Welcome dear students of HSLC GURU! In this lesson we present a complete English-medium guide to Class 12 Logic and Philosophy Chapter 4 — Mill’s Experimental Methods of Inquiry, prepared strictly according to the latest ASSEB (Assam State School Education Board) syllabus for the Higher Secondary Second Year examination. The British philosopher and logician John Stuart Mill (1806-1873), in his famous work “A System of Logic” (1843), formulated five experimental methods for discovering and demonstrating causal connections between natural phenomena. These methods — the Method of Agreement, Method of Difference, Joint Method of Agreement and Difference, Method of Residues and Method of Concomitant Variations — are collectively known as Mill’s Canons or Mill’s Methods of Eliminative Induction. They are the backbone of modern scientific inquiry and form one of the most important chapters of the Logic and Philosophy course. This article gives you the complete chapter summary, every textbook question with answer (Very Short, Short and Long types), additional MCQs, fill-in-the-blanks, true/false, matching items, glossary, comparison table and a short biography of Mill — everything an ASSEB student needs to score full marks.
Chapter Summary — Mill’s Experimental Methods of Inquiry
The chief problem of inductive logic is the discovery and proof of causal connection. In nature, phenomena are intermixed in a very complex manner; many antecedents accompany every consequent. To separate the genuine cause from the bundle of irrelevant antecedents, John Stuart Mill devised the technique of elimination. Eliminating those antecedents that are not the cause leaves us with the antecedent that is the cause. This technique is embodied in five experimental methods, which Mill called the methods of “experimental inquiry” because they extend the experimental procedure of physics and chemistry to all kinds of investigation.
Mill’s methods rest on the Law of Universal Causation — every event has a cause — and on three Canons of Elimination:
- Whatever antecedent can be left out, without prejudice to the effect, can be no part of the cause.
- An antecedent which cannot be left out, without the consequent disappearing, must be the cause or part of the cause.
- An antecedent and a consequent rising and falling together in numerical concomitance must be connected as cause and effect.
The five methods are:
- Method of Agreement — based on the first canon; if two or more instances of the phenomenon under investigation have only one circumstance in common, that circumstance is the cause (or effect) of the phenomenon. Symbolic form: ABCD/abcd, AEFG/aefg → A is the cause of a.
- Method of Difference — based on the second canon; if an instance in which the phenomenon 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 cause or part of the cause. Symbolic form: ABCD/abcd vs BCD/bcd → A is the cause of a.
- Joint Method of Agreement and Difference — combines both methods using positive and negative groups of instances. It is more reliable than the Method of Agreement and easier to apply than the Method of Difference.
- Method of Residues — subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents; the residue of the phenomenon is the effect of the remaining antecedents. Symbolic form: ABC is the cause of abc; A is known to cause a; B is known to cause b; therefore C is the cause of c.
- 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. Symbolic form: A₁BC/a₁bc, A₂BC/a₂bc, A₃BC/a₃bc → A and a are causally connected.
The first two are the fundamental methods; the others are derived from or supplement them. Together they form the most important set of rules for scientific discovery yet devised, and have guided countless real discoveries — for example, Ronald Ross discovering that the female Anopheles mosquito causes malaria (Method of Agreement), James Lind proving that citrus fruits cure scurvy (Method of Difference), the discovery of Neptune from perturbations in the orbit of Uranus (Method of Residues), the discovery of argon by Lord Rayleigh and William Ramsay (Method of Residues), and Boyle’s Law relating gas pressure to volume (Method of Concomitant Variations).
Textbook Questions and Answers
A. Very Short Answer Type Questions (1 mark)
Q1. Who is the founder of the Experimental Methods of Inquiry?
Answer: John Stuart Mill (1806–1873) is the founder of the Experimental Methods of Inquiry.
Q2. In which book did Mill formulate his experimental methods?
Answer: Mill formulated his experimental methods in his celebrated work “A System of Logic” published in 1843.
Q3. How many experimental methods did Mill recognise?
Answer: Mill recognised five experimental methods of inquiry.
Q4. Name the five experimental methods of Mill.
Answer: (i) Method of Agreement, (ii) Method of Difference, (iii) Joint Method of Agreement and Difference, (iv) Method of Residues, and (v) Method of Concomitant Variations.
Q5. Which two are the fundamental methods of Mill?
Answer: The Method of Agreement and the Method of Difference are the two fundamental methods of Mill.
Q6. Which method is pre-eminently a method of observation?
Answer: The Method of Agreement is pre-eminently a method of observation.
Q7. Which method is pre-eminently a method of experiment?
Answer: The Method of Difference is pre-eminently a method of experiment.
Q8. What is the basic principle on which Mill’s methods are based?
Answer: Mill’s methods are based on the principle of elimination resting on the Law of Universal Causation.
Q9. State the canon of the Method of Agreement.
Answer: “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.”
Q10. State the canon of the Method of Difference.
Answer: “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.”
Q11. How many instances are required in the Method of Difference?
Answer: Only two instances — one positive and one negative — are required in the Method of Difference.
Q12. Which method is regarded as essentially deductive?
Answer: The Method of Residues is regarded as essentially deductive in nature.
Q13. Which method is most useful for studying permanent causes?
Answer: The Method of Concomitant Variations is most useful for studying permanent causes.
Q14. Name the method by which Neptune was discovered.
Answer: Neptune was discovered by the Method of Residues.
Q15. Which method is also called the Double Method of Agreement?
Answer: The Joint Method of Agreement and Difference is also called the Double Method of Agreement.
Q16. Define cause according to Mill.
Answer: According to Mill, the cause of a phenomenon is “the sum total of the antecedents — positive and negative — taken together; the whole of the contingencies of every description, which being realised, the consequent invariably follows.”
Q17. What is meant by “post hoc ergo propter hoc”?
Answer: It is the fallacy of mistaking a mere antecedent in time for the cause — assuming that because B follows A, therefore A is the cause of B.
Q18. Which method gives certain conclusions?
Answer: The Method of Difference gives certain (highly probable) conclusions when properly applied.
Q19. Give the symbolic form of the Method of Agreement.
Answer: Instance 1: ABCD → abcd; Instance 2: AEFG → aefg. ∴ A is the cause of a.
Q20. Give one example of the Method of Concomitant Variations.
Answer: As the temperature rises, the mercury column in a thermometer also rises; therefore heat is the cause of the expansion of mercury.
