Demonstration Through Causes and Effects: Limmī and Innī

1. Two kinds of demonstration

In the previous lesson, demonstration was linked to six kinds of certain premises. We now ask whether reasoning from a cause to its effect differs from reasoning from an effect to its cause.

البرهان قسمان: لمّي وإنّي
Demonstration is divided into two kinds: limmī and innī.

Both require sound reasoning and appropriately certain premises. Their distinction concerns the middle term: is it merely the reason we know the conclusion, or also a real cause of the predication asserted in that conclusion?

2. Recall what the middle term does

In a categorical syllogism, the middle term occurs in both premises and is absent from the conclusion. It connects the major predicate with the minor subject.

For example: “This metal is being heated”; “Metal heated under these conditions expands”; therefore “This metal expands.” Being heated supplies the shared link in this controlled illustration.

Simply repeating a word does not establish an inference. The form must be valid and the relevant premises justified. We must then ask whether the middle term is also a cause in the world.

3. Reason for knowing versus cause in reality

A reason for assenting in the mind is the evidential middle term through which we judge a conclusion to follow.

A cause in reality is what actually accounts for the property being instantiated in the subject under discussion. The first is an epistemic role; the second is an explanatory or causal role.

Seeing water drops on a wall may give us evidence that it has become wet. Our seeing the drops did not wet the wall. The reason we come to know something need not be what makes it happen.

4. Source definition of limmī demonstration

أما اللمّي: فهو الذي يكون الأوسط فيه علة لثبوت الأكبر للأصغر في الواقع كما أنه واسطة في الحكم
Limmī demonstration is one in which the middle term causes the major predicate to belong to the minor subject in reality, just as it mediates the judgment in reasoning.

The definition requires two functions:
1. The middle term establishes the conclusion in our reasoning.
2. The same middle term explains its truth in reality.

Thus limmī demonstration seeks not just that the conclusion holds, but why it holds.

5. Why it is called limmī

يسمى به لإفادته اللمية والعلية
It receives this name because it conveys the “why” and the causal explanation.

To report that something occurs is one achievement; to show what accounts for it is another. In limmī demonstration, the middle term connects the epistemic explanation with the real cause.

Merely labeling something a “cause” is insufficient. The middle term must genuinely explain the predication, the premise must be established, and the syllogism must validly yield its conclusion.

6. The textbook’s classical medical illustration

زيد محموم؛ لأنه متعفن الأخلاط، وكل متعفن الأخلاط محموم، فزيد محموم
Zayd has a fever because, in the classical humoral account used in the text, his humors are corrupted; on that account, corrupted humors lead to fever, so Zayd has a fever.

Here the minor term is Zayd, the major term is having a fever, and the middle term is corruption of the humors. The example is limmī within the historical causal theory assumed by the textbook.

This is an illustration of the logic of causation, not a reliable account of fever according to modern medicine.

7. Three links in the limmī example

Put the textbook's illustration into standard form:
Minor premise: Zayd has corrupted humors.
Major premise: In the historical theory assumed, everyone with corrupted humors has a fever.
Conclusion: Zayd has a fever.

“Corrupted humors” links the premises and, within that theory, is treated as the real cause of fever. It thus serves as both ground of inference and explanation of the occurrence.

Analyzing the conditional logical form is distinct from endorsing the historical medical major premise as a present-day scientific fact.

8. A more accessible cause-to-effect illustration

Imagine a metal rod heated in a controlled setting, with other relevant conditions held fixed. Under those stipulated conditions, heating makes the rod expand.

Minor premise: This rod was heated under those conditions.
Major premise: Such heating causes rods of this kind to expand.
Conclusion: This rod expanded.

Heating is both the evidential middle term and the real explanatory cause. The case illustrates the cause-to-effect orientation characteristic of limmī demonstration, provided the premises are suitably established.

9. Source definition of innī demonstration

وأما الإنّي: فهو الذي يكون الأوسط فيه علة للحكم في الذهن فقط، ولم يكن علة في الواقع، بل قد يكون معلولا له
Innī demonstration uses a middle term that grounds the judgment in the mind only, not the occurrence of the predicate in reality; it may even be an effect of what it indicates.

