Demonstration and the Six Kinds of Certain Premises

1. From the five arts to demonstration

The previous lesson distinguished syllogistic form from its matter. Two deductions may share a valid form but differ in evidential force: one uses certain premises; the other relies only on popular or probable claims.

Demonstration (burhān) is distinguished by premises that yield certainty. To understand it, we must examine the kinds of propositions treated as certain in the textbook.

This lesson defines demonstration and works through six traditional categories of certain premises, illustrating what does—and does not—establish each category.

2. The textbook definition of demonstration

اعلم أن البرهان قياس مؤلف من اليقينيات بديهية كانت أو نظرية منتهية إليها
Know that demonstration is a syllogism composed of certain premises, whether self-evident or inferential premises ultimately grounded in self-evident ones.

Syllogism specifies a valid inferential arrangement; certain premises distinguish demonstration from dialectic or rhetoric, whose premises have different epistemic statuses.

An inferred premise may also be used demonstratively if its certainty was already established through sound reasoning reaching an appropriate foundation. Mere complexity or popularity does not turn a proposition into certain knowledge.

3. What counts as a certain premise?

A certain premise is a proposition whose truth is established rather than merely asserted with confidence. In the classical framework, certainty concerns warranted assent corresponding to reality, not intensity of personal conviction.

“Every proper whole is greater than its proper part” is intelligible as a necessary relationship. By contrast, “It will rain next week” may be strongly probable without being a first principle.

Demonstration requires both valid logical form and warranted certain premises. Certainty cannot repair an invalid inference, and valid form cannot upgrade weak premises into certainty.

4. The six kinds of certainty

ثم البديهيات ستة
The foundational certain propositions are then divided into six kinds.

The source lists:
1. Awwaliyyāt — first principles
2. Fiṭriyyāt — propositions with their proofs at hand
3. Ḥadsiyyāt — intuitively apprehended propositions
4. Mushāhadāt — observations
5. Tajribiyyāt — experiential generalizations
6. Mutawātirāt — knowledge through convergent mass reports

They are grouped as foundations of certainty, but they do not all arise by the same cognitive route. Some depend on concepts, others on evident reasoning, perception, repeated experience, or sufficiently corroborated reports.

5. Definition of first principles

الأوليات هي قضايا يجزم العقل فيها بمجرد الالتفات والتصور، ولا يحتاج إلى واسطة
First principles are propositions on which the intellect makes a firm judgment simply by attending to and conceiving them, without requiring an intermediary proof.

Conception here means adequately understanding the subject, predicate, and their relation. Once the meanings are grasped, assent follows directly.

A claim is not a first principle merely because someone quickly or strongly believes it. The point is that the relation becomes evident through the concepts themselves, without a separate middle term.

6. First principle: whole and part

الكل أعظم من الجزء
The whole is greater than its part.

The comparison presupposes a proper part of that same whole. If a whole contains ten equal constituent units, three of those units cannot amount to the entire ten-unit whole.

The relation is immediately clear once whole and proper part are correctly understood. The example does not license comparing unrelated magnitudes or redefining a part as the entire object.

7. Source definition of innate inferences

الفطريات، وهي ما يفتقر إلى واسطة غير غائبة عن الذهن أصلاً
Innate inferential propositions require a middle term that is never absent from the mind.

Such judgments have a reason or inferential middle, but it is so immediately available with the concepts that no prolonged search is needed.

They are therefore called qadāyā qiyāsātuhā maʿahā—propositions whose syllogisms accompany them.

8. Why four is even

الأربعة زوج
Four is an even number.

The immediate middle term is the criterion of being divisible into two equal integers. Four divides into two and two, so it is even.

The inference can be unfolded:
1. An integer divisible into two equal integers is even.
2. Four satisfies that condition.
3. Therefore four is even.

The explanatory middle term is ready to hand. That is why the textbook treats this as a fiṭrī proposition rather than an inference-free first principle.

9. One is half of two

الواحد نصف الاثنين
One is half of two.

“Half” means one of two equal portions. Divide two into equal whole-number portions and each portion is one.

An explanatory middle is present: dividing into two equal parts. Unlike a difficult proof, that middle is immediately available.

The difference between first principles and fiṭriyyāt is therefore no middle term required versus a middle term present without a search, not simply whether learners answer quickly.

10. Comparing awwaliyyāt and fiṭriyyāt

First principle: “A whole exceeds its proper part”—the understood relation needs no distinct inferential middle.
Innate inference: “Four is even”—the criterion of divisibility into equal integers serves as an ever-present middle.

Ask two different questions:
1. Is the judgment evident from the terms without a distinct middle?
2. Or does an extremely familiar middle already establish it?