B. Short Answer Type Questions (2–3 marks)
Q1. What is the Method of Agreement? Give its symbolic form.
Answer: The Method of Agreement is the first of Mill’s experimental methods. According to Mill, “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.” It is essentially a method of observation, and its conclusions are only probable. Symbolic form:
Instance 1: A B C D → a b c d
Instance 2: A E F G → a e f g
Instance 3: A H I J → a h i j
∴ A is the cause of a.
Q2. What is the Method of Difference? Give its symbolic form.
Answer: The Method of Difference compares a positive instance (in which the phenomenon occurs) with a negative instance (in which it does not occur), the two instances agreeing in every other respect. The single circumstance in which they differ is the cause, or part of the cause, of the phenomenon. It is essentially a method of experiment and its conclusions are highly certain. Symbolic form:
Positive: A B C D → a b c d
Negative: B C D → b c d
∴ A is the cause of a.
Q3. State the Joint Method of Agreement and Difference.
Answer: Mill states it thus: “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 the cause, or an indispensable part of the cause, of the phenomenon.” It uses two groups — a positive group (where phenomenon is present) and a negative group (where it is absent) — and applies the Method of Agreement to each group separately.
Q4. State the Method of Residues with a symbolic example.
Answer: “Subduct from any phenomenon such part as is known by previous induction to be the effect of certain antecedents; the residue of the phenomenon is the effect of the remaining antecedents.” Symbolic form:
ABC is the cause of abc.
A is known to be the cause of a.
B is known to be the cause of b.
∴ C must be the cause of the residual c.
Q5. State the Method of Concomitant Variations.
Answer: “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.” It is applied where total elimination is impossible — where a factor cannot be removed but can only be increased or decreased. The variation may be direct (both increase together) or inverse (one increases as the other decreases). Example: Boyle’s Law — at constant temperature, the volume of a gas decreases as its pressure increases.
Q6. What is meant by “Plurality of Causes”?
Answer: Plurality of Causes means that the same effect may be produced by different causes on different occasions. For example, death may be caused by drowning, poisoning, shooting, disease, etc. This possibility weakens the conclusions of the Method of Agreement, because two instances of the same effect might in fact have different causes although they share one circumstance accidentally.
Q7. What is the fallacy of “Post Hoc Ergo Propter Hoc”?
Answer: The Latin phrase means “after this, therefore because of this.” It is the fallacy of supposing that because one event follows another in time, the first must be the cause of the second. The careless use of the Method of Difference often leads to this fallacy. For example, if a person catches a cold after walking in rain and then drinking cold water, concluding the cold water caused the cold ignores other antecedents.
Q8. Why is the Method of Agreement called a method of observation?
Answer: Because the investigator does not produce the instances himself; he merely observes the instances as they naturally occur and notes the circumstance common to them all. He has no power of arranging or modifying the instances — he is a passive observer. Hence the Method of Agreement is called a method of observation.
Q9. Why is the Method of Difference called a method of experiment?
Answer: Because the investigator deliberately produces the positive and negative instances, deliberately introducing or removing the suspected cause and keeping all other circumstances constant. He actively manipulates conditions in a laboratory or controlled setting; therefore the Method of Difference is called a method of experiment.
Q10. What is meant by Cause in Mill’s sense?
Answer: Mill defines cause as the unconditional, invariable antecedent of an event. More precisely, “The cause of a phenomenon is the sum total of all the conditions, positive and negative, taken together, the whole of the contingencies of every description, which being realised, the consequent invariably follows.” Thus cause is not merely an antecedent but an unconditional invariable antecedent.
Q11. Distinguish between cause and condition.
Answer: A condition is any circumstance which is necessary for the occurrence of an event. A cause is the entire set of conditions taken together. Popularly we single out one condition as “the” cause, but logically the cause includes every condition. The Method of Difference cannot strictly distinguish a cause from a mere condition.
Q12. What is the Law of Universal Causation?
Answer: The Law of Universal Causation states that every event has a cause; nothing happens without a cause. This is the metaphysical foundation of all inductive reasoning, including Mill’s experimental methods. Without it, elimination would not lead to any conclusion.
Q13. Why is the Method of Residues considered deductive?
Answer: The Method of Residues uses previously established causal laws (obtained by earlier inductions) and applies them to a complex phenomenon by subtraction. The conclusion follows necessarily from these established premises by deductive reasoning; therefore the method is essentially deductive, although it operates within the framework of inductive science.
Q14. Give one scientific example of the Method of Residues.
Answer: The discovery of the planet Neptune. Astronomers observed that the orbit of Uranus deviated from the path predicted by the gravitational influence of the known planets. Subtracting the known causes of perturbation, the residual perturbation was attributed to an unknown body — Neptune — whose existence was later confirmed by direct observation in 1846.
Q15. Give an everyday example of the Method of Agreement.
Answer: Several students of a class fall ill on the same day. Their meals, drinks and routines were different, but all of them drank water from the same tap. The single common circumstance is the tap-water; therefore by the Method of Agreement, the contaminated tap-water is the cause of their illness.
C. Long Answer Type Questions (5–8 marks)
Q1. Explain the Method of Agreement with its canon, symbolic form, characteristics, advantages, disadvantages and examples.
Answer: The Method of Agreement is the first and the most widely applicable of Mill’s five experimental methods.
Canon: “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.”
Principle of Elimination: Whatever antecedent can be left out (i.e., is absent in some instances) without affecting the consequent cannot be the cause; therefore the only circumstance present in all the instances must be the cause.
Symbolic form:
Instance 1: A B C D → a b c d
Instance 2: A E F G → a e f g
Instance 3: A H I J → a h i j
∴ A is the cause of a.
Characteristics: (i) It is essentially a method of observation. (ii) It requires plurality of instances. (iii) It can be applied both ways — from cause to effect and from effect to cause. (iv) Its conclusions are only probable.
Advantages: (a) It has the widest field of application; it can be used wherever experiment is impossible — astronomy, sociology, history, medicine. (b) It is useful for the discovery of causes (heuristic). (c) It can be applied to past events. (d) It does not require expensive apparatus.
Disadvantages: (i) Its conclusions are not certain but only probable. (ii) It cannot distinguish cause from mere co-existence. (iii) It is liable to the fallacy of plurality of causes. (iv) It does not enable the experimenter to vary the circumstances at will.
