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May 23 • ❓ Ask & Apply
Modus Ponens and its Tricky Fallacy - You Fall for it Everyday
There is a logical formula called modus ponens (Latin for "mode that affirms").
It is a valid deductive argument structure. This is fancy talk that just means it is a formula that works and is true.
It goes like this:
  1. If P, then Q. (Premise)
  2. P. (Premise)
  3. Therefore, Q. (Conclusion)
P and Q are used as variables in logic just like X and Y are used a lot in math.
Let's give some examples so it makes sense.
  1. Premise 1: If it is raining (P), then the ground is wet (Q).
  2. Premise 2: It is raining (P).Conclusion:
  3. Therefore, the ground is wet (Q).
  1. Premise 1: If a shape is a square (P), then it has four equal sides (Q).
  2. Premise 2: This shape is a square (P).
  3. Conclusion: Therefore, it has four equal sides (Q).
  1. Premise 1: If water is heated to 100°C at sea level (P), then it boils (Q).
  2. Premise 2: The water is heated to 100°C at sea level (P).
  3. Conclusion: Therefore, the water boils (Q).
  1. Premise 1: If the device is unplugged (P), then it will turn off (Q).
  2. Premise 2: The device is unplugged (P).
  3. Conclusion: Therefore, it will turn off (Q).
  1. Premise 1: If the train is delayed (P), then you will be late (Q).
  2. Premise 2: The train is delayed (P).
  3. Conclusion: Therefore, you will be late (Q).
Take a look at the order: it is P --> Q. This is important.
Now let's look at the fallacy using modus ponens that tricks you every day.
Let's start with an example first:
Premise 1: If it is a dog (P), then it has four legs (Q).
Premise 2: This animal has four legs (Q).
Conclusion: Therefore, it is a dog (P).
That sounds right, doesn't it?
But it's not. Not right at all.
Many other animals have four legs, it may not be a dog.
This fallacy is called Affirming the Consequent.
What is happening is we are switching the order of the last two statements.
Modus ponens looks like this:
If P→Q and P, then Q
Affirming the consequent fallacy looks like this:
If P→Q and Q, then P
This is a very important distinction.
Affirming the consequent is always invalid.
Let's look at more examples of affirming the consequent to help clarify it:
  1. Premise 1: If a language is tonal (P), then it is hard to learn (Q).
  2. Premise 2: This language is hard to learn (Q).
  3. Conclusion: Therefore, it is tonal (P).
  4. (Fallacy: Many non-tonal languages are hard.)
  1. Premise 1: If a drink is coffee (P), then it contains caffeine (Q).
  2. Premise 2: This drink contains caffeine (Q).
  3. Conclusion: Therefore, it is coffee (P).(
  4. Fallacy: Tea, soda, and chocolate contain caffeine.)
  1. Premise 1: If a bird is a penguin (P), then it cannot fly (Q).
  2. Premise 2: This bird cannot fly (Q).
  3. Conclusion: Therefore, it is a penguin (P).
  4. (Fallacy: Could be an ostrich, kiwi, etc.)
  1. Premise 1: If the economy is growing (P), then stocks rise (Q).
  2. Premise 2: Stocks are rising (Q).
  3. Conclusion: Therefore, the economy is growing (P).
  4. (Fallacy: Could be a bubble or speculation.)
  1. Premise 1: If a knife was the murder weapon (P), then it has fingerprints (Q).
  2. Premise 2: This knife has fingerprints (Q).
  3. Conclusion: Therefore, it was the murder weapon (P).
  4. (Fallacy: Could be from cooking.)
  1. Premise 1: If the battery is dead (P), then the car won’t start (Q).
  2. Premise 2: The car won’t start (Q).
  3. Conclusion: Therefore, the battery is dead (P).
  4. (Fallacy: Could be the alternator, spark plugs, etc.)
Why These Are Fallacies
  • Q can be true for reasons unrelated to P.
  • Ignores alternative explanations.
-------------
Why is this so tricky?
Because sometimes it can sound correct, and can be used as a weapon.
If the A party stole money from the budget, the budget will be insufficient.
The budget is insufficient.
Therefore A party stole money.
Now there will be mass media and social media attack campaigns agains A party and many people will falsely believe this.
It could be true that A party did steal money, but this does not prove it at all. There could be many many reasons the budget is insufficient.
Another common example is with the medical industry.
If person has disease X, he will die.
He died.
Therefore he has disease X.
Now we better wear masks, lockdown and take experimental drugs. If you don't follow orders, you are a science denier.
His dying does not prove in any way that disease X exists. It could have been from many things like the treatment or age or accident or doctor negligence.
Ask yourself: Can Q happen without P? If yes, it’s a fallacy.
Be careful out there.
Think.
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Tristan Van der Wereld
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Modus Ponens and its Tricky Fallacy - You Fall for it Everyday
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