In yesterday’s lesson, you learned how to evaluate arguments with multiple premises. All the examples that you’ve seen so far have been simple arguments—that is, ones with a single conclusion and one or more premises. In today’s lesson, you will learn about a type of complex argument that joins two or more simple arguments together.
One aspect of the complexity of argumentation is that real-life arguments are often connected. For instance, the conclusion of one argument may be the premise of another, so a series of arguments may be linked together like a chain. What links chain arguments together are statements that are the conclusion of one argument in the chain and the premise of the next.
Example: “The fact is that between the time the [dauphin’s] doll was placed on the exhibit platform and the time the theft was discovered no one and no thing touched it. Therefore between the time the doll was placed on the platform and the time the theft was discovered the dauphin [doll] could not have been stolen. It follows, simply and inevitably, that the dauphin [doll] must have been stolen outside that period.” (Source: Ellery Queen, The Dauphin’s Doll, italics in the original)
So, let’s analyze this passage:
1. There are three statements:
a. “The fact is that between the time the doll was placed on the exhibit platform and the time the theft was discovered no one and no thing touched it.”
b. “Between the time the doll was placed on the platform and the time the theft was discovered the dauphin could not have been stolen.”
c. “The dauphin must have been stolen outside that period.”
2. There are two conclusion indicators, “therefore” and “it follows … that.” This means that there are two arguments in the passage. Also, the placement of the indicators shows that statements b and c are conclusions. Statement a is not marked, so it must be a premise if it is a part of either argument.
3. That the first statement is a premise can be seen by the fact that the argument from a to b makes sense: If no one touched the doll during that time period, then it could not have been stolen then.
4. Statement b is also a premise by the fact that the argument from b to c makes sense: If the doll could not have been stolen in that time period, then it must have been stolen at some other time.
5. Therefore, this passage contains a chain of two arguments linked together by statement b, which is the conclusion of the first one and the premise of the second.
This passage is an example of the simplest and most common types of complex argument—that is, one in which two single-premised arguments are connected in a chain. Clearly, this process of linking together arguments in a chain can be extended as far as you please, so chain arguments can be made up of three or more simple arguments.
Evaluating a deductive chain argument is based on the familiar principle that a chain is only as strong as its weakest link. Thus, a deductive chain argument will be valid if and only if every simple argument in the chain is valid. Also, a deductive chain argument will be invalid if even a single argument in the chain is invalid. Therefore, to evaluate a chain of deductive arguments, you simply evaluate each argument in the chain. If you find even one invalid argument, the chain breaks: The whole chain is invalid.
Evaluating inductive chain arguments is similar but more complicated than evaluating deductive ones. The basic principle that a chain is no stronger than its weakest link holds for inductive chains, but unlike deductive arguments, an inductive chain as a whole may be weaker than any of its links. In fact, the longer an inductive chain gets, the weaker it is likely to be. However, that’s a topic for a more advanced course.
Congratulations on reaching the end of this series of lessons on logic! I hope you find what you have learned useful in your future life. Good luck!
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