Arguments with Multiple Premises
Episode #9 of the course Logic basics: Understanding arguments by Gary Curtis
In yesterday’s lesson, you learned the basic terminology for evaluating arguments. In today’s lesson, you’ll return to analyzing argument structure and dive deeper into arguments that have two or more premises.
Types of Support
The simplest arguments have only a single premise, but it’s common to have two or more. When arguments have multiple premises, there are two ways that those premises can logically support the conclusion:
1. Mutually. This means that the premises work together to support the conclusion. As a result, if you were to remove one or more premises, the argument would fail to support the conclusion.
Example:
A. If Colonel Mustard is innocent, then Miss Scarlet must be guilty.
B. Colonel Mustard did not murder the victim.
C. Therefore, Miss Scarlet must have done so.
This is a valid deductive argument, but remove one of the premises and the argument would fail to support the conclusion. Thus, the premises of the example support the conclusion mutually.
2. Independently. When the premises of an argument support the conclusion independently, this means that they don’t do so mutually, meaning each premise supports the conclusion on its own. Arguments with independent premises are, in effect, two or more arguments in one. So, if the argument can be split into two or more separate arguments that support the same conclusion, then the premises of the different arguments work independently.
Example: “We know two shots were fired almost simultaneously because Miss Porter and I heard them, and because we found a .22 caliber bullet in Ericsson’s head and a .38 shell on the floor near Ericsson’s .38 automatic.” (Source: Ellery Queen, “The Needle’s Eye”)
First of all, let’s analyze the structure of this argument. As an exercise, try it yourself before continuing.
1. There are three statements in this argument:
a. We know two shots were fired almost simultaneously.
b. Miss Porter and I heard them.
c. We found a .22 caliber bullet in Ericsson’s head and a .38 shell on the floor near Ericsson’s .38 automatic. (This statement could be treated as two separate premises joined by “and” that support the conclusion mutually—and it wouldn’t change the analysis significantly to do so. To keep things simple, I’m treating it as a single statement.)
2. There are two occurrences of the premise indicator “because,” indicating that statements b and c are premises.
3. There is no conclusion indicator, but the argument from b and c as premises to a as the conclusion makes sense.
This is an inductive argument, and each of the premises supports the conclusion independently. There are two premise indicators because there are two independent reasons for concluding that two shots were fired almost simultaneously. The argument is stronger with both premises, but it would not fail completely if either were removed.
Evaluating Arguments with Independent Premises
Deductive arguments that have multiple independent premises will be valid only if at least one premise validly supports the conclusion. So, you can evaluate such an argument premise by premise, and if you find one that validly supports the conclusion, then you can stop: The whole argument is valid. If you do not find such a premise, then the whole argument is invalid.
Warning: Because a deductive argument with independent premises is, in effect, two or more arguments in one, and because one or more of its premises may fail to support the conclusion, it may be tempting to reject the compound argument as a whole because one or more of the component arguments is invalid. However, if even one of the premises validly supports the conclusion, the whole argument is valid. So, don’t jump to conclusions: You must check each independent premise.
The situation with inductive arguments is much more complicated. An inductive argument with independent premises is usually weaker if some premises are removed and stronger if it contains them, but the independent premises may still support the conclusion individually.
In the final lesson tomorrow, you’ll get a brief look at how simple arguments can be linked to create complex ones.
Recommended book
Logic: A Very Short Introduction by Graham Priest
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