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Is the following reasoning correct: For a logical condition to be sufficient (but not necessary) there need to be other sufficient conditions that share/imply the same consequent; if there aren't any, then the above (seemingly) sufficient condition is also a necessary one.
Thank you.

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@Premiere71,

Sorry, I don't know the answer. All I know is an old Star Trek quote: "Logic is a little bird tweeting in meadow; logic is a wreath of pretty flowers which ... smell bad..." Good luck.

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@Premiere71,

Sounds reasonable to me. If there is only one sufficient condition then it must also be necessary and you have an iff scenario.

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@Premiere71,

You can have fun with this with "the virgin birth" and "sexual intercourse". Wink

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@Premiere71,

If A -> B and B -> A, then A is both necessary and sufficient. Without the converse being true, A is just sufficient, but not necessary.

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@Premiere71,

Premiere71 wrote:

Is the following reasoning correct: For a logical condition to be sufficient (but not necessary) there need to be other sufficient conditions that share/imply the same consequent; if there aren't any, then the above (seemingly) sufficient condition is also a necessary one.
Thank you.

Nothing can be sufficient without being necessary, although it can be necessary without being sufficient: being sufficient is being all that is necessary, which is being necessary.

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@guigus,

In logic terms, being necessary means being absolutely required. For example winning the lottery is sufficient to be rich, but it is not necessary since there are other ways to reach the same endpoint.

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@engineer,

engineer wrote:

In logic terms, being necessary means being absolutely required. For example winning the lottery is sufficient to be rich, but it is not necessary since there are other ways to reach the same endpoint.

In whatever terms, the concept of "enough" presupposes the concept of "needed": if it is enough that I win the lottery to get rich, then that is also needed, since "being needed" is part of the concept of "being enough". You are confusing the fact that another event can fulfill that need as well, for example, my success in an aggressive business move, which can make my winning the lottery no longer needed by my getting rich -- although not for my getting even richer. You can easily see this by just imagining a situation in which I can only get rich by winning the lottery, that is, in which no other event can fulfill that need, which is always there.

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@engineer,

Suppose at least one of two events A and B must happen so a third event C can happen. Sure it is false to say that both A and B are needed by C. But it is just as false to say that neither A nor B are needed by C. The key here is that both A and B are possibly needed by C, and neither one will become actually needed by C unless either A or B and C both happen. Unfortunately, your (classic) logic disregards possible necessity, trying to hide it behind sufficiency.

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@guigus,

guigus wrote:

Suppose at least one of two events A and B must happen so a third event C can happen. Sure it is false to say that both A and B are needed by C. But it is just as false to say that neither A nor B are needed by C. The key here is that both A and B are possibly needed by C, and neither one will become actually needed by C unless either A or B and C both happen. Unfortunately, your (classic) logic disregards possible necessity, trying to hide it behind sufficiency.

You realize this is a math problem right? There is no "disregarding" here, we are using the definitions for the words in the context of the problem.

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@engineer,

engineer wrote:

guigus wrote:

Suppose at least one of two events A and B must happen so a third event C can happen. Sure it is false to say that both A and B are needed by C. But it is just as false to say that neither A nor B are needed by C. The key here is that both A and B are possibly needed by C, and neither one will become actually needed by C unless either A or B and C both happen. Unfortunately, your (classic) logic disregards possible necessity, trying to hide it behind sufficiency.

You realize this is a math problem right? There is no "disregarding" here, we are using the definitions for the words in the context of the problem.

We are talking about necessity and sufficiency here, and as far as I know those terms are not inherently mathematical, are they?

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@engineer,

engineer wrote:

guigus wrote:

Suppose at least one of two events A and B must happen so a third event C can happen. Sure it is false to say that both A and B are needed by C. But it is just as false to say that neither A nor B are needed by C. The key here is that both A and B are possibly needed by C, and neither one will become actually needed by C unless either A or B and C both happen. Unfortunately, your (classic) logic disregards possible necessity, trying to hide it behind sufficiency.

You realize this is a math problem right? There is no "disregarding" here, we are using the definitions for the words in the context of the problem.

What classic logic, with its mathematical formalism, necessarily (see?) fails to understand -- since you disliked "disregards" -- is possible necessity. Take the example I gave you: if either A or B must happen so C can happen, then A and B are both possibly needed by C.

Premiere71 was close to see this with the original post of this thread, in which sufficiency suddenly reveals its necessity face in the absence of any other possible necessity.

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