Mills Methods

Inductive Inductive LogicLogic

Messiah Paranthaman KaliyaperumalMessiah Paranthaman Kaliyaperumal

University of DaytonUniversity of Dayton

PHL 302 Symbolic LogicPHL 302 Symbolic Logic

OverviewOverview Inductive LogicInductive Logic Biography of MillBiography of Mill Mill’s MethodsMill’s Methods

– Method of agreementMethod of agreement– Method of DifferenceMethod of Difference– Joint method of agreement & differenceJoint method of agreement & difference– Method of residuesMethod of residues– Method of concomitant variationMethod of concomitant variation

Critique of Mill’s MethodsCritique of Mill’s Methods

InductionInduction Inductive arguments Inductive arguments (or simply (or simply

induction)induction)– Reasoning from particular cases to Reasoning from particular cases to

general conclusions. general conclusions.

Causal inductive argumentsCausal inductive arguments– – Special type of induction in which the Special type of induction in which the

premises suggest the conclusion that premises suggest the conclusion that there is a causal relation between two there is a causal relation between two properties or factors.properties or factors.

CauseCause??

A variable, some of whose values bring about A variable, some of whose values bring about or increase the value of the effect variableor increase the value of the effect variable

Two more specific notions of cause: Two more specific notions of cause: – The cause is The cause is sufficient sufficient to bring about the effectto bring about the effect– The cause is The cause is necessary necessary to bring about the effectto bring about the effect

Neither works completely, but each is Neither works completely, but each is suggestive of important features of causation suggestive of important features of causation and help us understand how to test causal and help us understand how to test causal claimsclaims

Sufficient causes

Examples of factors sufficient to bring about an effect– Dead battery is sufficient for car not

starting– Ingesting (enough) hemlock is sufficient for

dying– Placing water in a normally operating

freezer is sufficient for it freezing– Increased exercise without eating more is

sufficient for weight loss

The value of sufficient causes

A sufficient cause gives us a guidelines for producing an effect we want– If you don’t want someone to drive your car,

totally run down the battery– If you want to loose weight, exercise

“Whenever I get the urge to exercise, I lie down until the feeling passes away.”

- Robert M. Hutchins, former President of the University of Chicago

I have never taken any exercise, except for sleeping and resting, and I never intend to take any. Exercise is loathsome.

- Mark Twain, Essays: Seventieth Birthday

The difficulty with sufficientcauses

For many conditions in which you think you have found a sufficient cause, an exception can be found– If you take an antidote with

your hemlock (should one be found), you might escape death

– If you put salt in the water, it may not freeze even when temperature is less than 320 F

Necessary causesSomething that is necessary to

produce an effect:

– Oxygen is necessary for burning– Herpes zoster is a necessary cause of

chickenpox– Early exposure to language is necessary

for normal language development

The value of necessary causes

Provide a way of preventing something

–Eliminating oxygen does stop fires

–Not having Herpes zoster in you prevents chickenpox

Key conceptsKey concepts Necessary Necessary cause of cause of ee: a causal factor that is present in all : a causal factor that is present in all

cases of an effectcases of an effect e e..

SufficientSufficient cause of cause of ee: a causal factor that guarantees the : a causal factor that guarantees the existence of effect existence of effect ee. .

Central factorCentral factor of of e:e: The factor that made the biggest The factor that made the biggest difference to difference to e’s e’s occurring.occurring.

Causal relate may be singular events, properties, or variablesCausal relate may be singular events, properties, or variables

The deterministic principle: The same causal antecedents The deterministic principle: The same causal antecedents produce the same effectsproduce the same effects

– Underlies Mill’s 5 Methods.Underlies Mill’s 5 Methods.

John Stuart MillJohn Stuart Mill

““John Stuart Mill was the most John Stuart Mill was the most influential English-speaking influential English-speaking

philosopher of the 19th philosopher of the 19th century. His views are of century. His views are of

continuing significance, and continuing significance, and are generally recognized to are generally recognized to be among the deepest and be among the deepest and

certainly most effective certainly most effective defenses of a liberal political defenses of a liberal political view of society and culture. view of society and culture.

