A foolproof system to distinguish necessary and sufficient conditions. Of interest to philosophy students.
* * *
I think it best to start with an example.
It is necessary to be in Scotland while in St Andrews.
It is sufficient to be in St Andrews to be in Scotland.
Umbrellas
The relationship between necessary and sufficient conditions is umbrella-like. The ribbing is the necessary condition; it envelops the sufficient conditions.
For example: the ribbing might be ‘Being a woman.’ it might cover ‘Being a female nurse.’, ‘Being a mother.’, ‘Being a female writer.’,..

Being a woman is necessary for being a mother. Being a mother is sufficient for being a woman.
The System
An assertion is given. We must find what the ribbing is and then what it covers. Consider:
“If it’s hot then I will go for a walk.”
1. Strip the assertion of its particulars.
“If…then…”
2. Substitute in ‘woman’ and ‘mother’ into (1) in all its combinations:
(i) “If [woman] then [mother].”
(ii) “If [mother] then [woman].”
3. Recognise which makes sense:
(i) “If women then mother.”
(ii) “If mother then woman.”
4. Using the recognised form, substitute <necessary condition> for woman, and <sufficient condition> for mother:
“If <necessary condition> then <sufficient condition>”
You’ve distilled the form.
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Returning to the original assertion:
“If it’s hot then I will go for a walk.”
So, “It’s hot” is sufficient for “Going for a walk”. And, “Going for a walk” is necessary for “It’s hot.”
Further Example
Another example without description.
Assertion: “You will get a room provided that you have no pets.”
1.
“… provided …”
2.
(i) “Mother provided woman.”
(ii) “Woman provided mother.”
3.
(i) “Mother provided woman.”
(ii) “Woman provided mother.”
4.
“<necessary condition> provided <sufficient condition>”
“Getting a room.” is necessary for “Having no pets.” And, “Having no pets.” is sufficient for “Getting a room.”
April 03rd 2009