What is the difference between necessary and sufficient conditions in philosophy

Louise is shorter than Sandra , and 2 yR 2 x guarantees xR 1 y. These two-place relations are not converses of one another For it is false that "y is a parent of x" guarantees "x is a daughter of y". Or, consider this case Again, these two relations are not converses of one another. In this instance the first condition of the definition of "converse relation" does not hold.

From "x is not taller than y" it does not follow that "y is shorter than x". Perhaps x and y are exactly the same height. If so, "x is not taller than y" will be true, but "y is taller than x" will be false. If x is a necessary condition for y, then y is a sufficient condition for x. And, equivalently, If y is a sufficient condition for x, then x is a necessary condition for y.

Let's look at some examples that illustrate the claim in the box above: "Since having a microscope is necessary for seeing viruses, then seeing viruses guarantees that one has a microscope i.

James Dean was not a father, but was male]; and being a male is not a sufficient condition for being a father [again the case of James Dean]. Pick any two conditions whatsoever. The relationship between the two conditions must be exactly one of the following four possibilities: The first is a necessary, but not a sufficient, condition for the second; or The first is a sufficient, but not a necessary, condition for the second; or The first is both a necessary and a sufficient condition for the second; or The first is neither a necessary nor a sufficient condition for the second.

Examples 8. Different kinds or modes of necessary condition To be written. NOTES Strictly, although the batteries' being good is usually a necessary condition for a Walkman's working, it is not absolutely necessary. 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. Moreover, he tells us further that some real definitions are to be understood as meaning analyses , or as analytic definitions , of the term in question.

The validation of such claims requires only that we know the meanings of the constituent expressions, and no empirical investigation is necessary to determine the correctness of the analysandum Hempel , 8. This is, of course, precisely what McGinn has in mind with respect to conceptual analysis. It is, then, worth making the obvious point that conceptual analysis is the operation of analyzing concepts via proposing definitions, but to point that out is not enough to fully grasp the view.

It is true that SPM is a method that takes as inputs our concepts, but it involves the clear recognition that the definitions involved are to be understood as meaning analyses rather than as nominal or stipulative i. So, for example, the question of whether knowledge is justified true belief is just the question of the analysis of the concept of knowledge in terms of definitions constituted by sets of necessary and sufficient conditions understood as a meaning analysis.

Conceptual analysis is then a method of doing something with concepts that we already possess— wherever they have ultimately come from. It then appears to be the case that the defenders of SPM must believe that concepts have the form of sets of necessary and sufficient conditions, that such analyses are meaning analyses, and that analyses of our pre-analytic concepts are informative. Typical analysanda are thus kinds of decompositions of pre-analytic concepts.

They are conceptual truths with the form of analytic definitions. So, for McGinn and other like-minded thinkers, analysanda have a very simple logical form, and we can see this via the example of the analysis of the concept of knowledge. This analysis is supposed to tell us the true nature, or essence, of the concept of knowledge in terms of a finite set of defining essential features, with the logical form of a set of jointly necessary and sufficient conditions.

So, providing such an analysis involves decomposing the analysans into a list of features, thus exposing in some important sense the content of the concept. Many recent critics have attacked SPM in terms of 2 - 5 by challenging the reliability of the faculty of intuition.

This is the main line of criticism against SPM offered by many defenders of what is called experimental philosophy , and it is an interesting criticism of orthodox philosophy indeed. However, some critics have alternatively attacked SPM by challenging 1 on the basis of the theory of concepts it assumes; specifically, the idea that concepts can be adequately captured by sets of necessary and sufficient conditions. This criticism is based on the contention that SPM wrongly assumes that concepts take the form of necessary and sufficient conditions at all.

Call this the potential vacuity problem. He addressed the matter of the reliability of SPM in his Philosophical Investigations and The Blue and Brown Books , and therein Wittgenstein attacks the foundation of the project of conceptual analysis by attempting to undermine 1 via examination of the claim that concepts have the form of sets of necessary and sufficient conditions.

This important revelation was made by noting that philosophical attempts at conceptual analysis have systematically failed to produce the goods. He tells us explicitly that,. Wittgenstein , Second, he sought to replace the notion of concepts understood as sets of necessary and sufficient conditions with an alternative theory of concepts. Wittgenstein specifically argued that the concept of a game cannot be correctly analyzed in terms of a set of necessary and sufficient conditions.

This is because games do not share some set of defining features in common. Rather, the members of the set of games are only similar to one another in some respects, and it is these relations of similarity that constitute the family of games.

As we have seen, SPM assumes the following principle:. CON For any concept C, there exists a set of necessary and sufficient conditions that constitutes the content of C. Essentially, the gist of the problem is that if there are no or even just very few concepts that can be correctly regimented as sets of necessary and sufficient conditions, there can be no or very few correct conceptual analyses in the sense of SPM.

This is because, for any proposed set of necessary or sufficient conditions intended to be the correct analysis of a concept, there are instances of that concept that do not meet the set of proposed defining conditions.

Poker and soccer are both plausibly taken to be games and so we might, for example, posit that something is a game, if and only if, that activity involves a winner and a loser. But, the game patty cake is another plausible case of a game and does not have a winner and a loser.

So, this definition of a game in terms of a set of necessary and sufficient conditions fails. Some conditions are both necessary and sufficient. For example, pressing a key on a piano is necessary and sufficient for making the intended sound of that instrument. It is sufficient for making the sound because pressing a key is enough to produce the corresponding note.

It is also necessary because the piano will not produce that sound unless the key is pressed. It is also possible for something to be neither necessary nor sufficient. But typing is not a necessary step either. An understanding of necessity and sufficiency helps us reason through the relationships between and within various statements. It also helps us define difficult concepts and establish conditions for certain positions, like the qualifications for a US president.

Necessity and sufficiency are prevalent in the legal system, too, as they help determine the conditions that render someone guilty or innocent of a crime. For most crimes, a person is guilty if it is proven that they had actus reus, the physical action of a crime, and mens rea, a guilty intention. These are the necessary conditions for establishing guilt. Necessity and sufficiency are prevalent in mathematics, as well.

For example, a whole number ending in the digit 2 is sufficient for the number to be even. It is not necessary, though, because an even number can also end in 0, 4, 6, or 8. In sum, these concepts play important roles wherever reason is used, so they influence nearly every aspect of everyday life.