usman logic

8/7/2019 usman logic

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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



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



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.

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