Everyday example: Several friends who attended a wedding feast became sick. They ate different sweets, drank different drinks, but all consumed the chicken curry. ∴ The chicken curry is the cause of illness.
Scientific example: Sir Ronald Ross observed many cases of malaria in different climates, regions and populations; the only common antecedent was the bite of the female Anopheles mosquito. By the Method of Agreement he concluded that the mosquito-bite is the cause of malaria.
Q2. Explain the Method of Difference with canon, symbolic form, characteristics, advantages, disadvantages and examples.
Answer: The Method of Difference is the second and the most rigorous of Mill’s experimental methods.
Canon: “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.”
Principle of Elimination: An antecedent which cannot be left out without the consequent disappearing must be the cause or part of the cause.
Symbolic form:
Positive instance: A B C D → a b c d
Negative instance: B C D → b c d
∴ A is the cause of a.
Characteristics: (i) It is essentially a method of experiment. (ii) Only two instances are required. (iii) It is applied chiefly in laboratory science. (iv) It yields highly certain conclusions.
Advantages: (a) It is the most rigorous of all methods. (b) Conclusions are nearly certain. (c) It positively establishes the causal connection. (d) It is well-suited to controlled experiments.
Disadvantages: (i) Its scope is narrow — it cannot be used where experiment is impossible (astronomy, history). (ii) It cannot distinguish a cause from a condition. (iii) It cannot reason from effect to cause. (iv) Careless application leads to the fallacy of post hoc ergo propter hoc.
Everyday example: A bell is rung in a glass jar full of air — sound is heard. The air is then pumped out and the bell is rung again — no sound is heard. The two instances differ only in the presence/absence of air. ∴ Air is the cause of the transmission of sound.
Scientific example: James Lind’s classic 1747 experiment on scurvy. He took twelve sailors suffering from scurvy, divided them into pairs, and gave each pair a different supplement (cider, vinegar, sea-water, etc.) keeping all other conditions constant. The pair given oranges and lemons recovered while the others did not. The only difference was citrus fruit. ∴ Vitamin C (citrus) cures scurvy.
Q3. Distinguish between the Method of Agreement and the Method of Difference.
Answer: Although both are fundamental methods of Mill, they differ in many respects, as shown below:
| Point of Difference | Method of Agreement | Method of Difference |
| Nature | Method of observation | Method of experiment |
| Number of instances | Many instances required | Only two instances required |
| Type of instance | All positive instances | One positive, one negative |
| Canon | Whatever can be left out is not the cause | Whatever cannot be left out must be the cause |
| Direction of reasoning | Both ways — cause to effect, effect to cause | Only from cause to effect |
| Certainty of conclusion | Only probable | Highly certain |
| Field of application | Wider — wherever experiment is impossible | Narrower — only where experiment is possible |
| Plurality of causes | Vulnerable to it | Not affected by it |
| Distinguishing cause from condition | Cannot distinguish | Cannot strictly distinguish |
| Example | Discovery of cause of malaria | Bell-jar experiment for sound |
Q4. Explain the Joint Method of Agreement and Difference. Why is it called the Indirect Method of Difference?
Answer: The Joint Method of Agreement and Difference is the third of Mill’s experimental methods. It combines the Method of Agreement applied to two groups of instances — positive and negative.
Canon: “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 the cause, or an indispensable part of the cause, of the phenomenon.”
Symbolic form:
Positive group: ABC → abc; ADE → ade; AFG → afg. (Common: A, a)
Negative group: BC → bc; DE → de; FG → fg. (A absent, a absent)
∴ A is the cause of a.
Why called Indirect Method of Difference: The Method of Difference proves causation by directly producing a positive and a negative instance differing in only one circumstance. The Joint Method achieves the same result indirectly by separately applying Agreement to two groups (positive and negative) and noting that the disputed circumstance is present in all positive instances and absent in all negative ones — the conclusion is reached by a “double agreement” rather than by direct difference. Hence Mill called it the Indirect Method of Difference.
Advantages: (i) Highly probable conclusions. (ii) Reduces the danger of plurality of causes. (iii) Applicable in fields where direct experiment is impossible. (iv) More reliable than the Method of Agreement alone.
Disadvantages: (i) Conclusions are still only probable, not absolutely certain. (ii) Requires a large number of instances. (iii) Cannot identify which exact factor is the cause when several factors are correlated.
Example: Wherever malaria-mosquitoes are found, malaria is also found (positive group). Wherever the mosquitoes are absent (cold high-altitude regions), malaria is also absent (negative group). ∴ Mosquito-bite is the cause of malaria.
Q5. Explain the Method of Residues with canon, symbolic form, advantages, disadvantages and scientific examples.
Answer: The Method of Residues is the fourth of Mill’s experimental methods.
Canon: “Subduct from any phenomenon such part as is known by previous induction to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.”
Principle: If a complex phenomenon abc has antecedents ABC, and we already know that A causes a and B causes b, then the remaining part c must be the effect of the remaining antecedent C.
Symbolic form:
ABC is the cause of abc.
A is known to be the cause of a.
B is known to be the cause of b.
∴ C is the cause of c (the residue).
Characteristics: (i) It is essentially deductive. (ii) It depends on previously established laws. (iii) It is highly fruitful in scientific discovery. (iv) Its conclusions are nearly certain.
Advantages: (a) It has been used to make many great discoveries. (b) It can deal with complex phenomena. (c) Its conclusions are highly probable, almost certain. (d) It does not require fresh experiments.
Disadvantages: (i) It depends on the accuracy of previous inductions. (ii) The residue may itself be due to several unknown factors. (iii) Quantitative measurement of the known causes must be exact. (iv) It is essentially deductive, not purely inductive.
Scientific example 1 — Discovery of Neptune: Astronomers calculated the orbit of Uranus assuming it was disturbed only by the known planets. The actual orbit deviated from the calculated orbit. After subtracting the gravitational influence of all known planets, the residual deviation remained. This residual was attributed to the gravitational pull of an unknown planet. In 1846, Galle observed the new planet — Neptune — almost exactly where Le Verrier predicted.
Scientific example 2 — Discovery of Argon: Lord Rayleigh found that nitrogen extracted from air was slightly heavier than nitrogen prepared chemically. Subtracting the weight of pure nitrogen, the residual mass had to be due to some unknown gas. William Ramsay isolated this residue and named it Argon (1894).