A reason in the mind only does not mean a fantasy or unsupported guess. It means that the middle term is our evidence for the conclusion, not its producing cause.

Thus in innī demonstration, what establishes our knowledge and what produces the reality known are different.

10. The textbook example of innī

زيد متعفن الأخلاط لأنه محموم، وكل محموم متعفن الأخلاط، فزيد متعفن الأخلاط
Zayd has corrupted humors because he has a fever; in the classical account assumed here, every feverish person has corrupted humors, so Zayd has corrupted humors.

Now fever is the middle term. Within that theory, fever is considered an effect, not the cause, of corruption of the humors. It may therefore be used as a sign for knowing the cause without producing that cause.

The illustration is historical and is not a diagnostic rule for contemporary medicine.

11. Logical structure of the innī example

The innī example can be arranged as follows:
Minor premise: Zayd has a fever.
Major premise: According to the historical theory assumed in the textbook, every feverish person has corrupted humors.
Conclusion: Zayd has corrupted humors.

“Fever” is the ground on which the conclusion is inferred, yet within the same theory it is not the real cause of the alleged corruption.

Logical entailment still depends on accepting the major premise. A fever does not diagnose “corrupted humors” in modern medicine.

12. Two directions within one causal account

Within the historical causal scheme of the text, alleged corruption of humors is taken to produce fever, while fever is taken as evidence from which that earlier condition may be inferred.

Cause to effect: if the middle term is also the real cause, the argument is limmī.
Effect to cause: if it indicates the cause without producing it, the argument is innī.

These are not mere verbal reversals. From “A causes B” it does not automatically follow that every B was caused by A. A converse inference requires an independently warranted premise.

13. When does an effect establish a cause?

Suppose a lamp is off. Perhaps its switch is open, its bulb failed, or the power supply stopped. The observation “the lamp is off” does not by itself entail “the switch is open.”

If a carefully restricted setup excludes the alternatives and establishes that, in those conditions, the lamp is off only when the switch is open, a warranted inferential premise becomes available.

Innī does not mean inferring one unique cause from any effect whatsoever. The inference must still be valid and its premises warranted.

14. A sign of a cause is not the cause

Seeing dark clouds can suggest rain, but our observation does not cause rain, and clouds do not guarantee it. Likewise, a warning light may indicate a fault without producing the fault itself.

These examples clarify the difference between an epistemic sign and a real cause.

They are illustrations of the distinction, not automatically conclusive demonstrations. For a true burhān, the relevant conditional premises, alternatives, and level of certainty must be independently established.

15. Comparing the two middle terms

Limmī: the middle term grounds the judgment and is also the real cause of the major predicate belonging to the minor subject.
Innī: the middle term grounds the judgment but is not the real cause; sometimes it is an effect of the relevant cause.

Both share an epistemic middle term. The defining difference is whether that term also has the relevant causal role in reality.

To classify an argument, identify its conclusion, locate the middle term, and investigate how that term is related to the concluded fact in the world.

16. Do not confuse cause and effect

Here a cause is what explains why the relevant state occurs, and an effect is the state resulting from it.

When heating accounts for a rod’s expansion under controlled conditions, heating is the cause and expansion the effect. Inferring the expansion from heating illustrates a limmī direction; inferring heating from the expansion may illustrate an innī direction, provided alternative causes are addressed.

Reversing word order does not reverse causation. The real explanatory relationship determines the classification.

17. Not every valid deduction is limmī

Consider the inference:
Minor premise: This animal has four legs.
Major premise: Every four-legged animal is a horse.
Conclusion: This animal is a horse.

The syllogistic form can be represented as valid, but the major premise is false: many non-horses have four legs. This is therefore not a sound demonstration, still less a limmī one.

Separate three questions: valid form, certain and true premises, and the middle term's causal role.

18. Innī does not automatically mean a guess

Reasoning from a sign to an underlying cause can be merely probable, or sufficiently conclusive under justified conditions. The label innī identifies the role of the middle term; it does not automatically condemn the inference as a guess.

