Different Types of Arguments

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Notice that these two arguments each have the same logical pattern or form: If A then B.
A.
Therefore, B.

This pattern, as we have seen, is called modus ponens. Arguments with this pattern consist of one conditional premise, a second premise that asserts as true the antecedent (the if part) of the conditional, and a conclusion that asserts as true the consequent (the then part) of the conditional. Other common varieties of hypothetical syllogisms include •chain argument

modus tollens (denying the consequent)
denying the antecedent
affirming the consequent

Chain arguments consist of three conditional statements that link together in the following way: If A then B.
If B then C.
Therefore, if A then C.

Here is an example of a chain argument:
If we don't stop for gas soon, then we'll run out of gas. If we run out of gas, then we'll be late for the wedding. Therefore, if we don't stop for gas soon, we'll be late for the wedding.

Modus tollens8 arguments have the following pattern:
If A then B.
Not B.
Therefore, not A.

Arguments of this pattern are sometimes called "denying the consequent" because they consist of one conditional premise, a second premise that denies (i.e., asserts to be false) the consequent of the conditional, and a conclusion that denies the antecedent of the conditional. Here is an example: If we're in Sacramento, then we're in California.

We're not in California.
Therefore, we're not in Sacramento.

Modus ponens, chain argument, and modus tollens are all logically reliable patterns of deductive reasoning. That is, any argument that has one of these patterns is absolutely guaranteed to have a true conclusion if the premises are also true. But not all patterns of deductive reasoning are completely reliable in this way. Two patterns that are not logically reliable are denying the antecedent and affirming the consequent. Denying the antecedent arguments have the following pattern: If A then B.

Not A.
Therefore, not B.
O most lame and impotent conclusion!
—Shakespeare
Here is an example:
If Shakespeare wrote War and Peace, then he's a great writer. Shakespeare didn't write War and Peace.
Therefore, Shakespeare is not a great writer.
Notice in this example that the premises are true and the conclusion is false. This shows straightaway that the pattern of reasoning of this argument is not logically reliable. Another faulty pattern of deductive reasoning is affirming the consequent. Its pattern is as follows: If A then B.

B.
Therefore, A.

Here is an example:
If we're on Neptune, then we're in the solar system.
We are in the solar system.
Therefore, we're on Neptune.

Given that this argument has true premises and a false conclusion, it is clear that affirming the consequent is not a logically reliable pattern of reasoning. Because modus ponens, modus tollens, and chain argument are logically reliable patterns of reasoning, they should always be treated as deductive. Denying the antecedent and affirming the consequent are not logically reliable patterns of reasoning; nevertheless, they should generally be treated as deductive because they have a pattern of reasoning that is characteristically deductive.

exercise 3.2

For each of the following, indicate which type of hypothetical syllogism it is: modus poiiens, modus tolkns, chain argument, denying the antecedent, or affirming the consequent. In some cases, the argument may need to be rephrased slightly to make the logical pattern explicit. 1. If we're in London, then we're in England. We are not in England. So, we are not in London. 2. If we're in Paris, then we are in France, If we're in France, then we are in Europe. So, if we are in Paris, then we are in Europe. 3. We are not in Mexico, because if we are in Mexico City, we are in Mexico, and we are not...
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