Everyday example: A loaded cart weighs 600 kg; the empty cart weighs 200 kg; ∴ the load weighs 400 kg.
Q6. Explain the Method of Concomitant Variations with canon, symbolic form, types, advantages, disadvantages and examples.
Answer: The Method of Concomitant Variations is the fifth of Mill’s experimental methods.
Canon: “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.”
When applied: When complete elimination is impossible — for example, with permanent causes that cannot be removed (gravitation, sun, earth’s magnetism) — we apply this method by varying the suspected cause quantitatively and observing whether the effect varies correspondingly.
Symbolic form:
A₁ B C → a₁ b c
A₂ B C → a₂ b c
A₃ B C → a₃ b c
∴ A and a are causally connected.
Types: (i) Direct variation — both vary in the same direction (heat ↑, expansion ↑). (ii) Inverse variation — they vary in opposite directions (pressure ↑, volume ↓ in Boyle’s Law).
Advantages: (a) The only quantitative method among Mill’s methods. (b) Useful where elimination is impossible. (c) Useful for permanent causes. (d) Helps establish numerical/mathematical laws of nature.
Disadvantages: (i) Cannot prove causation conclusively (correlation is not causation). (ii) Both phenomena may be effects of a common cause. (iii) Limited to a definite range — the law may break down at extreme values. (iv) Cannot be used where the phenomenon does not admit of degree.
Scientific example 1 — Boyle’s Law: At constant temperature, the pressure (P) of a gas varies inversely with its volume (V): PV = constant. Robert Boyle established this by gradually changing pressure and observing volume changes.
Scientific example 2 — Tides and Moon: The height of ocean tides varies regularly with the position and phase of the moon. ∴ The moon’s gravitational pull is causally connected with the tides.
Everyday example: The temperature reading on a thermometer rises as the surrounding heat increases and falls as the heat decreases. ∴ Heat causes the expansion of mercury.
Q7. State and explain Mill’s Five Canons.
Answer: Mill formulated five canons (rules), one for each of his experimental methods. They are:
Canon 1 — 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.”
Canon 2 — Method of Difference: “If an instance in which the phenomenon 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.”
Canon 3 — Joint Method: “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 the cause, or an indispensable part of the cause, of the phenomenon.”
Canon 4 — Method of Residues: “Subduct from any phenomenon such part as is known by previous induction to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.”
Canon 5 — 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.”
These canons together embody the principle of elimination — discovering the cause by removing the irrelevant antecedents — and form the rules of inductive scientific procedure.
Q8. Discuss the relative merits and demerits of all five methods of Mill.
Answer:
(a) Method of Agreement: Wide applicability and useful for discovery; but only probable conclusions and vulnerable to plurality of causes.
(b) Method of Difference: Most rigorous and yields certain conclusions; but limited to cases where experiment is possible.
(c) Joint Method: Combines the strengths of Agreement and Difference; reliable but never absolutely certain.
(d) Method of Residues: Powerful for discovering new causes; but depends on previously known causal laws.
(e) Method of Concomitant Variations: Useful for permanent causes and quantitative laws; but limited to phenomena admitting of degrees and cannot prove causation absolutely.
Of all the five, Mill himself regarded the Method of Difference as the most rigorous because it alone can establish causation with near-certainty. The Method of Agreement is the most widely applicable. The Method of Residues and Concomitant Variations are supplementary methods used where the fundamental two cannot be applied directly. In modern science, all five methods are used in combination.
Additional Questions for Practice
D. Multiple Choice Questions (MCQs)
Q1. Who is the founder of the experimental methods of inquiry?
(a) Aristotle (b) Bacon (c) John Stuart Mill (d) Hume
Answer: (c) John Stuart Mill
Q2. How many experimental methods are there in Mill’s logic?
(a) Three (b) Four (c) Five (d) Six
Answer: (c) Five
Q3. Which of the following is a method of observation?
(a) Method of Difference (b) Method of Agreement (c) Method of Residues (d) Joint Method
Answer: (b) Method of Agreement
Q4. Which method is pre-eminently a method of experiment?
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Joint Method
Answer: (b) Method of Difference
Q5. Mill’s experimental methods are based on the principle of —
(a) Probability (b) Elimination (c) Generalisation (d) Analogy
Answer: (b) Elimination
Q6. Which method is essentially deductive?
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Method of Concomitant Variations
Answer: (c) Method of Residues
Q7. The discovery of Neptune is an example of —
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Method of Concomitant Variations
Answer: (c) Method of Residues
Q8. The discovery of Argon was made by —
(a) Boyle (b) Lord Rayleigh and Ramsay (c) Lavoisier (d) Mendeleev
Answer: (b) Lord Rayleigh and Ramsay
Q9. Boyle’s Law is an example of —
(a) Method of Concomitant Variations (b) Method of Agreement (c) Joint Method (d) Method of Residues
Answer: (a) Method of Concomitant Variations
Q10. James Lind’s experiment on scurvy is an example of —
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Joint Method
Answer: (b) Method of Difference
Q11. Discovery of mosquito as cause of malaria is an example of —
(a) Method of Agreement (b) Method of Residues (c) Method of Difference (d) Joint Method
Answer: (a) Method of Agreement
Q12. The book in which Mill stated his methods is —
(a) Novum Organum (b) A System of Logic (c) Critique of Pure Reason (d) Treatise on Human Nature
Answer: (b) A System of Logic
Q13. Which method is also called the Double Method of Agreement?
(a) Method of Difference (b) Joint Method (c) Method of Residues (d) Method of Concomitant Variations
Answer: (b) Joint Method
Q14. The phrase “post hoc ergo propter hoc” denotes a fallacy of —
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Method of Concomitant Variations
Answer: (b) Method of Difference
Q15. Symbolic form ABCD/abcd, AEFG/aefg → A is cause of a represents the —
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Joint Method
Answer: (a) Method of Agreement
Q16. Symbolic form ABCD/abcd vs BCD/bcd → A is cause of a represents the —
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Joint Method
Answer: (b) Method of Difference
Q17. Which method requires only two instances?