An unlit lamp ordinarily permits several explanations. But in a specified closed system, if alternatives have been ruled out and the diagnostic relation established, the inference may become much stronger.

Do not confuse the kind of middle-term explanation with the certainty or probability of the premises.

19. Analyze the minor and major premises

Do not classify an inference from a surface impression. Write down its premises and conclusion first.

Step 1: Identify the subject and predicate of the conclusion.
Step 2: Locate the term common to both premises.
Step 3: Test whether the conclusion follows validly.
Step 4: Ask about the middle term in reality: is it a cause, effect, or another indicator?

The final question distinguishes limmī from innī, but the earlier checks are indispensable for a reliable classification.

20. Worked analysis: cause to effect

Assume the following experimentally grounded premises are true:
Minor premise: This wax has been heated to a specified temperature.
Major premise: Wax of this kind melts when heated to that temperature under these conditions.
Conclusion: This wax has melted.

Middle term: being heated to the relevant temperature under those conditions.
Epistemic function: it grounds the inference to melting.
Real function: heating brings about the change.

Under the stated assumptions, this illustrates limmī reasoning because the middle term also explains the occurrence.

21. Worked analysis: effect to cause

In the same experimental setting, assume alternative explanations for melting have been properly excluded.

Minor premise: This wax is melted.
Major premise: In this closed setup, melting reliably indicates that the stipulated heating threshold was reached.
Conclusion: The wax reached that temperature.

Middle term: being melted. It is our evidence for the heating, but is not what causes the heating; it is an effect in this causal account.

The direction is therefore innī. Without exclusion of alternatives, the conclusion would not automatically be certain.

22. Reading the source example precisely

In the textbook's limmī illustration, corrupted humors are hypothesized as both a real cause of fever and the middle term through which fever is inferred. In the innī illustration, fever indicates the supposed humoral condition without producing it.

A concise distinction is:
Limmī: the argument answers “Why does it occur?” by identifying the cause.
Innī: the argument answers “How do we know it?” through evidence, potentially an effect of the cause.

Neither classification can be justified by word choice alone. The actual relation between middle term and concluded predicate must be examined.

23. Common errors to avoid

Error 1: Every argument containing “because” is limmī. “Because” may introduce evidence rather than a real cause.

Error 2: Every guess from an effect to a cause is certain innī demonstration. Effects often have several possible causes, and premises must be warranted.

Error 3: A true conclusion automatically makes an inference demonstrative. Accidental truth does not repair false premises or invalid reasoning.

Error 4: Limmī and innī differ by the number of premises. Their central difference is the real causal status of the middle term.

24. A comparison of the two demonstrations

AspectLimmīInnī
ReasoningMiddle term is evidenceMiddle term is evidence
Real causationMiddle term is the causeMiddle term is not the cause
Typical directionCause to effectEffect or sign to reality
Central questionWhy does it occur?How is it known?

Both require sound inferential form and appropriately certain premises. Their difference concerns the middle term's causal role in reality.

25. Practice in classifying arguments

Classify these cases by examining the real status of the middle term:
1. Inferring a rod's expansion from established heating under controlled conditions — limmī-type, since heating causes expansion.
2. Inferring heating from that expansion in a suitably restricted setup — innī-type, since expansion is the effect.
3. Inferring the state of a switch merely from an unlit lamp — underdetermined, because alternatives remain.
4. Inferring “horse” from “has four legs” through a false universal premise — not demonstrative.

Classifying an inferential direction and establishing the soundness of the inference are different tasks.

26. Lesson synthesis and next topic

In limmī demonstration, the middle term both grounds the conclusion in reasoning and causes the relevant predication in reality. In innī demonstration, it grounds the inference but does not cause the fact; it may even be an effect of its real cause.

The textbook's fever-and-humors illustration represents these two directions within a historical theory. The enduring logical lesson is to distinguish evidence from causation and to assess the argument's form and premises independently.

The following section is dialectical syllogism (al-qiyās al-jadalī), which uses commonly accepted or conceded premises rather than the certain foundations of demonstration.