Does 'A caused B' mean that A is a necessary and sufficient condition for B?

Imagine that we go to a shop and buy two items with a total cost 40 dollars (30 for 1st item and 10 for the 2nd). Is the price of the two items the reason we paid 40 dollars? But if the prices were different we still could be paying 40 dollars so we have no relation of necessary and sufficient condition.

What do you think ?

  • I made an edit which you may roll back or further edit. – Frank Hubeny Jul 28 at 22:04
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    "we have no relation of necessary and sufficient condition." - wrong, sufficient condition is here, but not the necessary. Suppose x + y = ? Then having x = 30 and y = 10 is sufficient to say that x + y = 40. – rus9384 Jul 28 at 22:30
  • @rus9384. Are mathematical relations causal ? Logical or 'conventional', I'd have thought. – Geoffrey Thomas Aug 1 at 7:53
  • @GeoffreyThomas, well, dunno about causality, but mathematics operates with conditions and criteria. – rus9384 Aug 1 at 9:10
  • @rus9384. Thanks but isn't causality the precise point ? Good to be exchanging comments again ! Best - Geoff – Geoffrey Thomas Aug 1 at 9:14

Simply put, causality would imply that the cause is a sufficient condition for the effect.

That A caused B would only mean that A is a sufficient condition for B -- not that A is a necessary condition for B. This is because there may be other things that can bring about state B. For it to be a necessary condition, it must be the only condition that can bring this about.

So considering your example with a bit of variation,

I had $40. Now I have zero.

This current state of having zero can be caused by an of a number of sufficient causes:

  1. I lost the $40 in a bet to you
  2. I spent $10 on one thing and $30 on another.
  3. I bought 40 things that cost $1 each
  4. My money was stolen.

etc., etc. Any of these is sufficient for me and my money to part.

Second, causality is a slightly different notion than being either logically necessary or logically sufficient. Necessary and sufficient refer to the relation between statements and do not (necessarily) imply causation between the two things.

Person X is my wife is a sufficient but not necessary condition for me being married. But in no way does this mean that "me being married" is the cause of "X being my wife."

To make it causal, we can

say I married X, therefore X is my wife.

An important distinction between that and the above one I said was not causal is that we now have a temporal sequence.

For much more on causality, see the SEP entry.


Maybe to summarize:

  1. Causality is different from necessary/sufficient in that the former is a metaphysical relation between events (more than but related to the sequence of events) and the latter terms are about logical conditions.
  2. The cause of something can be said to be sufficient to the effect.
  3. The cause of something is not (normally) necessary to the effect.
  4. Something can be necessary or sufficient with respect to something else without being its cause.
  • i am reffering in everyday speech where we say that i did "x" because of "y". So if x didnt occured i wouldnt do y. – ado Jul 30 at 13:09
  • I'm not seeing why that changes much, In that case y is seen as a sufficient condition for x and simultaneously a cause of x. Can you clarify what you else you were expecting? – virmaior Jul 30 at 13:20

Is causality a type of necessary and sufficient condition? NO.

I don't understand your example, but you might consider another: If it is raining, then it is cloudy. Or equivalently, rain is sufficient for clouds. Or clouds are necessary for rain.

This does not mean that clouds cause rain or that rain causes clouds. It means simply that it is not the case that it is raining and not cloudy at a given instant in time. It says nothing about causality, historical data or probabilities.

The following are logically equivalent statements:

  • P implies Q
  • If P then Q
  • Q if P
  • P only if Q
  • P is sufficient for Q
  • Q is necessary for P
  • ~P or Q
  • ~(P and ~Q)

What then is causality? What do we mean, for example, by smoking causes cancer? There is nothing "metaphysical" about. Nor does it just mean that there is a strong correlation between smoking and cancer. It means that scientists have documented and repeatedly confirmed precisely how, at the molecular level, certain chemicals found in tobacco smoke can lead to the growth of cancerous cells in the human body.

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