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HarrietHarriet TaylerTayler (Later, Harriet(Later, Harriet
Mill;1807Mill;1807--58)58)
A Social Theorist ConcernedA Social Theorist Concerned
Particularly with WomensParticularly with Womens
Statuses;A Friend with JohnStatuses;A Friend with John
Stuart, and Getting MarriedStuart, and Getting Married
withhim in 1851.withhim in 1851.
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Mills MethodsMills Methods
In order to identify the cause of some
event or condition, we will use Mills
Methods.
Mills Methods are five rules of causal
reasoning in inductive logic.
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The JointThe Joint MethodMethod ofof
Agreement and DifferenceAgreement and Difference
The joint method is a matter of
applying both the method of
agreement and the method of
difference
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SYMBOLICSYMBOLIC
REPRES
ENTATIO
N:REPRES
ENTATIO
N:Symbolically, the Joint method of
agreement and difference can be
represented as:A BC occur together with x y z
A D E occur together with x v w also BC occur with y z
Therefore A is the cause, or the effect,
or a part of the cause of x.
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First we make two groups, one group
have set of all cases in which a type ofevents occurs. The other group have theset of all the cases in which they do notoccur.
the Method of Agreement is applied to(1) the set of as well as to (2)
compare the two sets of cases, i.e., (1)
and (2), to find an antecedentcircumstance that is present in all casesof (1), but that is absent in all cases of(2).
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Example:Example:
In postmortem examinations of five Alzheimers
patients and five people without the disease, it
was found that all the diseased patients had lost
neurons from the nucleus basalis (a tiny areadeep in the brain), while all the people without
the disease had the normal member of cells in
this area. Scientists who conducted this study
believe that the loss of neurons from the nucleusbasalis may be responsible for the decreased
activity in the cortex.
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A Schematic Representation ofthe JointA Schematic Representation ofthe Joint
Method ofAgreement & DifferenceMethod ofAgreement & Difference
Case Antecedent Event for Which
Circumstances Cause is Sought
1 X, S, T, U Eoccurs
2 X, S, U, V, Eoccurs
3 X, S, T Eoccurs
4 X, S Eoccurs
5 S, T, U, V Edoes not occur
6 S, T Edoes not occur
7 T, U Edoes not occur
8 S, U, V Eodes not occur
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Case 2Case 2
In the above gastrointestinal illness case, thedoctor specifiedthe omelets, among otheringredients of a meal, as the cause for thesickness in focusing on the following married
couple.Ahusband and a wife were on the sameflight and were served identical meals. The wifewas hungry but allergic to eggs, so she ate all ofthe meal butthe omelet. Thehusband was alsohungry but not allergic to eggs, so he ate all. Thehusband became ill, butthe wifedid not. Thedoctor, having suspectedthe foodpoisoning,
identifiedthe omelet as the cause ofthe illness.
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A BC D occurs together W X Y Z
BC D occurs together X Y Z
-----------------------------------------------Therefore , it is probable that A is the
cause / effect of W.
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A Schematic Representation ofA Schematic Representation of
the Method of Differencethe Method of Difference
Case Antecedent Event for Which
Circumstances Cause is Sought
1 X, S, T, U, V, W E occurs
2 S, T, U, V, W E does not occur
In the above example, the case 1 is the case of ahusband;
the case 2 is the case of his wife;
Eis the gastrointestinal illness; and,
Xis eating the omelet prepared by a cook with an
infected finger.
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3. The Joint Method of3. The Joint Method of
Agreement and DifferenceAgreement and Difference In order to identify a cause by using the Method
of Difference, wehaveto findthe following twocases:
one in whichtheevent or state in question is present,another in which it is absent, that areexactly alikeexcept for thepresence or absence of a singleantecedent circumstance.
We can rarely find such a pair of cases. Thus, Mill proposes the Joint Method of
Agreement and Difference, which applies to morethan two cases withvarying antecedent
circumstances.
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Case 3Case 3
In postmortem examinations of fiveAlzheimers patients and fivepeople withoutthedisease, it was foundthat all thediseased
patients had lost neurons from the nucleusbasalis (a tiny area deep in the brain), while allthepeople withoutthediseasehadthe normalmember of cells in this area. Scientists who
conductedthis study believethatthe loss ofneurons from the nucleus basalis may beresponsible for thedecreased activity in thecortex.(Salmon 2002, p.184)
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A Schematic Representation ofthe JointA Schematic Representation ofthe Joint
Method ofAgreement & DifferenceMethod ofAgreement & Difference
Case Antecedent Event for Which
Circumstances Cause is Sought
1 X, S, T, U Eoccurs
2 X, S, U, V, Eoccurs
3 X, S, T Eoccurs
4 X, S Eoccurs
5 S, T, U, V Edoes not occur
6 S, T Edoes not occur
7 T, U Edoes not occur
8 S, U, V Eodes not occur
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A Schematic Representation ofA Schematic Representation of
the Joint Methodthe Joint Method
The number of cases can be smaller or larger,
depending on the number of occurrences ofthe
events or states under consideration.