Failing to state a readily available proof does not remove the proof. The distinction matters particularly when classifying elementary arithmetic propositions.

11. The nature of intuitive propositions

الحدسيات، وهو ظهور المبادئ دفعة واحدة
Intuitive propositions involve the relevant principles becoming apparent to the mind at once.

Ḥads concerns an immediate grasp of the principles needed for an inference and their connection to the sought result. It is not synonymous with an unsupported hunch or arbitrary speculation.

The source contrasts ḥads with discursive thought (fikr), in which the mind searches for suitable starting points and then arranges them into a proof. In ḥads the needed insight occurs without that extended step-by-step search.

12. The two movements of discursive thinking

When the desired conclusion is unknown, discursive thought commonly involves two movements:
1. From the question to potential principles or previously known concepts relevant to answering it.
2. From the selected and arranged principles to the conclusion.

For example, one looking for a traditional definition of the human may search for the terms “animal” and “rational” and arrange them appropriately.

When the relevant starting points and their relationship become evident without such an extended search, the textbook discusses this under intuition (ḥads).

13. A precise distinction between intuition and thought

Discursive reasoning may involve deliberate searching, selecting, and arranging known propositions. In ḥads, the principles and their bearing on the answer are apprehended with unusual immediacy.

Speed alone is not a guarantee of truth. A person can reach a false conclusion quickly. The status of an allegedly certain intuition still depends on a sound connection between principles and conclusion.

The source also allows for differences among thinkers: what one person apprehends at once may require an explicit chain of thought for another.

14. Definition of observed propositions

المشاهدات، وهي قضايا يحكم فيها بواسطة المشاهدة والإحساس
Observed propositions are judgments made through observation and sensation.

Unlike first principles, which become evident through concepts, mushāhadāt are grounded in sensory awareness: seeing a light, hearing a sound, or undergoing some other perceptual experience.

The book distinguishes perception through the external senses and the internal senses. Its discussion of internal faculties follows the traditional philosophical psychology of this curriculum.

15. The five external senses

The source identifies five external sensory faculties:
1. Sight — color and shape.
2. Hearing — sound.
3. Smell — odors.
4. Taste — flavors.
5. Touch — heat, cold, softness, hardness, and similar qualities.

Hearing a nearby bell is a direct auditory perception. Determining exactly who rang it, however, may require evidence beyond that immediate sensory impression.

16. Traditional classification of internal senses

The main text and notes use five traditional internal faculties:
1. Common sense (ḥiss mushtarak) — unified awareness of sensible forms.
2. Imagination (khayāl) — retaining sensible forms after the object is absent.
3. Estimative faculty (wahm) — apprehending particular nonsensible meanings tied to particular things.
4. Memory (ḥāfiẓah) — retaining those particular meanings.
5. Compositive faculty (mutaṣarrifah) — combining and separating retained representations.

These are terms from the text's historical philosophical psychology, useful for interpreting its treatment of inner perception; they should not be mistaken for a modern neuroscientific map.

17. Inner experience and claims about the world

Feeling one's own hunger or thirst is a form of inner awareness. A corresponding first-person judgment may be grounded directly in that sensation.

But my own thirst cannot establish that another person must be thirsty; additional evidence or reliable testimony would be needed.

Similarly, seeing smoke and concluding that fire exists adds an inference based on a relationship. The sensory datum and an inference drawn from that datum are not identical.

18. Definition of experiential judgments

التجربيات، وهي قضايا يحكم العقل بها بواسطة تكرار المشاهدة وعدم التخلف حكماً كلياً
Experiential propositions are general judgments the intellect makes through repeated observation and the absence of observed counterinstances.

A single observation differs from repeatably encountering the same relevant pattern under suitable conditions. The latter may support a more general judgment.

Still, the circumstances and possible causes must be examined. The mere repeated coexistence of two events does not automatically establish a single necessary cause.

19. The textbook example of experience

The source uses an old medical example, شرب السقمونيا مسهل للصفراء, describing the ingestion of scammony as facilitating the expulsion of bile. This is a historical example in the logic text, not a contemporary therapeutic recommendation.

Its logical function is to illustrate moving from repeated observations to a general statement about an effect. Knowing the name of a substance is conception; encountering a single effect is observation; seeking a general rule from repeated observations is experience.

Classification as a textbook example does not establish modern scientific or clinical validity of the underlying medical claim.

20. Experience and incomplete induction

Incomplete induction generalizes from examined cases while leaving unexamined cases. The traditional text nevertheless lists certain forms of established experience among the sources of demonstrative certainty.

In that framework, repetition is not treated merely as counting events; the intellect also recognizes a dependable connection under the relevant conditions.

