The previous note explained the parts of a conditional sentence, how the parts relate to one another, and how to build a valid syllogism. Nonetheless, it is easy to jump to false conclusions when considering conditional sentences.
The most common fallacy when interpreting conditional statements is technically called denying the antecedent. Denying the antecedent is what happens when someone asks the reverse “And if the fabric is not made of silk, what then?” This is the form of the invalid syllogism:
If this fabric is made of silk, then it will be smooth.
This fabric is not made of silk,
Therefore, this fabric is not smooth.
The syllogism is not valid because the conclusion is not true by necessity. The fabric may or may not be smooth depending on what it is made of; other types of fiber could cause the fabric to be smooth. When one denies the antecedent, he cannot infer any conclusion at all because the condition, the “if,” has not been met.
The second fallacy is called affirming the consequent. Affirming the consequent looks like this:
If you throw a rock, then you will break a window.
You broke a window.
Therefore, you threw a rock.
The problem here is similar to the one above. More than one possible cause for the broken window exists. The person may have thrown a rock, a hammer, or a shot a rifle. The point is that the conclusion is not logically necessary.
Thus, we have looked at valid conditional statements, and invalid conditional statements. Part III introduces conditional statements as the Greeks formed them.