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Joint Method
Answer: (b) Method of Difference
Q18. The most rigorous method of inquiry according to Mill is —
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Method of Concomitant Variations
Answer: (b) Method of Difference
Q19. The method useful for permanent causes is —
(a) Method of Agreement (b) Method of Difference (c) Method of Concomitant Variations (d) Joint Method
Answer: (c) Method of Concomitant Variations
Q20. The plurality of causes weakens the conclusion of —
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Method of Concomitant Variations
Answer: (a) Method of Agreement
Q21. Bell-jar experiment for sound illustrates the —
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Method of Concomitant Variations
Answer: (b) Method of Difference
Q22. Tides being caused by the moon’s pull illustrates —
(a) Method of Agreement (b) Method of Concomitant Variations (c) Method of Residues (d) Method of Difference
Answer: (b) Method of Concomitant Variations
Q23. Mill’s methods rest ultimately on the —
(a) Law of Excluded Middle (b) Law of Identity (c) Law of Universal Causation (d) Law of Contradiction
Answer: (c) Law of Universal Causation
Q24. The two fundamental methods of Mill are —
(a) Agreement and Residues (b) Agreement and Difference (c) Difference and Residues (d) Joint and Variations
Answer: (b) Agreement and Difference
Q25. The only quantitative method of Mill is —
(a) Method of Agreement (b) Method of Difference (c) Method of Residues (d) Method of Concomitant Variations
Answer: (d) Method of Concomitant Variations
E. Fill in the Blanks
1. Mill’s experimental methods were stated in the book ____. Answer: A System of Logic.
2. Mill recognised ____ experimental methods of inquiry. Answer: five.
3. The Method of Agreement is essentially a method of ____. Answer: observation.
4. The Method of Difference is essentially a method of ____. Answer: experiment.
5. The Method of Difference requires only ____ instances. Answer: two.
6. The Method of ____ is essentially deductive. Answer: Residues.
7. Conclusions of the Method of Agreement are only ____. Answer: probable.
8. Conclusions of the Method of Difference are nearly ____. Answer: certain.
9. The discovery of Neptune is an example of the Method of ____. Answer: Residues.
10. The Joint Method is also called the ____ Method of Difference. Answer: Indirect.
11. The Method of ____ is the only quantitative method. Answer: Concomitant Variations.
12. Mill’s methods rest on the principle of ____. Answer: elimination.
13. Boyle’s Law illustrates the Method of ____. Answer: Concomitant Variations.
14. The two fundamental methods of Mill are Agreement and ____. Answer: Difference.
15. The Latin phrase ____ refers to the fallacy of mistaking sequence for causation. Answer: post hoc ergo propter hoc.
16. The Method of ____ is most vulnerable to plurality of causes. Answer: Agreement.
17. A loaded cart weighs 600 kg, empty cart 200 kg; load is 400 kg — illustrates Method of ____. Answer: Residues.
18. Mosquito-bite as the cause of malaria was discovered by the Method of ____. Answer: Agreement.
19. Citrus fruit cures scurvy — discovered by the Method of ____. Answer: Difference.
20. Argon was discovered by the Method of ____. Answer: Residues.
F. True / False
1. Mill recognised six experimental methods. — False (he recognised five).
2. The Method of Agreement is a method of observation. — True.
3. The Method of Difference yields only probable conclusions. — False (highly certain).
4. The Method of Difference requires many instances. — False (only two).
5. The Method of Residues is essentially deductive. — True.
6. The Joint Method is also called the Indirect Method of Difference. — True.
7. The Method of Concomitant Variations is the only quantitative method. — True.
8. Mill’s methods are based on the Law of Universal Causation. — True.
9. The Method of Agreement is free from the fallacy of plurality of causes. — False.
10. The Method of Difference is essentially a method of experiment. — True.
11. Boyle’s Law is an example of the Method of Difference. — False (Concomitant Variations).
12. Neptune was discovered by the Method of Residues. — True.
13. Argon was discovered by the Method of Agreement. — False (Residues).
14. Sir Ronald Ross discovered the cause of malaria by Method of Agreement. — True.
15. James Lind’s scurvy experiment is an example of Method of Difference. — True.
16. Mill’s “A System of Logic” was published in 1843. — True.
17. The Method of Difference can reason from effect to cause. — False.
18. The Method of Agreement can be applied where experiment is impossible. — True.
19. Plurality of Causes affects the Method of Difference more than Agreement. — False.
20. Mill is the founder of modern inductive logic. — True.
G. Match the Following
| Column A | Column B |
| 1. Method of Agreement | (c) Method of observation |
| 2. Method of Difference | (d) Method of experiment |
| 3. Method of Residues | (a) Discovery of Neptune |
| 4. Concomitant Variations | (b) Boyle’s Law |
| 5. Joint Method | (e) Indirect Method of Difference |
| 6. John Stuart Mill | (f) A System of Logic, 1843 |
| 7. Plurality of Causes | (g) Weakens Method of Agreement |
| 8. Post hoc ergo propter hoc | (h) Fallacy of Method of Difference |
| 9. Argon | (i) Lord Rayleigh and Ramsay |
| 10. Scurvy and citrus fruit | (j) James Lind |
Comparison Table — Mill’s Five Experimental Methods
| Feature | Agreement | Difference | Joint Method | Residues | Concomitant Variations |
| Nature | Observation | Experiment | Both | Deductive | Quantitative |
| No. of instances | Many | Two | Two groups | One complex | Many varying |
| Symbolic form | ABCD/abcd, AEFG/aefg → A→a | ABCD/abcd vs BCD/bcd → A→a | +ABC/abc, ADE/ade; –BC/bc, DE/de → A→a | ABC→abc; A→a, B→b ∴ C→c | A₁BC→a₁bc; A₂BC→a₂bc → A↔a |
| Certainty | Probable | Highly certain | Highly probable | Nearly certain | Probable correlation |
| Direction | Both ways | Cause→Effect | Both ways | By subtraction | Co-variation |
| Strength | Wide scope | Rigorous | Reliable | Discovers new causes | For permanent causes |
| Weakness | Plurality of causes | Narrow scope | Many instances needed | Depends on prior knowledge | Correlation ≠ causation |
| Famous example | Malaria & mosquito (Ross) | Scurvy & citrus (Lind); Bell-jar | Malaria positive & negative groups | Neptune; Argon | Boyle’s Law; Tides |
| Mill’s canon no. | 1st | 2nd | 3rd | 4th | 5th |
Glossary of Important Terms
| Term | Meaning |
| Cause | The unconditional, invariable antecedent of an event. |
| Effect | The consequent which invariably follows the cause. |
| Antecedent | That which precedes another event in time. |
| Consequent | That which follows another event in time. |
| Elimination | The process of removing irrelevant factors to find the real cause. |
| Plurality of Causes | The doctrine that the same effect may be produced by different causes. |
| Post hoc ergo propter hoc | Latin: “after this, therefore because of this” — fallacy of mistaking sequence for causation. |
| Law of Universal Causation | The principle that every event has a cause. |
| Canon | A rule or principle stating the standard of valid reasoning. |
| Positive Instance | An instance in which the phenomenon is present. |
