Friday, January 2, 2015

Modus ponens & Affirming the Consequent

One of the most basic rules of validity is known as modus ponens, "the affirming way."  In short, it says that if I have a conditional statement and the first part of the statement is true, the second part must also be true.  This is often written as "If P, then Q.  P is true, so Q must be true."

Here are a few examples:

If it is raining, the ground is wet.  It is raining, so the ground is wet.

If you are human, you are also a mammal.  You are a human, therefore you're a mammal.

If you get 3 strikes, you're out.  You have three strikes, so you're out.

Each example follows the same logical structure.  If (something happens), then (something else will happen).  Since (the first thing happened), I know that (the second thing happens).  I know that the ground is wet because it is raining.  I know that I am a mammal because I am human.  I know that I'm out because I got 3 strikes.

Keep in mind that this does not work in reverse. I do not know that it is is raining just because the ground is wet (someone could be washing their car).  I do not know that I am human because I'm a mammal (I could be a horse).  I do not know that I got 3 strikes because I'm out (I could have hit a pop fly).  If I were to make an argument this way, I would commit the formal fallacy known as affirming the consequent.

The consequent is the Q part of "If P, then Q."  This fallacy effectively says, "If P, then Q.  I know that Q is true, so P must be true."  As shown in the examples above, this isn't true.  There could be other reasons Q is true without P being true.

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