Philosophy homework

SYMBOLIZATION AND THE FIVE FAMOUS FORMS

· Argument form: A pattern of reasoning.

· Symbolizing an argument: Symbolize each statement by uniformly replacing statements with variables while preserving the most logically sensitive form.

· Substitution instance: an argument that results from uniformly replacing the variables in a symbolic argument with statements or terms.

Examples for symbolized statements:

1) No operator (atomic statement)

Statement: “Geese like to beat up kids.”

Symbolized: “A”

2) Negation (NOT)

Statement: “It is not the case that geese like to beat up kids.”

Symbolized: “NOT A”

3) Disjunction (OR)

Statement: “Either geese like to beat up kids, or seagulls like to poop on people.”

Symbolized: “A OR B”

4) Conjunction (AND)

Statement: “Geese like to beat up kids and seagulls like to poop on people.”

Symbolized: “A AND B”

5) Conditional (IF...THEN)

Statement: “If geese like to beat up kids, then seagulls like to poop on people.”

Symbolized: “IF A THEN B”

6) Biconditional (IF AND ONLY IF)

Statement: “Geese like to beat up kids if and only if seagulls like to poop on people.”

Symbolized: “A IF AND ONLY IF B”

FIVE FAMOUS FORMS

Modus Ponens:

An Argument

1. If voter suppression is an effective means to win swing states, then you should expect voter suppression to be more prevalent in swing states.

2. Voter suppression is an effective means to win swing states.

3. So, you should expect voter suppression to be more prevalent in swing states.

Symbolized form:

1. If P, then Q.

2. P.

3. So, Q.

Modus Tollens:

1. If voter suppression is an effective means to win swing states, then you should expect voter suppression to be more prevalent in swing states.

2. It is not the case that you should expect voter suppression to be more prevalent in swing states.

3. So, it is not the case that voter suppression is an effective means to win swing states.

Symbolized form:

1. If P, then Q.

2. NOT Q.

3. So, NOT P.

Hypothetical Syllogism:

1. If voter suppression is an effective means to win swing states, then you should expect voter suppression to be more prevalent in swing states.

2. If you should expect voter suppression to be more prevalent in swing states, then you should expect lower voter turnout in swing states.

3. So, if voter suppression is an effective means to win swing states, then you should expect lower voter turnout in swing states.

Symbolized form:

1. If P, then Q.

2. If Q, then R.

3. So, if P, then R.

Disjunctive Syllogism:

1. Either cats are cute, or dogs are dumb.

2. It is not the case that dogs are dumb.

3. So, cats are cute.

OR

1. Either cats are cute, or dogs are dumb.

2. It is not the case that cats are cute.

3. So, dogs are dumb.

Symbolized form:

1. Either P or Q.

2. Not P.

3. So, Q.

OR

1. Either P or Q.

2. Not Q.

3. So, P.

Constructive Dilemma

1. Either republicans will win the next election, or democrats will win the next election.

2. If republicans win the next election, then we should expect fewer fiscal regulations.

3. If democrats win the next election, then we should expect more environmental regulations.

4. So, either we should expect fewer fiscal regulations, or we should expect more environmental regulations.

Symbolized form:

1. Either P or Q.

2. If P, then R.

3. If Q, then S.

4. So, either R or S.