The overall aim of his The overall aim of his philosophy is to develop a philosophy is to develop a positive view of humans’ positive view of humans’ place in the universe, one place in the universe, one which contributes to the which contributes to the progress of knowledge, progress of knowledge, individual freedom, and individual freedom, and

human well-being.”human well-being.”


Born 1806, to James Born 1806, to James Mill, economist and Mill, economist and psychologistpsychologist

Learns Greek by age Learns Greek by age 3, Latin by age 83, Latin by age 8

By age 14, has read By age 14, has read almost all the classical almost all the classical textstexts

Raised among some of Raised among some of the most prominent the most prominent intellectual radicals of intellectual radicals of the day (notably, the day (notably, Jeremy Bentham)Jeremy Bentham)


At age 22, gains post At age 22, gains post in East India Companyin East India Company

Has nervous Has nervous breakdown at age 24breakdown at age 24

Overcomes breakdown Overcomes breakdown at age 26, and throws at age 26, and throws himself into attempts himself into attempts to reform societyto reform society

Serves as member of Serves as member of Parliament in his 60sParliament in his 60s

Dies 1873Dies 1873

Mill’s BooksMill’s Books System of LogicSystem of Logic Principles of Political Principles of Political

EconomyEconomy On LibertyOn Liberty UtilitarianismUtilitarianism On the Subjection of On the Subjection of

WomenWomen Considerations on Considerations on

Representative GovernmentRepresentative Government Three Essays on ReligionThree Essays on Religion AutobiographyAutobiography

Mill’s Five MethodsMill’s Five Methods

Method of AgreementMethod of AgreementMethod of DifferenceMethod of Difference Joint Method of Agreement and Joint Method of Agreement and

DifferenceDifferenceMethod of ResiduesMethod of ResiduesMethod of Concomitant Method of Concomitant

VariationVariation

Method of AgreementMethod 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.”

Method of AgreementMethod of Agreement

If there is only one common condition If there is only one common condition AA for all cases resulting in for all cases resulting in a, a, then then AA is a is a cause of cause of aa..

Form:Form:A B C D A B C D occur together with occur together with a b c da b c d..A E F G A E F G occur together with occur together with a e f ga e f g._____._____Therefore Therefore AA is cause (or the effect) of is cause (or the effect) of aa

AA is a necessary cause of is a necessary cause of aa..

Illustration of Method of Illustration of Method of AgreementAgreement

Find cases in which the effect has occurred– Determine if there is only one thing that they all

share– If there is, that is (the likely) cause

Example: some cities have markedly lower rates of tooth decay– If fluoride in the water is the only (potentially

relevant) thing in common, then it is the likely cause

Method of Method of AgreementAgreement

Table for Method of Table for Method of AgreementAgreement

SaladSalad SoupSoup PorkPork Illness Illness

RoiRoi YesYes YesYes YesYes YesYes

KumarKumar YesYes NoNo YesYes YesYes

JoyJoy NoNo YesYes YesYes YesYes

SumanSuman NoNo YesYes YesYes YesYes

Table for Method of Table for Method of AgreementAgreement

SaladSalad SoupSoup PorkPork Illness Illness

RoiRoi YesYes YesYes YesYes YesYes

KumarKumar YesYes NoNo YesYes YesYes

JoyJoy NoNo YesYes YesYes YesYes

SumanSuman NoNo YesYes YesYes YesYes

Method of DifferenceMethod of Difference

““If an instance in which the phenomena If an instance in which the phenomena under investigation occurs and an under investigation occurs and an

instance in which it does not occur, instance in which it does not occur, have every circumstance in common have every circumstance in common

save one, that one occurring only in the save one, that one occurring only in the former, the circumstance in which alone former, the circumstance in which alone the two instances differ, is the effect, or the two instances differ, is the effect, or the cause, or an indispensable part of the cause, or an indispensable part of

the cause, of the phenomenon.”the cause, of the phenomenon.”

Method of DifferenceMethod of Difference If the only difference between cases If the only difference between cases

is the condition is the condition AA and the result and the result a, a, then then A A caused caused a. a.

Form:Form:A B C D A B C D occur together with occur together with a b c d;.a b c d;.B C D B C D occur together with occur together with b c d;______b c d;______Therefore, Therefore, AA is causally connected to is causally connected to a.a.

