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Direct Method of agreement
For a property to be a necessary condition it must always be present if the effect is present. Since this is so, then we are interested in looking at cases where the effect is present and talking not of which porperties, among those considered to be 'possible necessary conditions' are present and which are absent. Obviously, any properties which are absent when the effect is present cannot be necessary conditions for the effect
Method of difference
If one set of circumstances leads to a given phenomenon, and another set of circumstances does not, and the sets differ only in a single factor that is present in the first set but not in the second, then the phenomenon can be attributed to that factor.
Joint method of agreement and difference
Also called simply the "joint method," this principle simply represents the application of the methods of agreement and difference.
Method of residues
If a range of factors are believed to cause a range of phenomena, and we have matched all the factors, except one, with all the phenomena, except one, then the remaining phenomenon can be attributed to the remaining factor.
Method of concomitant variations
If across a range of circumstances leading to a phenomenon, some property of the phenomenon varies in tandem with some factor existing in the circumstances, then the phenomenon can be attributed to that factor. For instance, suppose that various samples of water, each containing both salt and lead, were found to be toxic. If the level of toxicity varied in tandem with the level of lead, one could attribute the toxicity to the presence of lead.
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