In Case3, there are five cases wheretheevent,
i.e., thedecreased activity in the cortex, occurs,
and five cases where itdoes not.
The Joint Method is usedto identify a cause as anecessary and sufficient causal condition for the
effect in question.
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The Use ofThe Use of thethe Joint MethodJoint Method
The use of the Joint Method of Agreement andDifference has promoted the study of the causesand cures for diseases.
The joint method is, like any other of Mills
methods, most effective when they are appliedwithin a good specific causal theory
However, this method can be used to guide andrestrict the search for causes when no specificcausal theory is available (though we need some
general background knowledge about the causalstructure of the world). Mills joint method canhelp investigators formulate new causal theoriesthat can then be subjected to further testing.
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A Limitation of the Methods So FarA Limitation of the Methods So Far
Mills Methods wehave studied so far apply only tothe collection of cases wherethe suspected causalsource is present in some cases and absent in others.
In other words, these methods are concerned only
with qualitative similarities anddifferences amongcases.
In many cases, however, we wishto investigate acausal question wherethe suspected causal agent ispresent in all cases anddifferences in effect aredueto
merely thevarying strength ofthe causal agent. In other words, we need a method sensitiveto
quantitative differences among cases.
Mills Method of Concomitant Variation is one of
such methods.
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Case 4Case 4
In England, records ofthe last100 years show a
steady increase in per capita consumption of
sugar, from about 20 lbs/year in 1820to over 100
lbs/year today. Present consumption of sugar inthe US is aboutthe same.Attendant withthis
increased consumption of sucrosehas been an
almostparallel rise in theprevalence of cavities.
Conversely, surveys in Europe and Japan
demonstratedthat cavities weredramatically
reducedduring periods of wartime restrictions of
sugar.
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4. The Method of Concomitant4. The Method of Concomitant
VariationVariation
When thevariation in onephenomena arehighlycorrelated withvariation in another phenomena .one ofthat is likely to be cause or effectthe other one.
The Method of Concomitant Variation says that in orderto identify the cause ofthevariation in someparticularquality ofthe conditions under consideration, we should
look for a correlative variation in someparticularquality ofthe antecedentphenomena.
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Direct and Inverse CorrelationDirect and Inverse Correlation
The variation of one thing can be correlatedwith the variation of another thing in twoways.
First, it can be directly correlated: that is, itchanges in the same direction as anotherthing changes.
The above example reports that the relative
frequency of cavities is directly correlated withthe rate of the consumption of sugar.
Second, it can be inversely correlated: thatis, it changes in the opposite direction as
another thing changes.
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A Schematic Representation of theA Schematic Representation of the
Method of Concomitant VariationMethod of Concomitant VariationCases or Groups Antecedent Varying Quantity ofEffect
of Cases Circumstances Whose Cause is Sought
1 X+, T, U, V E+ (or E-)
2 X-, T, U, V E- (or E+)
The symbol + represents the larger amount ofEthe cases 1having.
The symbol - the smaller amount ofEthe cases2 have.
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The Use of the Method ofThe Use of the Method of
Concomitant VariationConcomitant Variation
If the effect under consideration and thesuspected cause(s) are always present to someextent, we cannot apply the Method of Differenceor the Joint Method.
The Method of Agreement can apply, but if thereare several common antecedent circumstances,this method cannot identify the real cause.
However, if the condition or events under
investigation varies in degree, then the Method ofConcomitant Variation can still apply.
Thus, this method is indispensable where, forinstance, the effect is the relative frequency ofsome event, such as the occurrence of some
disease.
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Case 5Case 5
You haveplanted a dogwoodtreethat is notgrowing well.You consult a specialist whosuggests three causes for poor growth indogwoodtrees: insufficient watering, not giving
proper amount of fertilizer, and not removinggrasses aroundtheir trunks.You have giventhe adequate water every week andtherecommendeddosage of fertilizer once a year,following a forestation guidebook.You inspectthetree and noticethat grass is growing rightupto thetree.You concludethat not removingtheturf cover growing right upto thetrunk iscausally responsible for thepoor growth ofthe
dogwoodtree.
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5. The Method of Residues5. The Method of Residues
Mills underlying idea behindthe Methods ofDifference and of Concomitant Variation is that achange in someeffect is to be accounted by achange in the cause.
This idea is also behindthe Method of Residues.It says that in order to identify the cause of aneffect, we should subtract from theeffect under
investigation what is already known to betheresult of some antecedent circumstances.
It is likely thatthe remaining effect is caused bythe remaining antecedent circumstances.
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The Use of the Method ofThe Use of the Method of
ResiduesResidues
As wehave seen in theexample, the Method of Residuescan be appliedeven to a single case.
This is a useful characteristic that is not shared by any other ofMills Methods.
However, we need specific knowledge of causalrelationships between antecedent circumstances andtheeffect in question in order to apply the Method ofResidues.
Otherwise, we cannot subtractthe results ofknowncauses from thateffect in order to findthe residue.
The Method of Residues can be applied bothto the caseswheretheeffect is some qualitativedifference, andto the
cases wheretheeffect is the change in some quantity.