Analogy: Original and New Cases, Common Cause, Co-variation and Elimination

1. From induction to analogy

Induction examines particular cases and draws a general conclusion about their class. Analogy (tamthīl) begins with a ruling known about one particular case and attempts to establish it in another particular case through a relevant shared feature.

Suppose a property and its consequence are known in one object. Another object shares that property. The question is whether the same consequence extends to the second object.

Resemblance by itself is insufficient: the shared feature must have an appropriate connection to the judgment.

2. The source definition of analogy

التمثيل وهو إثبات حكم في جزئي لوجوده في جزئي آخر لمعنى جامع مشترك بينهما
Analogy is establishing a judgment in one particular because that judgment exists in another particular, on account of a common unifying feature shared between them.

The definition specifies four elements: a case with an established judgment, a second case whose judgment is sought, a common meaning, and the proposed transfer of the judgment through that meaning.

Its distinctive direction is from one particular to another particular. The common feature is offered as the ground of transfer.

3. The original case, new case, ruling, and cause

The four principal elements of analogy are:
Original case (aṣl): the particular whose judgment is already known.
New case (farʿ): the particular for which the judgment is sought.
Judgment (ḥukm): what is established for the original and proposed for the new case.
Cause or unifying feature (ʿillah / jāmiʿ): the relevant shared meaning proposed to justify the transfer.

If the unifying feature is not relevant to the judgment, cataloging similarities between the cases cannot complete the inference.

4. The textbook example: world and house

العالم مؤلف فهو حادث كالبيت
The world is composite, so it is originated, like a house.

Here the house is the original case, whose origination is taken as known. The world is the new case. Being composite is the unifying feature proposed for both.

This classical example illustrates the structure of analogy. Its conclusion requires the further substantive premise that being composite is indeed a sufficient ground for origination; the analogy alone does not establish that premise.

5. Analyzing the classical example

Break the source analogy into its components:
Original case: house.
New case: world.
Original judgment: being originated.
Unifying feature: composition (taʾlīf).

The key question is whether the house is originated *because* it is composite, or for another reason. If its judgment depends on something not established in the new case, the shared feature does not justify transfer.

This is why the text proceeds to methods for establishing the proposed cause.

6. Analogy in juristic terminology

The source note explains that jurists commonly call this form of inference qiyās. The known case is the aṣl, the new case the farʿ, and the operative common feature the ʿillah.

In theological discourse, the pattern can be described as inferring from the observed (shāhid) to the unobserved (ghāʾib). The former is the known case and the latter the case to which the judgment is being extended.

The focus here is the logical structure of analogy, not a ruling about any particular juristic case.

7. Analogy versus categorical syllogism

In a categorical syllogism, the conclusion follows from the premises through a valid form, provided the relevant conditions are met. Analogy proposes transferring a judgment through a claimed shared cause.

Analogy: This copper rod conducts electricity; the second rod is also copper; therefore we expect it to conduct.
Syllogism: Every pure copper rod conducts under suitable conditions; this rod is pure copper; therefore it conducts under those conditions.

The second inference explicitly contains a universal premise. The first must establish the general relevance of the shared property.

8. Analogy versus induction

Induction: examining a number of individuals and proposing a general judgment about their class.
Analogy: extending a known judgment from one individual to another on the basis of a relevant common feature.

Examining the leaves of many trees and inferring a pattern for the entire species is induction. Suspecting the same disease in another tree because it shares a particular symptom with a diagnosed tree is analogy.

Both need testing, but their direction of inference differs: particulars to a universal versus particular to particular.

9. Similarity is not necessarily causation

Two objects may have the same color, weight, location, or shape, yet not every similarity causes the judgment we wish to transfer.

Two medicines may share a color without having identical effects. The color is a shared attribute, but not necessarily the cause of their effects.

The strength of analogy depends on selecting a pertinent shared feature and establishing its relation to the judgment.

10. The two source methods for identifying the cause

والعمدة فيها طريقان
The principal reliance is on two methods.

The first is dawarān, named in the text as the term of later scholars, linked with the earlier expression ṭard wa-ʿaks. The second is sabr wa-taqsīm, examining possible attributes and excluding those unfit to explain the ruling.

Both seek more than surface resemblance: they investigate which feature actually grounds the judgment.

11. Defining co-variation (dawarān)

وهو أن يدور الحكم مع المعنى المشترك وجودا وعدما
It means that the judgment accompanies the common feature both in presence and in absence.

When the relevant feature is present, the judgment is present; when the feature is absent, the judgment is absent. This two-directional pattern is called dawarān.

The definition demands more than a single coincidence. It requires examination in both positive and negative cases.

12. The positive side of co-variation

The positive direction is observed when the shared feature and the judgment are both present.

Imagine a particular electrical circuit where closing the switch lights a bulb. Repeating the procedure provides positive observations. But the result also depends on power, wiring, and a working bulb.

Thus seeing the closed switch and illuminated bulb together reveals an association under specified conditions; it does not on its own establish a complete causal explanation.

13. The negative side of co-variation

The negative direction occurs when the proposed feature is absent and the judgment is absent.

In the same intact circuit, opening the switch extinguishes the bulb. Repeating both states strengthens the argument, because the presence and absence have each been examined.

The other relevant conditions must stay constant. If the power supply also fails, the observations do not isolate the switch as the causal factor.

14. The paired language of ṭard and ʿaks

الدوران عند المتأخرين، والقدماء كانوا يسمونها بالطرد والعكس
Later scholars call this dawārān, whereas earlier scholars referred to it as ṭard and ʿaks.

Here ṭard is the positive accompaniment of a feature and its judgment, while ʿaks is their corresponding absence. Together they make up the two sides of co-variation.