| Negative Instance | An instance in which the phenomenon is absent. |
| Concomitant | Going together, accompanying. |
| Residue | The remaining part after subtraction; the unexplained portion. |
| Permanent Cause | A cause that cannot be removed (gravity, sun’s heat). |
| Direct Variation | Both quantities increase or decrease together. |
| Inverse Variation | One increases as the other decreases. |
| Induction | Reasoning from particular instances to general law. |
| Deduction | Reasoning from general law to particular case. |
| Hypothesis | A tentative explanation to be tested by observation. |
| Probability | Degree of certainty less than full proof. |
Brief Biography — John Stuart Mill (1806-1873)
John Stuart Mill was a British philosopher, political economist and one of the greatest thinkers of the 19th century. Born in London on 20 May 1806, he was the eldest son of the historian and philosopher James Mill, who gave him a remarkable home education — Mill learned Greek at three, Latin and arithmetic at eight, logic at twelve and political economy at thirteen. He became a leading exponent of Utilitarianism, championing the moral principle of “the greatest happiness of the greatest number.” He was an early defender of women’s rights, individual liberty and democratic reform, serving briefly as a Member of Parliament. His major works include “A System of Logic” (1843), “Principles of Political Economy” (1848), “On Liberty” (1859), “Utilitarianism” (1861) and “The Subjection of Women” (1869). In “A System of Logic,” he laid down the five experimental methods of inquiry that bear his name and have become the foundation of scientific methodology. He died at Avignon, France, on 7 May 1873. Mill’s methods continue to guide scientists, social researchers, medical investigators and detectives wherever causal connections must be discovered from observed instances.
Conclusion: Mill’s five Experimental Methods of Inquiry — Agreement, Difference, Joint, Residues and Concomitant Variations — together provide a complete framework for the discovery and proof of causal relations. From the discovery of malaria’s vector and the cure for scurvy to the prediction of Neptune and the formulation of Boyle’s Law, these methods have shaped modern science and remain essential tools of inductive reasoning. ASSEB Class 12 students should master each method’s canon, symbolic form, characteristics, advantages, disadvantages and famous examples, as questions from this chapter regularly appear in the Higher Secondary Final Examination. Practise the questions in this guide thoroughly to score full marks.
For more chapter-wise English-medium notes and solutions for ASSEB Class 12 Logic and Philosophy, keep visiting HSLC GURU. All the best for your examinations!
Extra Long Answer Practice Questions
Q1. “The Method of Difference is the most rigorous of all Mill’s methods.” Discuss this statement with examples.
Answer: Mill himself regarded the Method of Difference as the most rigorous and conclusive of his five experimental methods. The reasons are as follows:
(i) Direct proof of causation: The Method of Difference establishes a direct causal connection between an antecedent and a consequent. By comparing a positive instance (where the phenomenon occurs) with a negative instance (where it does not), differing in only one circumstance, the investigator can pinpoint the precise factor responsible for the effect. No other method offers such a direct demonstration.
(ii) Active control: Unlike the Method of Agreement, the investigator does not depend on chance. He arranges the conditions of the experiment, deliberately introducing or removing the suspected cause, while keeping all other circumstances constant. This active control eliminates the possibility of accidental coincidence.
(iii) Immunity from plurality of causes: Because the Method of Difference operates on a pair of instances differing in only one factor, it is not weakened by the possibility that the same effect may have several causes — a defect that seriously limits the Method of Agreement.
(iv) Highly certain conclusions: Where the experimental conditions are properly controlled, the conclusion of the Method of Difference is virtually certain — far more reliable than the merely probable conclusion of the Method of Agreement.
(v) Foundation of laboratory science: The Method of Difference forms the basis of every controlled scientific experiment. From physics to chemistry, biology to medicine, every laboratory depends on the comparison of experimental and control groups — exactly the procedure prescribed by Mill’s second canon.
Examples: (a) The bell-jar experiment: a bell rung in air produces sound, but the same bell rung in a vacuum produces no sound — therefore air is the cause of sound transmission. (b) The discovery of penicillin: Alexander Fleming noticed that a culture plate contaminated by mould had no bacterial growth around the mould while the rest of the plate had bacteria — by the Method of Difference, the mould (penicillin) was the cause of bacterial death. (c) Lind’s scurvy experiment proving citrus fruit cures scurvy. (d) Modern double-blind clinical trials testing new drugs. In every case, the rigour of the Method of Difference yields a near-certain causal conclusion. However, its scope is limited — it cannot be used where experiment is impossible (astronomy, history, sociology). Where applicable, it is the most rigorous method ever devised.
Q2. Explain the role of the Method of Residues in scientific discovery, with at least three notable examples.
Answer: The Method of Residues, though essentially deductive, has been one of the most fruitful methods in the history of scientific discovery. Its principle is simple: from a complex phenomenon abc produced by complex antecedents ABC, if previous inductions have established that A causes a and B causes b, then the residual c must be caused by the residual C. Many famous discoveries have been made by this method:
(i) Discovery of Neptune (1846): Astronomers carefully observed the motions of Uranus and calculated its orbit on the basis of the gravitational pull of all the known planets — Mercury, Venus, Earth, Mars, Jupiter and Saturn. The actual orbit, however, deviated systematically from the calculated one. After subtracting the known gravitational influences (the known antecedents), a residual perturbation remained. This residual could only be explained by the gravitational pull of an unknown planet beyond Uranus. The French astronomer Le Verrier and the English astronomer Adams independently calculated the position of this hypothetical planet, and the German astronomer Galle observed it on 23 September 1846, almost exactly where predicted. The new planet was named Neptune.
(ii) Discovery of Argon (1894): Lord Rayleigh observed that nitrogen extracted from atmospheric air was about 0.5% heavier than nitrogen prepared chemically (from ammonia). After subtracting the weight contributed by pure nitrogen, the residual mass demanded the presence of an unknown heavier gas in the atmosphere. Working with William Ramsay, Rayleigh isolated this residue and named it Argon (Greek argos = lazy, because it is chemically inert). This discovery led to the identification of the entire family of noble gases — Helium, Neon, Krypton, Xenon and Radon.
