Modus Ponens
Modus Ponens (MP) is one of the most common rules of inference. From the Latin, “the way to affirm by affirming”, it follows the form of affirming the antecedent of an implication and inferring its consequent.
a → b
a
b
Note: MP is based on the implication: You can review it here.
Although the words that describe MP can sound intimidating, MP is very straightforward. One easy way to think about it is by using the geography analogy from the implication lesson:
“If you are in Los Angeles (L), then you are in California (C). You are in Los Angeles (L), thus, you are in California (C)”.
- L → C
- L
- C MP 1, 2
Using this example, it becomes clear that whenever “something” that is sufficient is true, whatever is necessary for that “something” must also be true. In the example above, if you are in Los Angeles, then it is necessary that you are in California.
Here are some more examples:
-
“If the dog barks (B), then the cat runs away (R). The dog barked (B). So, the cat ran away (R).”
- B → R
- B
- R MP 1, 2
-
“Fewer and fewer people are voting (V). Democracy ceases to exist (E) if fewer and fewer people vote (V). So, democracy will cease to exist (E).”
- V
- V → E
- E MP 2, 1
Note: The implication is on line two in the example above. The order of the premises is interchangeable as long as the form is followed.
-
“We should bail out the banks (B) only if there is a method of ensuring we will not have to bail them out again (M). We bailed out the banks (B). Therefore, there is a method of ensuring we will not have to bail them out again (M).”
- B → M
- B
- M MP 1, 2
Note: Although the argument above is valid, it is not sound.
In each example, there is some condition a, where if that condition is affirmed, it necessitates some conclusion b given an implication a → b.
The most common pitfall when using MP is the fallacy of the converse, which occurs when the sufficient condition of the given implication is confused for the necessary condition. This was touched upon on the lesson for the Implication and is also one of the most common errors in the Validity and Inference activities that are found in the Symbols Logic app.
Restated briefly, the fallacy of the converse follows this form:
a → b
b
a
Note: The fallacy of the converse affirms the consequent of the given implication and concludes its antecedent. That is like saying “If you live in Los Angeles, then you live in California. You live in California, so, you live in Los Angeles, which is invalid because you can potentially be anywhere in California, so you may or may not be in Los Angeles.
In the next lesson, we will look at the “the way that denies by denying”, better known as, Modus Tollens (MT).
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app now:
Modus Ponens (MP) is one of the most common rules of inference. From the Latin, “the way to affirm by affirming”, it follows the form of affirming the antecedent of an implication and inferring its consequent.
a → b
a
b
Note: MP is based on the implication: You can review it here.
Although the words that describe MP can sound intimidating, MP is very straightforward. One easy way to think about it is by using the geography analogy from the implication lesson:
“If you are in Los Angeles (L), then you are in California (C). You are in Los Angeles (L), thus, you are in California (C)”.
- L → C
- L
- C MP 1, 2
Using this example, it becomes clear that whenever “something” that is sufficient is true, whatever is necessary for that “something” must also be true. In the example above, if you are in Los Angeles, then it is necessary that you are in California.
Here are some more examples:
-
“If the dog barks (B), then the cat runs away (R). The dog barked (B). So, the cat ran away (R).”
- B → R
- B
- R MP 1, 2
-
“Fewer and fewer people are voting (V). Democracy ceases to exist (E) if fewer and fewer people vote (V). So, democracy will cease to exist (E).”
- V
- V → E
- E MP 2, 1
Note: The implication is on line two in the example above. The order of the premises is interchangeable as long as the form is followed.
-
“We should bail out the banks (B) only if there is a method of ensuring we will not have to bail them out again (M). We bailed out the banks (B). Therefore, there is a method of ensuring we will not have to bail them out again (M).”
- B → M
- B
- M MP 1, 2
Note: Although the argument above is valid, it is not sound.
In each example, there is some condition a, where if that condition is affirmed, it necessitates some conclusion b given an implication a → b.
The most common pitfall when using MP is the fallacy of the converse, which occurs when the sufficient condition of the given implication is confused for the necessary condition. This was touched upon on the lesson for the Implication and is also one of the most common errors in the Validity and Inference activities that are found in the Symbols Logic app.
Restated briefly, the fallacy of the converse follows this form:
a → b
b
a
Note: The fallacy of the converse affirms the consequent of the given implication and concludes its antecedent. That is like saying “If you live in Los Angeles, then you live in California. You live in California, so, you live in Los Angeles, which is invalid because you can potentially be anywhere in California, so you may or may not be in Los Angeles.
In the next lesson, we will look at the “the way that denies by denying”, better known as, Modus Tollens (MT).
Want an interactive way to learn logic?
Enhance your critical thinking skills with Symbols Logic. Unlock access to the first studycard and the first level of all activities for free. Get the app now: