An * argument* is a sequence of sentences,
the last of which (the conclusion) is supposed to follow from the others (the
premises).

A. 1. The Bible says that it's wrong to eat pork.

2. If the Bible says that it's wrong to eat pork, then it's wrong to eat pork.

3. Therefore, it's wrong to eat pork.B. 1. If the Bible says that it's wrong to eat pork, then it's wrong to eat pork.

2. The Bible says that it's wrong to eat pork.

3. Therefore, it's wrong to eat pork.C. 1. Everyone believes that it's wrong to eat salty food.

2. If everyone believes that it's wrong to eat salty food, then it's wrong to eat pickles.

3. Therefore, it's wrong to eat pickles.D. 1. The Bible says that it's wrong to murder innocent children.

2. The Bible is the word of God.

3. Therefore, it's wrong to murder innocent children.D1: Argument A is

=df. in virtue of A's logical form, A's conclusion must be true,valid

if A's premises are all true.D2: Argument A is

=df. (1) A is valid, and (2) all of A's premises are true.sound

Modus Ponens(MP)1. P

2. if P, then Q

3. therefore, Q1. if P, then Q

2. P

3. therefore, Q

Multiple Modus Ponens(MMP)1. P

2. if P, then Q

3. if Q, then R

4. therefore, R

Modus Tollens(MT)1. if P, then Q

2. not-Q

3. therefore, not-P

Multiple Modus Tollens(MMT)

- if P, then Q
- if Q, then R
- not-R
- Therefore, not-P

Disjunctive Syllogism(DS)

- P or Q
- not-Q
- Therefore, P

**A Note on Conditionals**

**Conditionals** are sentences of the form **if P, then
Q**. Conditionals play a huge role in philosophical argumentation; this
can be gleaned from all of the "if, then" constructions you see on
this little logic sheet. If you are going to succeed in this class, you will
have to learn the procedure by which we will reject conditionals as false, or
as not worthy of our belief. But first, consider the parts of a conditional.
Conditionals are constructed from the words "if", "then",
and two independent clauses (very similar to declarative sentences). The independent
clause that comes after the word "if" is the **antecedent**.
The independent clause that comes after the word "then" is the **consequent**.
Consider the following conditional:

If David eats a half-gallon of ice cream every night, then David is bound to gain some weight.

The **antecedent** of this conditional is **David eats a
half-gallon of ice cream every night**. The **consequent**
of the conditional is **David is bound to gain some weight**.

Many conditionals should be rejected: some are false; some are such that we
don't have any good reasons to believe them to be true. We will adopt the following
as the procedure required for rejecting any given conditional: Imagine or suppose
the antecedent to be true and then show either that the consequent doesn't follow
from the antecedent or that we have no good reasons to believe that the consequent
follows from the antecedent. **Do not form the habit of rejecting a conditional
because you believe its antecedent to be false.**