Mill's Methods
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Mill's methods
Five methods of experimental reasoning distinguished by John Stuart Mill in his System of Logic (1843). Suppose one is interested in determining what factors play a role in causing a specific effect, E, under a specific set of circumstances. The method of agreement tells us to look for factors present on all occasions when E occurs. The method of difference tells us to look for some factor present on some occasion when E occurs and absent on an otherwise similar occasion when it does not. The joint method of agreement and difference combines the two previous methods. The method of residues applies when part of E is explicable by reference to known factors, and tells us to attribute the residue to the remaining circumstances under which E occurs. The method of concomitant variation is used when E can be present in various degrees; if we identify a factor F, such as temperature, whose variations are positively or negatively correlated with variations in E, for instance, size, then we can infer that F is causally connected with E.
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Mill's methods
(or canons) The five inductive principles proposed by J. S. Mill as those regulating scientific enquiry. They are (i) The method of agreement. If two cases of a phenomenon share only one feature, that feature is their cause or their effect. (ii) The method of difference. If a case in which a phenomenon occurs and one in which it does not differ by only one other feature, that feature is the cause, or a necessary part of the cause of the phenomenon, or it is its effect. (iii) The joint method of agreement and difference. This combines the previous two. (iv) The method of residues. If we subtract from a phenomenon what is already known to be the effect of some antecedent events, then the remainder is the result of the remaining antecedents. (v) The method of concomitant variation. Phenomena that vary together are linked through some causal relationship. While the methods make good scientific sense they do depend upon a preceding analysis of the relevant factors, and they are not immediately applicable to cases where causation proceeds more ‘holistically’, or in virtue of a field of interlocking factors.
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Mill's Methods
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Mill's Methods are five methods of induction described by philosopher John Stuart Mill in his 1843 book A System of Logic. They are intended to illuminate issues of causation.
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Contents
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Direct method of agreement
"If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon."
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 taking note of which properties, 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.
Symbolically, the method of agreement can be represented as:
- A B C D occur together with w x y z
- A E F G occur together with w t u v
- ——————————————————
- Therefore A is the cause of w.
Method of difference
“If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon.”
A B C D occur together with w x y z
B C D occur together with x y z
——————————————————
Therefore A is the cause, or the effect, or a part of the cause of w.
Joint method of agreement and difference
"If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance: the circumstance in which alone the two sets of instances differ, is the effect, or cause, or a necessary part of the cause, of the phenomenon."
Also called simply the "joint method," this principle simply represents the application of the methods of agreement and difference.
Symbolically, the Joint method of agreement and difference can be represented as:
- A B C occur together with x y z
- A D E occur together with x v w also B C occur with y z
- ——————————————————
- Therefore A is the cause, or the effect, or a part of the cause of x.
Method of Residue
"Deduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents."
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.
Symbolically, the Method of Residue can be represented as:
- A B C occur together with x y z
- B is known to be the cause of y
- C is known to be the cause of z
- ——————————————————
- Therefore A is the cause or effect of x.
Method of concomitant variations
"Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation."
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.
Symbolically, the method of concomitant variation can be represented as (with ± representing a shift):
- A B C occur together with x y z
- A± B C results in x± y z.
- —————————————————————
- Therefore A and x are causally connected
Unlike the preceding four inductive methods, the method of concomitant variation doesn't involve the elimination of any circumstance. Changing the magnitude of one factor results in the change in the magnitude of another factor.
See also
Notes
References
- Copi, Irving; Carl Cohen (2001). Introduction to Logic. Prentice Hall. ISBN 0-13-033735-8.
- Ducheyne, Steffen (2008). "J.S. Mill’s Canons of Induction: From true causes to provisional ones". History and Philosophy of Logic 29 (4): 361–376. doi:10.1080/01445340802164377.
- Kreeft, Peter (2009). Socratic Logic, A Logic Text Using Socratic Method, Platonic Questions, and Aristotelian Principles. St. Augustine's Press, South Bend, Indiana. ISBN 1-890318-89-2.
External links
- Causal Reasoning — Provides some examples
- Mill's methods for identifying causes — Provides some examples
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Mentioned in
enumerative induction
(philosophy)
Baconian method
(philosophy)
Francis Bacon
(philosophy)
induction
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John Stuart Mill
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