Some Logical Concepts

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

Some Sample Arguments

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

D2:      Argument A is sound =df. (1) A is valid, and (2) all of A's premises are true.

Some Common Valid Argument Forms:

Modus Ponens (MP)

1. P
2. if P, then Q
3. therefore, Q

1. 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)

  1. if P, then Q
  2. if Q, then R
  3. not-R
  4. Therefore, not-P

Disjunctive Syllogism (DS)

  1. P or Q
  2. not-Q
  3. 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.