Valid Argument Patterns
Read this tutorial on how to reduce valid arguments to their basic structure through the use of argument patterns. This reading provides a preview of the kind of analysis we will be doing a lot more of in unit 4. This kind of strategy is sometimes useful with analyzing arguments in real-life situations. For example, you might see these types of questions and find identifying argument patterns useful for the Law School Admission Test (LSAT).
In our earlier discussion of valid patterns of arguments, we focus on patterns which can be described using letter symbols that stand for inpidual statements. Here is modus ponens again:
If P then Q.
P.
Therefore, Q.
As you may recall, the letters P and Q stand for statements. The patterns of valid arguments below are somewhat different though, because the patterns involve breaking down statements into their inpidual components. We hope the examples given make it easy to understand what the patterns are.
Every F is G.
X is F.
So x is G.
Example: Every whale is a mammal. Moby Dick is a whale. So Moby Dick is a mammal.
Every F is G.
Every G is H.
So every F is H.
Example: Every whale is a mammal. Every mammal is an animal. So every whale is an animal.
Every F is G.
X is not G.
So X is not F.
Example: Every whale is a mammal. Nemo is not a mammal. So Nemo is not a whale.
No F is G.
X is F.
So X is not G.
Example: No whale is an insect. Moby Dick is a whale. So Moby Dick is not an insect.
Every F is either G or H.
X is F.
So X is either G or H.
Example: Every human being is either alive or dead. Einstein is a human being. So Einstein is either alive or dead.
Obviously there are lots of such valid patterns of arguments. See if you can construct some more of your own. There are also patterns of arguments that look similar but which are not valid patterns, e.g.
No F is G.
No G is H.
So no F is H.
Example: No whale is a spider. No spider is warm-blooded. So no whale is warm-blooded.
Source: Joe Lau and Jonathan Chan, https://philosophy.hku.hk/think/arg/valid3.php
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