Department of Philosophy (PHI)

Conditional Statements

Conditional statements and arguments often take very similar forms. In each of the following sentence pairs, the first sentence expresses an argument, while the second expresses only a single conditional statement.
ARG1. Because Zeke studied hard, he will do well on the test.
COND1. If Zeke studied hard, he will do well on the test.

ARG2. Ed will go to Air Force One, since he likes Harrison Ford.
COND2. Ed will go to Air Force One, provided that he likes Harrison Ford.

ARG3. Since Amy is a minor and minors never drink, Amy doesn't drink.
COND3. If Amy is a minor and minors never drink, Amy doesn't drink.

In an argument, to assert the whole (i.e., give the argument) is to assert each of the premises and (on that basis) to assert the conclusion. In a conditional statement, to assert the whole is not to assert either of the components, the antecedent or the consequent.
For example, in arguing that because Zeke studied hard, he will do well on the test, one is stating that Zeke studied hard and (on that basis) stating that he will do well on the test. But in stating that if Zeke studied hard, he will do well on the test, one is not stating that Zeke studied hard and one is not stating that he will do well on the test.

Arguments with Conditionals as Parts

Although a conditional statement is not an argument, conditional statements can be premises and/or conclusions of arguments. In the type of argument known as hypothetical syllogism, the conclusion is a conditional statement and each premise is a conditional statement. Example:

• Sally is here if Timmy is here. (conditional premise)
• Timmy is here if Uma is here. (conditional premise)
• So Sally is here if Uma is here. (conditional conclusion)

In asserting the above argument one is asserting each of the three conditional statements. For instance, one is asserting that Sally if here if Timmy is. But one is not asserting the components of these conditional statements. That is, one is not saying that Sally is here, or that Timmy is here, or that Uma is here.
Note that a true conditional statement can have false components, so there is nothing absurd in the type of argument known as modus tollens (denying the consequent) in which a conditional statement is asserted and both of its components are denied. An example:

• Sally is here if Timmy is, but Sally isn't here, so Timmy isn't either.

In asserting the conditional premise Sally is here if Timmy is, the arguer is not asserting either of the conditional's components, so she can deny those components in the remainder of the argument without contradicting herself.
An argument can have a conditional conclusion without having conditional premises. For example:

• All men are mortal, so Socrates is mortal if he is a man.

In spite of this argument's resemblance to the classic textbook syllogism, All men are mortal is the only premise, and the conclusion is the conditional statement Socrates is mortal if he is a man. In giving this argument, one is not asserting either that Socrates is mortal or that he is a man.
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