A A is a sufficient cause of is a sufficient cause of aa..


Find two things that differ in that one has the effect and the other doesn’t– If there is only one factor on which they differ,

that is the likely cause

Example: four people apply for a loan, and only two get it– The only difference is that the one who was

denied once declared bankruptcy– The declaration of bankruptcy is the likely

cause of the loan being turned down

Table of Method of Table of Method of DifferenceDifference

College Education

Earn Rs. 400

Own Business

Declared Bankruptcy

Loan Approved

Rai Yes Yes No Yes No

Dung Yes Yes No No Yes

Ashok Yes Yes No No Yes

Joy Yes Yes No Yes No


The Example of Yellow The Example of Yellow FeverFever

Once Walter Reed Once Walter Reed suspected mosquitoes as suspected mosquitoes as the transmitter of yellow the transmitter of yellow feverfever

He had one set of He had one set of volunteers sleep on the volunteers sleep on the soiled clothes and beds of soiled clothes and beds of yellow fever patients in a yellow fever patients in a room screened so that no room screened so that no mosquitoes could get in.mosquitoes could get in.

None of these people None of these people contracted the disease.contracted the disease.

The Example of Yellow The Example of Yellow FeverFever

He had another group He had another group of volunteers stay of volunteers stay completely away from completely away from sick patients, except sick patients, except he let mosquitoes that he let mosquitoes that had been allowed to had been allowed to feast first on people feast first on people sick with the disease sick with the disease bite the patients.bite the patients.

These volunteers did These volunteers did get sick.get sick.

Joint method of Joint method of agreement and agreement and

differencedifference If If A A is present in otherwise diverse cases is present in otherwise diverse cases

exhibiting a result exhibiting a result x, x, and is absent in otherwise and is absent in otherwise similar cases not resulting in similar cases not resulting in xx, then , then AA caused caused xx..

Form:Form:A B C A B C occur together with occur together with x y z.x y z.A D EA D E occur together with x t v; occur together with x t v; B C, B C, with just y and with just y and

z._z._Therefore, Therefore, A A is causally connected to is causally connected to xx..

A A is both a necessary and sufficient cause of is both a necessary and sufficient cause of x.x.

Joint method of agreement Joint method of agreement and differenceand difference

The methods of agreement and difference can be used jointly:

– Find something in common amongst all cases where the effect appears

– Find matches for all these cases except that they lack the effect and the common ingredient

Joint method of agreement Joint method of agreement and differenceand difference

Example: Five factory workers are found to be inefficient relative to others who are doing the same work.– The efficient workers and the inefficient

workers were found to be similar in all relevant ways except one: the inefficient were not part of a profit sharing plan.

Conclusion: profit sharing causes efficiency.

Method of ResiduesMethod of Residues

““Subduct form any Subduct form any phenomenon such part as is phenomenon such part as is

known by previous inductions known by previous inductions to be the effect of certain to be the effect of certain

antecedents, and the residue antecedents, and the residue of the phenomenon is the of the phenomenon is the

effect of the remaining effect of the remaining antecedents.”antecedents.”

Method of ResiduesMethod of Residues Isolate known causes from unknown Isolate known causes from unknown

causes to discern the specific contribution causes to discern the specific contribution x x of a specific causal factor of a specific causal factor A A to a causal to a causal system.system.

Form:Form:– A B C A B C occur together with occur together with x y z.x y z.– B B is known to be the cause of is known to be the cause of y.y.– C C is known to be the cause of is known to be the cause of z.z.– Therefore Therefore A A is causally connected to is causally connected to x.x.

Illustration Method of Illustration Method of ResiduesResidues

Suman Dungdung steps on a scale Suman Dungdung steps on a scale carrying a dog. The scale reads carrying a dog. The scale reads 125 Kg.125 Kg.

Suman knows that he weighs 95 Suman knows that he weighs 95 Kg.Kg.

Therefore, the dog weighs 30 Kg.Therefore, the dog weighs 30 Kg.

Method of Method of Concomitant VariationConcomitant Variation

“ “Whatever phenomenon varies in Whatever phenomenon varies in any manner whenever another any manner whenever another

phenomenon varies in some phenomenon varies in some particular manner is either a particular manner is either a

cause or an effect of that cause or an effect of that phenomenon or is connected phenomenon or is connected with it through some fact of with it through some fact of

causation.”causation.”

