Mills Methods

Inductive Logic

Messiah Paranthaman Kaliyaperumal University of Dayton PHL 302 Symbolic Logic

Overview  Inductive

Logic  Biography of Mill  Mill’s Methods – – – – –

Method of agreement Method of Difference Joint method of agreement & difference Method of residues Method of concomitant variation

 Critique

of Mill’s Methods

Induction  Inductive

arguments (or simply induction) – Reasoning from particular cases to general conclusions.

 Causal

inductive arguments

– Special type of induction in which the premises suggest the conclusion that there is a causal relation between two properties or factors.

Cause? A

variable, some of whose values bring about or increase the value of the effect variable  Two more specific notions of cause: – The cause is sufficient to bring about the effect – The cause is necessary to bring about the effect  Neither

works completely, but each is suggestive of important features of

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 sufficient causes 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 causes Something 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 concepts



Necessary cause of e: a causal factor that is present in all cases of an effect e.

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Sufficient cause of e: a causal factor that guarantees the existence of effect e.

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

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Causal relate may be singular events, properties, or variables

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The deterministic principle: The same causal antecedents produce the same effects – Underlies Mill’s 5 Methods.

John Stuart Mill “John Stuart Mill was the most influential English-speaking philosopher of the 19th century. His views are of continuing significance, and are generally recognized to be among the deepest and certainly most effective defenses of a liberal political view of society and culture. The overall aim of his philosophy is to develop a positive view of humans’ place in the universe, one which contributes to the progress of knowledge, individual freedom, and human well-being.”

John Stuart Mill 

 



Born 1806, to James Mill, economist and psychologist Learns Greek by age 3, Latin by age 8 By age 14, has read almost all the classical texts Raised among some of the most prominent intellectual radicals of the day (notably, Jeremy Bentham)

John Stuart Mill   

 

At age 22, gains post in East India Company Has nervous breakdown at age 24 Overcomes breakdown at age 26, and throws himself into attempts to reform society Serves as member of Parliament in his 60s Dies 1873

Mill’s Books      

 

System of Logic Principles of Political Economy On Liberty Utilitarianism On the Subjection of Women Considerations on Representative Government Three Essays on Religion Autobiography

Mill’s Five Methods  Method

of Agreement  Method of Difference  Joint Method of Agreement and Difference  Method of Residues  Method of Concomitant Variation

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.”

Method of Agreement  If

there is only one common condition A for all cases resulting in a, then A is a cause of a.  Form: A B C D occur together with a b c d. A E F G occur together with a e f g._____ Therefore A is cause (or the effect) of a A

is a necessary cause of a.

Illustration of Method of Agreement 

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 Agreement

Table for Method of Agreement Salad

Soup

Pork

Illness

Roi

Yes

Yes

Yes

Yes

Kumar

Yes

No

Yes

Yes

Joy

No

Yes

Yes

Yes

Suman

No

Yes

Yes

Yes

Table for Method of Agreement Salad

Soup

Pork

Illness

Roi

Yes

Yes

Yes

Yes

Kumar

Yes

No

Yes

Yes

Joy

No

Yes

Yes

Yes

Suman

No

Yes

Yes

Yes

Method of Difference “If an instance in which the phenomena 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

Method of Difference  If

the only difference between cases is the condition A and the result a, then A caused a.  Form: A B C D occur together with a b c d;. B C D occur together with b c d;______ Therefore, A is causally connected to a. 

A is a sufficient cause of a.

Method of Difference 

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 Difference  

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

Method of Difference

The Example of Yellow Fever 

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

Once Walter Reed suspected mosquitoes as the transmitter of yellow fever He had one set of volunteers sleep on the soiled clothes and beds of yellow fever patients in a room screened so that no mosquitoes could get in. None of these people contracted the disease.

The Example of Yellow Fever 



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

Joint method of agreement and difference 



If A is present in otherwise diverse cases exhibiting a result x, and is absent in otherwise similar cases not resulting in x, then A caused x. Form: A B C occur together with x y z. A D E occur together with x t v; B C, with just y and z._ Therefore, A is causally connected to x.



A is both a necessary and sufficient cause of

Joint method of agreement and 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 and 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 Residues “Subduct form 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.”

Method of Residues 



Isolate known causes from unknown causes to discern the specific contribution x of a specific causal factor A to a causal system. Form: – – – –

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 causally connected to x.

Illustration Method of Residues Suman Dungdung steps on a scale carrying a dog. The scale reads 125 Kg. Suman knows that he weighs 95 Kg. Therefore, the dog weighs 30 Kg.

Method of Concomitant Variation “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.”

Method of Concomitant Variation  If

changing the value of one causal factor A changes the value of a resulting condition x, then A is causally connected to x.  Form: – A B C occur together with x y z. – A∆ B C occur together with x ∆ y z. – A is causally connected with x.

Illustration for Method of Concomitant Variation A

former establishes that therer is a causal connection between the application of fertilizer to his ground and the harvest.  A business man verifies the efficacy of advertising by running larger and smaller advertisements at different intervals.

Attractions of Mill’s Methods  Nicely

captures the reasoning in controlled experiments and everyday causal reasoning

 Describes

how our background beliefs restrict our conclusion

What is Mill saying? 



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

Mill’s Methods: probability, but not 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, but not 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

Summary  Inductive

Logic  Causal Connections  Biography of Mill  Mill’s Five Methods: – Agreement, Difference, Joint, Residues, and Concomitant Variation  Critique

of Mill’s Methods

– Strengths – Weaknesses

Thanks

Dr. Rani Thanikachalam Libin Tete Norendro Nayak Roshan Dang Roy Cheriyan Mylamvelil Vinod V.T Rajmohan. C Suman Dungdung Ashok Kumar Dung Dung Kumarasamy Kambhampati Jesuraj. U

Presented by Messiah Paranthaman Kaliyaperumal