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In the last lesson you learned that the contrapositive is a valid inference. However, beware of invalid inferences:
Let’s use this example to teach the inverse and the converse:
If I press the stop button (A), then the motor will turn off (B).
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.
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).
“In order to be irreplaceable one must always be different.” (Coco Chanel)
irreplaceable → different
1. If you are different, then you are irreplaceable.
different → irreplaceable
This is an invalid inference because this is the converse of the original statement. A statement and its converse are not logically equivalent.
2. If you are not different, then you are not irreplaceable.
~different → ~irreplaceable
This is a valid inference because this is the contrapositive of the original statement. A statement and its contrapositive are logically equivalent.
3. If you are not irreplaceable, then you are not different.
~irreplaceable → ~different
This is an invalid inference because this is the inverse of the original statement. A statement and its inverse are not logically equivalent.
Statement | Symbols | Valid/Invalid | Description |
1. In order to be irreplaceable one must always be different. | irreplaceable → different | Given | Given |
2. If you are different, then you are irreplaceable. | different → irreplaceable | Invalid | Converse |
3. If you are not different, then you are not irreplaceable. | ~different → ~irreplaceable | Valid | Contrapositive |
4. If you are not irreplaceable, then you are not different. | ~irreplaceable → ~different | Invalid | Inverse |
Next LSAT: June 14/15th
The Fallacy of the Converse and the Fallacy of the Inverse end up as the same thing (see video).
Identfiy whether the following inferences are valid or invalid.
Whenever a siren is heard, my dog becomes scared. My dog did not become scared.
If the above statements are true, which one of the following is also true?
(A) A siren is not heard.
(B) A siren is heard.
(A) A siren is not heard.
Statement |
Symbols |
Valid/Invalid |
Description |
1. Whenever a siren is heard, my dog becomes scared. |
siren → dog scared |
Valid |
Given |
2. If my dog does not become scared, then a siren is not heard. |
~dog scared → ~siren |
Valid |
Contrapositive |
3. If a siren is not heard, then my dog does not become scared. |
~siren → ~dog scared |
Invalid |
Inverse |
4. If my dog becomes scared, then a siren is heard. |
dog scared → siren |
Invalid |
Converse |
“In order to write about life first you must live it.” (Ernest Hemingway)
write → live
1. If you did not live life, then you cannot write about it.
~live → ~write
This is a valid inference because this is the contrapositive of the original statement. A statement and its contrapositive are logically equivalent.
2. If you lived life, then you can write about it.
~write → ~live
This is an invalid inference because this is the inverse of the original statement. A statement and its inverse are not logically equivalent.
3. If you did not write about life, then you cannot live it.
live → write
This is an invalid inference because this is the converse of the original statement. A statement and its converse are not logically equivalent.
“If you’re changing the world, you’re working on important things.” (Larry Page)
change → important things
1. If you are not changing the world, then you are not working on important things.
~change → ~important things
This is an invalid inference because this is the inverse of the original statement. A statement and its inverse are not logically equivalent.
2. If you are not working on important things, then you are not changing the world.
~important things → ~change
This is a valid inference because this is the contrapositive of the original statement. A statement and its contrapositive are logically equivalent.
3. If you are working on important things, then you are changing the world.
important things → change
This is an invalid inference because this is the converse of the original statement. A statement and its converse are not logically equivalent.
“Those who cannot remember the past are condemned to repeat it.” (George Santayana)
~remember → condemned
1. If you remembered the past, then you are not condemned to repeat it.
remember → ~condemned
This is an invalid inference because this is the inverse of the original statement. A statement and its inverse are not logically equivalent.
2. If you are condemned to repeat the past, then you did not repeat it.
condemned → ~remember
This is an invalid inference because this is the converse of the original statement. A statement and its converse are not logically equivalent.
3. If you are not condemned to repeat the past, then it means you remembered it.
~condemned → remember
This is a valid inference because this is the contrapositive of the original statement. A statement and its contrapositive are logically equivalent.
This is an adaptive drill: The questions will get harder or easier depending on your performance. You can't go backwards or change prior answers.
Complete: 0 / 11 correct
Next LSAT: June 14/15th