Method of Method of Concomitant VariationConcomitant Variation

If changing the value of one causal If changing the value of one causal factor factor AA changes the value of a changes the value of a resulting condition resulting condition xx, then , then AA is is causally connected to causally connected to xx..

Form:Form:– A B C A B C occur together with occur together with x y z.x y z.– AA∆∆ B C B C occur together with occur together with x x ∆∆ y z. y z.– A A is causally connected with is causally connected with x.x.

Illustration for Method Illustration for Method of of

Concomitant VariationConcomitant Variation A former establishes that therer is a A former establishes that therer is a

causal connection between the causal connection between the application of fertilizer to his ground application of fertilizer to his ground and the harvest.and the harvest.

A business man verifies the efficacy of A business man verifies the efficacy of advertising by running larger and advertising by running larger and smaller advertisements at different smaller advertisements at different intervals. intervals.

Attractions of Mill’s Attractions of Mill’s MethodsMethods

Nicely captures the reasoning in Nicely captures the reasoning in controlled experiments and controlled experiments and everyday causal reasoningeveryday causal reasoning

Describes how our background Describes how our background beliefs restrict our conclusionbeliefs restrict our conclusion

What is Mill saying?What is Mill saying? Once you have identified the reasonable Once you have identified the reasonable

candidate causes, correlation (of a simple candidate causes, correlation (of a simple matching sort) can isolate the actual causematching sort) can isolate the actual cause

Assumption behind Mill’s methods: one and only one factor Assumption behind Mill’s methods: one and only one factor is the cause, and it is one you have considered: - the is the cause, and it is one you have considered: - the Scientific Drinker drank scotch and soda on the first night Scientific Drinker drank scotch and soda on the first night and became drunk. On the second night, he drank brandy and became drunk. On the second night, he drank brandy and soda and became drunk again. On the third night, he got and soda and became drunk again. On the third night, he got drunk on bourbon and water. He therefore decided that the drunk on bourbon and water. He therefore decided that the soda was the cause of his getting drunk because it was the soda was the cause of his getting drunk because it was the common element each time. He swore a solemn oath that common element each time. He swore a solemn oath that never to touch soda again!never to touch soda again!

Mill’s Methods: probability, butnot Definitive

As the previous example shows, Mill’s methods do not always correctly identify the cause

– Something might correlate with the effect but not be the cause

– The causal structure might be complex, involving interactions of multiple factors

Mill’s Methods: probability, butnot Definitive

Nonetheless, Mill’s methods are useful in clarifying parts of our understanding of cause

The development of modern statistics came after Mill and provided a much more potent tool for identifying the factors Mill was seeking to identify

Mill’s Methods: probability, but

not Definitive To make a correct analysis requires

previous knowledge of causal laws, which must have been discovered by means other than Mill’s Methods.

Mill’s Methods are not sufficient instruments for discovery, because their successful use requires a proper analysis of the factors of the antecedent circumstances, and the Methods themselves do not tell how to distinguish between a proper and an improper analysis.

SummarySummary Inductive LogicInductive Logic Causal ConnectionsCausal Connections Biography of MillBiography of Mill Mill’s Five Methods: Mill’s Five Methods:

– Agreement, Difference, Joint, Residues, Agreement, Difference, Joint, Residues, and Concomitant Variationand Concomitant Variation

Critique of Mill’s MethodsCritique of Mill’s Methods– StrengthsStrengths– WeaknessesWeaknesses

ThanksThanksDr. Rani ThanikachalamDr. Rani Thanikachalam

Libin TeteLibin TeteNorendro NayakNorendro Nayak

Roshan DangRoshan DangRoy Cheriyan MylamvelilRoy Cheriyan Mylamvelil

Vinod V.TVinod V.TRajmohan. CRajmohan. C

Suman DungdungSuman DungdungAshok Kumar Dung DungAshok Kumar Dung Dung

Kumarasamy KambhampatiKumarasamy KambhampatiJesuraj. UJesuraj. U

Presented byPresented byMessiah Paranthaman KaliyaperumalMessiah Paranthaman Kaliyaperumal

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Mills Methods