(iii) Discovery of Radioactivity: Madame Marie Curie, processing tons of pitchblende ore, found that its radioactivity was greater than could be accounted for by the uranium it contained. Subtracting the contribution of uranium, the residual radioactivity led her to discover two new elements — Polonium and Radium.
(iv) Discovery of Helium in the Sun: Spectroscopic analysis of sunlight showed bright lines that did not match any known terrestrial element. Subtracting the lines of all known elements, the residual lines pointed to an unknown element — first detected on the Sun and named “Helium” (from helios = sun). It was later isolated on Earth by Ramsay.
(v) Everyday application: A merchant weighs his loaded cart at 800 kg. The empty cart weighs 250 kg. ∴ The load (residue) weighs 550 kg.
These examples show that the Method of Residues can lead to spectacular discoveries, but it depends entirely on the accuracy of previously known causal laws. Despite being deductive in form, it is one of the most powerful tools of inductive science.
Q3. Why is the Method of Concomitant Variations especially valuable for the study of permanent causes? Illustrate with examples.
Answer: A “permanent cause” is one that cannot be removed or eliminated in the course of investigation — for example, the gravitational pull of the earth, the heat of the sun, the rotation of the planet, the magnetism of the earth, atmospheric pressure. With respect to such causes, the Method of Difference is inapplicable, because we cannot create a negative instance by removing the cause. The Method of Agreement is also unreliable, because the cause is present in every instance and cannot be distinguished from other constant factors. In such cases the Method of Concomitant Variations becomes indispensable.
The principle is: if we cannot make the cause vanish, we can at least make it vary in degree, and observe whether the effect varies correspondingly. If they vary together — directly or inversely — they are causally connected.
Examples:
(a) Tides and the Moon: The moon cannot be removed from the sky, but the height of the tide varies regularly with the moon’s position and phase. Spring tides occur at full moon and new moon (greater pull); neap tides occur at half moon. ∴ The moon’s gravitational pull is the cause of tides.
(b) Heat and Expansion (Boyle’s Law and Charles’s Law): Heat applied to a gas cannot be eliminated, but as heat increases, volume increases proportionally. Robert Boyle (1662) and Jacques Charles (1787) used this method to derive the gas laws.
(c) Sun’s heat and seasons: The sun is a permanent cause; it cannot be removed. But the angle and intensity of sunlight vary with the seasons, and so do the temperatures on earth. ∴ The sun’s heat causes the seasonal changes.
(d) Pendulum and gravity: Gravity cannot be removed; but the period of a pendulum varies as gravity varies (pendulums swing slower at higher altitudes). ∴ Gravity influences the pendulum.
(e) Wages and prices: In economics, when wages rise, the cost of production rises, and prices rise too. The variation establishes the causal relation.
(f) Smoking and lung cancer: The amount of tobacco consumed varies directly with the incidence of lung cancer in populations. The Method of Concomitant Variations was used in epidemiological studies to establish this connection.
Limitations: However, mere co-variation does not always prove direct causation. Two variables may co-vary because both are effects of a common third cause. For example, the number of ice-creams sold and the number of people drowning both rise in summer — but ice-cream does not cause drowning; both are effects of warm weather. Hence concomitant variation must be used with care, and is most reliable when supplemented by the Method of Difference or the Joint Method.
Q4. “Mill’s methods presuppose the Law of Universal Causation.” Explain.
Answer: The Law of Universal Causation declares that every event has a cause; nothing happens without a cause. Mill’s experimental methods are tools for finding the cause of any given phenomenon — but the very task of “finding the cause” presupposes that there is a cause to find. If some events occurred uncaused, the methods would be useless: the absence of a cause among the antecedents would not prove anything, because the event might be uncaused.
The principle of elimination — “whatever can be left out without affecting the consequent is not the cause” — works only because the consequent has some cause; eliminating the false candidates leaves the true cause as the residue. Without the assumption of universal causation, no induction would ever reach a conclusion. Hence Mill himself wrote: “Of the universality of causation in the sense in which we have explained that doctrine, no proof can be given… But the doctrine, as we have stated it, was never doubted by any school of speculation, and is in fact assumed in all our reasonings.”
Thus the Law of Universal Causation is the metaphysical postulate on which the entire structure of inductive logic and Mill’s methods rests.
Q5. What are the limitations of Mill’s experimental methods?
Answer: Although Mill’s methods provide an excellent framework for scientific investigation, they have several limitations:
(i) Identification of antecedents: The methods presuppose that all relevant antecedents are known and isolated. In practice, hidden or unknown factors may distort the conclusions.
(ii) Plurality of causes: The same effect may have different causes on different occasions, weakening the Method of Agreement.
(iii) Intermixture of effects: When several causes act jointly, their effects may blend in a way that defies analysis.
(iv) Cause vs. condition: The methods cannot strictly distinguish a cause (or sufficient condition) from a mere condition (necessary co-factor).
(v) Permanent causes: Where causes cannot be removed (sun, gravity), only Concomitant Variations is applicable, and it gives only correlation, not strict proof.
(vi) Post hoc fallacy: Carelessness can mistake mere temporal sequence for genuine causation.
(vii) Limited to observable phenomena: The methods cannot deal with unobservable theoretical entities (atoms, fields) without auxiliary hypotheses.
(viii) Heuristic vs. probative: The methods are powerful for testing causal hypotheses but less effective in discovering them; the original hypothesis must come from creative imagination.
(ix) Quantitative limitation: Only Concomitant Variations handles quantitative relations; the others remain qualitative.
(x) Dependence on previous knowledge: Especially the Method of Residues depends critically on the accuracy of previously established causal laws.
