Module: Argument analysis
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All truly wise thoughts have been thought already thousands of times; but to make them truly ours, we must think them over again honestly, till they take root in our personal experience.
- Johann Wolfgang von Goethe
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In our earlier discussion of valid patterns of arguments, we focus on patterns which can be described using letter symbols that stand for individual statements. Here is modus ponens again:
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 individual 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.
As you can see, this argument is not valid. If you are interested, you can read the tutorials on Venn diagrams, since they are useful tools for evaluating the validity of such arguments. In formal logic, predicate logic is used to formalize and study such arguments more systematically.