Converse and Inverse

In the last few lessons you’ve learned about the valid inferences of the contrapositive and the transitive property. But there are also invalid formal logic inferences, like the converse (flipping a conditional) and the inverse (just taking the negative of a conditional).

A → B

If I press the stop button (A), then the motor will turn off (B).

Fallacy of the Converse

Invalid Inference: reverse A → B into B → A
The motor is off (B); therefore I pressed the stop button (A).
(There are other ways it could have shut off.)

Nice guys finish last: NG → FL
Then you take the converse of that:
If you finish last, you are a nice guy: FL →  NG
To reason that you must be a nice guy because you finished last is the Fallacy of the Converse.

Fallacy of the Inverse

Invalid Inference: negate A → B into ~A → ~B
I didn’t press stop (~A); therefore the motor is on (~B).
(There are other ways it could have shut off.)

George: “Every instinct I have is always wrong.”
George’s principle: I (instinct) → W(wrong).

Jerry Seinfeld: “If every instinct you have is wrong, then the opposite would have to be right.”
Seinfeld uses the Fallacy of the Inverse to negate this:  ~I → ~W.
So, if George just does the opposite of his instincts, he’ll always be correct (the opposite of wrong).

The Fallacy of the Converse and the Fallacy of the Inverse end up as the same thing (see video).

This video is fairly intensive. It describes the Fallacy of the Converse (what they call “Affirming the Consequent”).

The Fallacy of the Inverse is just inverting the two values in a conditional. This is a complex philosophy video. No, you don’t need to understand it in-depth.

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