Lesson 9: Necessary and Sufficient condition

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You guys may be used to hear about “necessary and sufficient condition” in Maths. But this is just a shortcut, the full one must include 3 types: necessary condition, sufficient condition and necessary and sufficient condition. These concepts also play a very important role in philosophy reasoning, so understanding them will facilitate you in analyzing important arguments in philosophy.

Explanation of “the three”

Now, think about “mammals” and “cat”. The concept “mammals” has a wider meaning than the concept “cat” because: to be a mammal, an animal can have a lot of options such as cat, dog, goat, buffalo, cow, pig, horse, whale… while to be a cat, an animal only has a sole option, that is cat.

Therefore, we say:

  • Being a mammal is necessary condition to be a cat because a mammal can also be a dog, a goat, a buffalo, a cow, a pig, a horse, a whale
  • But, being a cat is sufficient condition to be a mammal because, of course, a cat is already a mammal!
  • All above refer to: with any cat, we will have a mammal but with any mammal, we will not know for sure that is a cat!

In general, we say:

A is a necessary condition of B if whenever we get B, we get A but not whenever we get A, we get B

A is a sufficient condition of B if whenever we get A, we get B but not whenever we get B, we get A

But, wait, what about the necessary and sufficient condition. It turns out to be very easy. That happens when both directions are true: A is a necessary and sufficient condition of B if whenever we get A, we get B and whenever we get B, we get A.

Applying to mind-body problem

If we say mind is a necessary condition of body, it means with any body, we have a mind but with any mind, we do not always have a body.

If we say mind is sufficient condition of body, it means with any mind, we have a body but with any body, we do not always have a mind.

If we say, mind is necessary and sufficient condition of body, it means whenever we have a mind, we have a body and whenever we have a body, we have a mind.

Please take note, because we will use these to analyzing Cogito the famous argument of Descartes

Practicing on necessary and sufficient conditions

These concepts are easy to understand but also easy to be confused. Let’s practice with a small quiz:

  1. Oxygen is … of fires.
  2. Being above 18 years old is … to own a driving license.
  3. A stop sign … to force a vehicle to stop.
  4. Smoke is … of fires.
  5. Learning philosophy is … to sharpen your mind.
  6. Fire is … of smoke.
  7. Have a medical diploma is … to become a doctor.
  8. Being a single is … to become a bachelor.
  9. Sum of digits is divisible by 3 is … for that number is divisible by 3.
  10. Being divisible by 2 and 3 is … for a number to be divisible by 6