That the glass contains mostly H 2 O is a necessary condition of its containing water. Despite its initial appeal, objections to the standard theory have been made by theorists from a number of backgrounds. However, the gaseous nature of the sun would not normally be regarded as either a conceptually, or even a contingently, necessary condition of the quadripedality of elephants. Indeed, according to the standard theory, any truth will be a necessary condition for the truth of every statement whatsoever, and any falsehood will be a sufficient condition for the truth of any statement we care to consider.
These odd results would not arise in some non-classical logics where it is required that premisses be relevant to the conclusions drawn from them, and that the antecedents of true conditionals are likewise relevant to the consequents.
These oddities might be dismissed as mere anomalies were it not for the fact that writers have apparently identified a number of other problems associated with the ideas of reciprocity and equivalence mentioned at the end of the previous section.
Consider, for example, the following case drawn from McCawley , p. While in the case of the door, using the key was necessary for opening it, no parallel claim seems to work for ii : in the natural reading of this statement, my screaming is not necessary for your touching me. The natural interpretation of ii is that my screaming depends on your touching me. To take my screaming as a necessary condition for your touching me seems to get the dependencies back to front.
A similar concern arises if it is maintained that ii entails that you will touch me only if I scream. A similar failure of reciprocity or mirroring arises in the case of the door example i above.
While opening the door depended, temporally and causally, on using the key first, it would be wrong to think that using the key depended, either temporally or causally, on opening the door. So what kind of condition does the antecedent state? To get clear on this, we can consider a baffling pair of conditional sentences a modification of Sanford , —6 :. While iii states a condition under which I buy Lambert a cello presumably he first learns by using a borrowed one, or maybe he hires one , iv states a necessary condition of Lambert learning to play the instrument in the first place there may be others too.
Indeed, if we take them together, the statements leave poor old Lambert with no prospect of ever getting the cello from me.
If iv were just equivalent to iii , combining the two statements would not lead to an impasse like this. A natural, English equivalent is surprisingly hard to formulate.
Perhaps it would be something like:. A still better but not completely satisfactory version requires further adjustment of the auxiliary, say:. This time, it is not so easy to read vi as implying that I bought Lambert a cello before he learned to play. Assessment of this claim lies beyond the scope of the present article see the entry on conditionals and the detailed discussion in Bennett What the case suggests is that different kinds of dependency are expressed by use of the conditional construction: iv is not equivalent to iii because the consequent of iii provides what might be called a reason for thinking that Lambert has learned to play the cello.
By contrast, the very same condition—that I buy Lambert a cello—appears to fulfil a different function in iv namely that I first have to buy him a cello before he learns to play. In the following section, the possibility of distinguishing between different kinds of conditions is discussed. The possibility of ambiguity in these concepts raises a further problem for the standard theory. According to it—as von Wright pointed out von Wright , 7 —the notions of necessary condition and sufficient condition are themselves interdefinable:.
Ambiguity would threaten this neat interdefinability. In the following section, we will explore whether there is an issue of concern here. The possibility of such ambiguity has been explored in work by Downing , , Wilson , and has also been raised more recently in Goldstein et al. These writers have argued that in some contexts there is a lack of reciprocity between necessary and sufficient conditions understood in a certain way, while in other situations the conditions do relate reciprocally to each other in the way required by the standard theory.
If these critics are right, and ambiguity is present, then there is no general conclusion that can safely be drawn about reciprocity, or lack of it, between necessary and sufficient conditions. Instead there will be a need to distinguish the sense of condition that is being invoked in a particular context. By means of a semi-formal argument, Carsten Held has suggested a way of explaining why necessary and sufficient conditions are not converses, making appeal to a version of truthmaker theory Held In what follows, we do not follow this route, but instead explore ways of making sense of the lack of reciprocity between the two kinds of conditions in terms of the difference between inferential, evidential and explanatory uses of conditionals.
What he probably means is that the occurrence of the battle explains the truth of the statement, rather than explanation being the other way around. Of course, people sometimes do undertake actions just to ensure that what they had formerly said turns out to be true; so there will be cases where the truth of a statement explains the occurrence of an event.
But this seems an unlikely reading of the sea battle case. If S is true today, it is correct to infer that a sea battle will occur tomorrow. That is, even though the truth of the sentence does not explain the occurrence of the battle, the fact that it is true licenses the inference to the occurrence of the event. From this observation, it would appear that there is a gap between what is true of inferences, and what is true of explanations.
There is an inferential sense in which the truth of S is both a necessary and sufficient condition for the occurrence of the sea battle.
However, there is an explanatory sense in which the occurrence of the sea battle is necessary and sufficient for the truth of S , but not vice versa. It would appear that in cases like vii and viii the inferences run in both directions, while explanations run only one way.
Why do you think necessary and sufficient conditions are confused so often? Teacher Resources. Download Lesson Plan. Download Worksheet. View On EdPuzzle. Sign up for our educators newsletter to learn about new content! Sign Up. Get updated about new videos! Learn More. Wireless Philosophy.
If x, then y sufficiency and necessity Article. Khan Academy. Brennan, A. Necessary and sufficient conditions. Zalta Ed. The counselor told me that if I wanted to graduate I must have at least credit hours. Well, I've got that, but they're saying I won't walk this semester. How misleading! The job description said that they were looking for someone with a Master's degree. I've got my MA, but I cannot understand why they did not hire me. My high school English teacher told me successful people have extensive vocabularies.
So, I've tried to learn a new vocabulary word every day since then. Sometimes there are things that are easily proven or are already guaranteed or are already given to be true which makes it a condition both necessary and sufficient. By using the necessary and sufficient conditions, it will be easier to prove statements. The former statement must be true for a statement to be true in a sufficient condition and later for the necessary condition.
A necessary condition should be proven by the next statement while a sufficient condition, if proven true, the next statement follows to be true as well.
Difference Between Necessary and Sufficient. Difference Between Similar Terms and Objects. MLA 8 Magno, Eva. Name required. Email required. Please note: comment moderation is enabled and may delay your comment.
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