Quick Revision Notes
| Method | Canon (in brief) | Symbolic Form | One Word Summary |
| Agreement | One common circumstance = cause | ABCD/abcd, AEFG/aefg → A→a | Observation |
| Difference | One differing circumstance = cause | ABCD/abcd vs BCD/bcd → A→a | Experiment |
| Joint | Both methods combined | +ABC, ADE; –BC, DE → A→a | Combined |
| Residues | Subtract known causes; residue is the cause | ABC→abc; A→a, B→b ∴ C→c | Subtraction |
| Concomitant Variations | Co-variation = causation | A₁BC→a₁bc; A₂BC→a₂bc → A↔a | Co-variation |
Important Exam Tips for ASSEB Class 12
1. Memorise all five canons word-for-word — examiners often ask for the exact statement.
2. Practice symbolic forms with letters; this fetches easy marks in short-answer questions.
3. Memorise at least one everyday and one scientific example for each method:
- Agreement → malaria (mosquito) or food-poisoning at a feast
- Difference → bell-jar / scurvy & citrus / penicillin
- Joint Method → malaria (positive and negative regions)
- Residues → Neptune / Argon / loaded cart
- Concomitant Variations → tides & moon / Boyle’s Law / heat & expansion
4. For comparison questions, prepare a clear table of differences (Agreement vs. Difference is asked almost every year).
5. Always include both advantages and disadvantages when answering long-answer questions.
6. Mill’s biographical details (1806–1873, “A System of Logic,” 1843) are short-answer favourites.
7. The fallacy “post hoc ergo propter hoc” is a frequently asked one-mark term.
8. The Law of Universal Causation as the foundation of Mill’s methods is a common short-answer question.
Final Note: Chapter 4 is one of the most scoring chapters in the ASSEB Class 12 Logic and Philosophy syllabus. With clear understanding of the five canons, their symbolic forms and famous examples, students can confidently attempt every question type — from one-mark MCQs to eight-mark long-answer questions. Revise the comparison table, glossary and the canons regularly. Best wishes from HSLC GURU!
Worked Examples — Applying Mill’s Methods Step by Step
Example 1 — Method of Agreement (Food poisoning at a wedding feast): Suppose 200 guests attended a wedding banquet. The next day, 25 of them suffered acute food-poisoning while 175 remained healthy. Investigators interviewed the 25 sick guests and found that they had eaten different rice dishes, different sweets, and drunk different beverages. The only common item all 25 had eaten was the prawn curry. By the Method of Agreement, the prawn curry is identified as the probable cause of the food-poisoning. Symbolically:
Guest 1: rice + prawn + ladoo + cola → sick
Guest 2: pulao + prawn + jalebi + lassi → sick
Guest 3: biryani + prawn + halwa + water → sick
∴ Prawn curry is the cause of food-poisoning (probable).
Example 2 — Method of Difference (Effect of fertiliser on plant growth): A farmer plants two identical seeds of the same variety in two adjacent identical pots, with the same soil, the same amount of water, the same sunlight and the same temperature. To one pot he adds a measured amount of fertiliser; to the other he adds nothing. After one month, the plant in the fertilised pot is twice as tall as the other. The two situations agree in every circumstance save the presence of fertiliser. ∴ The fertiliser is the cause of the increased growth.
Symbolic form:
Pot A: soil + water + sun + fertiliser → tall plant
Pot B: soil + water + sun → short plant
∴ Fertiliser is the cause of the additional growth.
Example 3 — Joint Method (Smoking and lung disease): A medical study compares two groups: (i) Group A — heavy smokers across various ages, occupations, diets and exercise levels — most show signs of chronic lung disease; (ii) Group B — non-smokers of comparable ages, occupations, diets and exercise — most do not show such signs. The single circumstance that the positive group shares is smoking; the negative group shares its absence. ∴ By the Joint Method, smoking is the cause of chronic lung disease.
Example 4 — Method of Residues (Mass of an unknown chemical compound): A chemist has a 100 g sample of an unknown mixture. By analysis he finds 40 g of sodium chloride and 35 g of potassium nitrate. The remaining 25 g (residue) must consist of some other component. Further chemical tests reveal it to be calcium carbonate. ∴ Calcium carbonate accounts for the residual 25 g.
Example 5 — Method of Concomitant Variations (Plant growth and sunlight): Five identical plants are placed under different light intensities — 0%, 25%, 50%, 75% and 100% of full sunlight — with all other conditions kept identical. After three weeks the heights of the plants are measured: 2 cm, 6 cm, 11 cm, 17 cm, 22 cm. As the light intensity increases, the plant height increases proportionally. ∴ Sunlight is causally connected to plant growth (direct concomitant variation).
Frequently Asked Examination Questions (Past Pattern)
1. Define cause. State the Method of Agreement and discuss its merits and demerits. (8 marks)
2. What is the Method of Difference? Distinguish it from the Method of Agreement. (6 marks)
3. Explain the Joint Method of Agreement and Difference with an example. Why is it called the Indirect Method of Difference? (5 marks)
4. State the canon of the Method of Residues. Discuss its importance with reference to the discovery of Neptune and Argon. (6 marks)
5. What is the Method of Concomitant Variations? Discuss its scope and limitations. (6 marks)
6. What are the differences between observation and experiment? Which of Mill’s methods is mainly observational and which is experimental? (4 marks)
7. Explain “post hoc ergo propter hoc” fallacy. Which of Mill’s methods is most liable to this fallacy? (3 marks)
8. Discuss the role of Mill’s methods in modern scientific discovery. (8 marks)
9. What is meant by “plurality of causes”? Which of Mill’s methods is particularly affected by it and why? (3 marks)
10. “All scientific discovery is a combined application of Mill’s methods.” Discuss. (8 marks)
Inter-relation among Mill’s Methods
Although Mill formulated five distinct methods, they are not isolated procedures; in practice every scientific investigation uses them in combination. The Method of Agreement helps to discover a probable cause; the Method of Difference verifies the cause with rigour; the Joint Method strengthens the conclusion when direct experiment is impossible; the Method of Residues handles complex phenomena by subtraction; and the Method of Concomitant Variations handles permanent causes and quantitative laws. The history of medicine, astronomy and chemistry shows this combined use clearly: Ronald Ross’s malaria research began with the Method of Agreement (mosquito common to all malaria cases) and was confirmed by Method of Difference (controlled laboratory experiments breeding mosquitoes and producing infection). The discovery of vitamins began with Method of Difference (Lind’s scurvy experiment) and was extended by Method of Concomitant Variations (dose-response studies). Modern epidemiological research routinely combines all five methods. Therefore the student should understand Mill’s methods as five complementary tools rather than five rival techniques.
End of Chapter 4 Notes — Mill’s Experimental Methods of Inquiry. HSLC GURU wishes every ASSEB student great success in the Higher Secondary Final Examination.