This use of ʿaks is distinct from conversion of propositions (ʿaks mustawī and ʿaks naqīḍ) studied previously.

15. The conditioning feature and dependent judgment

The text calls the feature considered as cause the madār, and the judgment that accompanies or ceases with it the dāʾir.

Suppose a material changes state when given sufficient heat and reverts when cooled under specified conditions. Heat is the proposed conditioning factor, and the change of state is the dependent outcome.

Separating the two terms makes clear which aspect is being tested as a cause and which is to be explained.

16. What co-variation does and does not prove

The source presents co-variation as evidence for identifying a cause. Its strength depends on context: co-variation can support a causal hypothesis without automatically proving causation in every case.

Both observations might depend on a third factor. A feature could be necessary but not sufficient for the judgment.

Accordingly ask whether other relevant factors were investigated, whether counterexamples exist, and whether the judgment really depends on the proposed common feature.

17. The method of examination and division

والطريق الثاني: السبر والتقسيم
The second method is examination and division (sabr wa-taqsīm).

Division (taqsīm) lists the plausible attributes of the original case that could explain the judgment. Examination (sabr) tests these candidates and eliminates those unfit to serve as causes.

The aim is not to treat every resemblance as explanatory, but to identify the relevant cause among the competing possibilities.

18. The stages of elimination reasoning

The method can be organized into four steps:
1. Identify the judgment known in the original case.
2. List the plausible causal properties.
3. Test each candidate for cases where the property is present but the judgment absent, or the reverse.
4. Eliminate unsuitable alternatives and evaluate the surviving candidate.

If the list of possible causes is incomplete, the final survivor is not proved to be the cause merely because other listed candidates were rejected.

19. Possible causes listed in the source

إن علة حدوث البيت إما الإمكان، أو الوجود، أو الجوهرية، أو الجسمية، أو التأليف
The cause of a house's origination is proposed as either possibility, existence, substantiality, corporeality, or composition.

This classical example illustrates division: a single judgment has several competing causal candidates. An original case may possess many attributes without each one being the cause of the judgment.

The next task is to assess the relation of each candidate to origination.

20. How a candidate cause is excluded

ثم يثبتون أن ما وراء المعنى المشترك غير صالح لاقتضاء الحكم
They then establish that attributes other than the common meaning are unfit to produce the judgment.

The text proposes testing an attribute in another case where the attribute is present but the judgment is absent. Such an observation can demonstrate that the attribute alone is not sufficient for the judgment.

If two things share a feature but only one exhibits the effect, that shared feature by itself provides a poor explanation of the effect.

21. The source's elimination argument and its limits

The source tests possibility, existence, substantiality, and corporeality as candidates and argues that none alone suffices for origination. It retains composition as the proposed shared feature.

Some of its supporting cases presuppose historical metaphysical doctrines, including claims about immaterial substances and celestial bodies. They illustrate a classical philosophical argument, not independently verified modern scientific facts.

The general methodological lesson is that each causal candidate needs its own assessment, and the remaining candidate is well supported only if plausible alternatives were adequately ruled out.

22. Comparing the two causal methods

Dawarān asks whether the proposed cause and judgment accompany one another across presence and absence. Its focus is patterned co-variation.

Sabr wa-taqsīm asks which of several plausible causes can account for the judgment. Its focus is enumerating, testing, and rejecting alternatives.

Both investigate relevance of the common feature. One emphasizes co-variation, while the other emphasizes elimination of competing explanations.

23. Worked analogy with a relevant feature

Suppose a rod made of a particular metal expands when heated under suitable conditions. A second rod is made of the same metal and is heated under corresponding conditions.

Original: first rod.
New case: second rod.
Judgment: expansion when heated.
Unifying feature: the same relevant metallic and thermal property.

The inference is stronger when we also check differences in construction, temperature, and other relevant factors. Good analogy considers both shared and differing features.

24. Correcting an irrelevant analogy

Someone argues: “A white medicine benefited a patient. This other medicine is also white; therefore it will have the same effect.” This is invalid: whiteness is not established as a cause of medicinal efficacy.

Relevant evidence would concern the medicines' active ingredients, dose, mode of use, and clinical evidence. A shared appearance does not transfer the therapeutic judgment.

The principle is that sharing an irrelevant attribute does not justify transferring a different judgment.

25. Four recurring mistakes in analogy

1. Treating superficial similarity as a cause: looking alike is insufficient.
2. Using an incomplete list of alternatives: overlooking a plausible cause undermines elimination reasoning.
3. Claiming certainty from mere association: even co-variation requires examination of other factors.
4. Confusing the original with the new case: doing so obscures what is already known and what is to be established.

A clear analysis separates the premises, shared meaning, and evidence for the cause.

26. A practical checklist for an analogy

Use these questions when evaluating an analogy:
1. What is the original case and its known judgment?
2. What new case is being considered and what is to be proved?
3. Which feature is shared?
4. Is it causally relevant or an accidental resemblance?
5. Is its relevance supported by co-variation, elimination, or other evidence?
6. Are there counterexamples or disanalogies that defeat the transfer?

Answering these questions separates the structure of the analogy from the strength of its supporting argument.

27. Lesson conclusion and transition

Analogy: attempting to transfer a judgment between particulars through a common cause.
Co-variation: examining whether a feature and judgment accompany each other in presence and absence.
Examination and division: listing plausible causes, testing them, and excluding those unfit.

Recognizing resemblance is a starting point, not a completed proof. A credible analogy must explain why the selected shared feature is relevant to the judgment.

The next section introduces proof by contradiction (qiyās al-khalf), which tests the denial of a proposition and derives an inconsistency.