In evaluating an actual claim, limited observations, varying conditions, or counterexamples weaken any assertion of necessity. Repeated occurrence should not be equated mechanically with warranted universal certainty.

21. Definition of mass-transmitted reports

المتواترات، وهي قضايا يحكم بها بواسطة إخبار جماعة يستحيل العقل تواطؤهم على الكذب
Mass-transmitted propositions are judgments based on reports from a group whose agreement on a lie is rationally impossible.

What matters is not sheer number alone but also the independence and convergence of the reporting routes. Repetition of one unreliable story by many people does not automatically create tawātur.

The classical claim is that a suitably convergent body of reporting can yield a kind of certainty beyond that supplied by a single isolated report.

22. Is there a fixed minimum number?

The textbook records differing proposed minimum numbers for tawātur—including four, ten, and forty—while noting that the circumstances and reliability structure of the reports matter.

Therefore, no single headcount in the passage should be treated as an automatic universal test. The central criterion is whether deliberate collusion on the report is rationally excluded.

Independent, convergent observations from different reporting paths differ from many people forwarding the same original claim, even if the total number of voices appears similar.

23. Widely repeated versus mass-transmitted

A report may be famous without meeting the classical criterion for tawātur. Popularity alone does not establish how the information was acquired.

A widely accepted claim may be useful in dialectic as a mashhūr proposition. A mass-transmitted report requires a sufficiently independent and convergent body of testimony to support certainty.

This difference links the present chapter back to the five logical arts: argument from what people commonly accept is not automatically demonstrative knowledge.

24. Transmission and rational assessment

A note raises an objection: reports are fallible, so how can transmitted knowledge supply demonstrative premises? It responds by considering the rational grounds and corroborative conditions that can make particular reports convincing.

The point is not that every transmitted assertion is certain. Rather, the traditional theory holds that reports meeting sufficiently stringent conditions can function as sources of certainty.

When assessing an actual report, separate the original event, the number of apparent reports, and the real independence of their sources.

25. Reason, perception, and testimony

The six categories rely on different epistemic paths:
1. First principles — direct judgment from understood concepts.
2. Innate inferences — judgment through an immediately available middle.
3. Intuitions — immediate grasp of relevant principles.
4. Observations — external or internal perception.
5. Experiences — repeated relevant observation supporting a general rule.
6. Mass reports — sufficiently independent and convergent testimony.

Appropriate testing differs: locate the middle term in fiṭriyyāt, assess repetition and conditions in tajribiyyāt, and inspect reporting paths in mutawātirāt.

26. Using the six sources in demonstration

Calling premises “certain” is not sufficient; their warrant must actually be established, and the argument's logical form must be productive.

For example:
1. Every integer divisible into two equal integers is even.
2. Four is divisible into two equal integers.
Conclusion: Four is even.

Here both the meanings and inferential relation are clear. The concept of evenness supplies the relevant basis.

If a merely probable statement were inserted into the same pattern, the inference might still be valid, but its conclusion would not thereby gain demonstrative certainty.

27. Correcting four common mistakes

Mistake 1: Every rapid judgment is a first principle. Correction: An obvious middle term may make a judgment fiṭrī instead.

Mistake 2: Every sudden idea is a certain intuition. Correction: Ḥads concerns a sound, immediate grasp of inferential principles.

Mistake 3: One observation establishes an experimental law. Correction: Experience concerns relevant repetition and generalization.

Mistake 4: Many repetitions of a statement prove tawātur. Correction: Independence of reports and the rational exclusion of collusion matter.

28. Worked classification exercise

Classify by the epistemic route:
1. “A whole exceeds its proper part” — first principle, with no separate middle required.
2. “Four is even” — innate inference, with the defining middle immediately present.
3. Relevant premises become clear at once — a case of intuition when they are sound.
4. Seeing clouds directly — observation.
5. A general rule established through suitable repeated observation — the domain of experience.
6. Independent convergent reports that eliminate rational doubt of collusion — mass transmission.

The deciding feature is how the proposition is warranted, not sentence length or familiarity.

29. Lesson synthesis and next step

Demonstration is a valid syllogism made from warranted certain premises. Its premises may be immediate or inferential, provided the latter are genuinely grounded in certain principles.

The six classes are first principles, innate inferences, intuitions, observations, experiences, and mass-transmitted reports. Their epistemic routes—direct rational insight, an available middle term, immediate discovery, perception, repeated observation, and independent testimony—must not be conflated.

The textbook next distinguishes burhān limmī from burhān innī, depending on whether the middle term explains the real cause of the conclusion or only why the conclusion is known.