecture 5: Argument Forms and Logic Patterns

Vocabulary flashcards covering the components of standard argument forms, deductively valid versus inductively cogent arguments, predicate and sentential logic connectives, and eleven valid and four invalid argument patterns.

Standard Form of an Argument

A presentation format where premises and conclusions are numbered, limited to one per line, preceded by "Therefore" before the conclusion, annotated with brackets showing justification, and structured to isolate relevant information.

Well-formed Argument

An argument in which the conclusion does follow from the premises.

Deductively Valid Argument

A well-formed argument where the premises provide logical, conclusive support for the conclusion, making it impossible for all premises to be true and the conclusion to be false.

Inductively Cogent Argument

A well-formed argument where the premises make the conclusion probable.

Predicate Logic

A system of logic dealing with quantified statements such as "All As Are Bs," consisting of a quantifier (All, Some, None), a subject ($As$), and predicates ($\text{Are } Bs$).

Conjunction (Sentential Logic)

A compound sentential statement expressed as "$A \text{ And } B$".

Disjunction (Sentential Logic)

A compound sentential statement expressed as "$A \text{ or } B$" or symbolized as $A \text{ v } B$.

Negation (Sentential Logic)

A sentential operation expressing "$\text{Not } A$", symbolized as $\sim A$.

Conditional (Sentential Logic)

A sentential statement expressing "$\text{If } A\text{, then } B$", symbolized as $A \rightarrow B$.

BiConditional (Sentential Logic)

A sentential statement expressing "$A \text{ if and only if } B$", symbolized as $A \leftrightarrow B$.

Denying the Antecedent

An invalid argument pattern of the form: 1. If $P$, Then $Q$. 2. $\sim P$. 3. Therefore, $\sim Q$.

Affirming the Consequent

An invalid argument pattern of the form: 1. If $P$, then $Q$. 2. $Q$. 3. Therefore, $P$.

Universal Modus Ponens

A valid argument pattern of the form: 1. $X$ is an $A$. 2. All $As$ are $Bs$. 3. Therefore, $X$ is a $B$.

Universal Modus Tollens

A valid argument pattern of the form: 1. All $As$ are $Bs$. 2. $X$ is not a $B$. 3. Therefore, $X$ is not a $A$.

Universal Hypothetical Syllogism

A valid argument pattern of the form: 1. All $As$ are $Bs$. 2. All $Bs$ are $Cs$. 3. Therefore, All $As$ are $Cs$.

Universal Ruling Out

A valid argument pattern of the form: 1. No $As$ are $Bs$. 2. $X$ Is an $A$. 3. Therefore, $X$ is not a $B$.

Argument by Elimination

A valid argument pattern of the form: 1. $P \text{ or } Q$. 2. $\sim P$. 3. Therefore, $Q$.

Conjunction (Argument Pattern)

A valid argument pattern of the form: 1. $P$. 2. $Q$. 3. Therefore, $P \text{ and } Q$.

Simplification

A valid argument pattern of the form: 1. $P \text{ and } Q$. 2. Therefore, $P$ (or Therefore, $Q$).

Modus Ponens

A valid argument pattern of the form: 1. If $P$, then $Q$. 2. $P$. 3. Therefore, $Q$.

Modus Tollens

A valid argument pattern of the form: 1. If $P$, Then $Q$. 2. $\sim Q$. 3. Therefore, $\sim P$.

Contraposition

A valid argument pattern of the form: 1. If $P$, Then $Q$. 2. Therefore, If $\sim Q$ then $\sim P$.

Hypothetical Syllogism

A valid argument pattern of the form: 1. If $P$, Then $Q$. 2. If $Q$, Then $R$. 3. Therefore, If $P$, Then $R$.