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Paper Presented at the 5th National Conference on Medical Sciences, 4-5 May 1999 organised by the School of Medicine, Universiti Sains Malaysia, Kota Bharu, Kelantan, Malaysia by Prof Omar Hasan Kasule, Sr. MB ChB (MUK), MPH, DrPH (Harvard), Kulliyah of Medicine, International Islamic University, Kuantan, Malaysia.
ABSTRACT
The paper explains how probability concepts can be taught to Muslim students using concepts and examples from the Islamic perspective. Each probability concept is correlated with the corresponding Islamic concept. Illustrative examples are given from the Qur'an and sunnat. The following methods were used in the correlation analysis: agreement, disagreement, similarity, and apposition. It was found that most concepts in probability could be related to corresponding Islamic concepts and could be illustrated by examples from Muslim history. The following correlations between probability and Islamic concepts were established: objectivity or fair trials with istiqamat; subjective bias with hiwa al nafs; predictability and consistency with sunan al llaah; evidence based knowledge with hujjiyat al burhan; adequate probability trials with khawatim al a'maal; conditionality with shart, consultation for decision-making with istikharat, certainty with yaqeen; doubt with shakk; gambler's fallacy with tanjiim; relativity/probability of knowledge with nisbiyat al ma'arifat, and gray zones shubuhaat. Examples of mutually exclusive events were found in divine attributes that could not co-exist with human attributes. Personal accountability and reward or punishment of each individual without regard to any other was found to exemplify independence of events. Abubakr al Siddiq was an example of how a strong prior belief in the honesty of Muhammad made him quickly believe the message and became a very strong believer. The mechanism or rationale of the correlation was explained. The paper concluded that complicated probability concepts can be taught from an Islamic concept making it easier for Muslim students to understand and internalize them.
(NB: The full text of the paper can be downloaded from http//www.iiu.edu/my/recoff/ttc/Lecmed_home.htm)
INTRODUCTION
AIMS and OBJECTIVES
Objectives: The concepts and applications of probability are difficult to teach to medical students because they appear very abstract with no apparent direct relationship with the students' socio-cultural and intellectual background. The paper presents suggestions on teaching probability that uses Islamic concepts as a basis for developing probability concepts. The paper has three main objectives: establishing an Islamic context and motivation for probability, ta'asil; correlation of probability to Islamic concepts; and illustrations of probability using Islamic themes. The paper urges that providing an Islamic context for other concepts in science and technology will make Muslims more creative. Basic Islamic concepts knowledge and some fundamentals of probability statistics are provided for the non-specialist.
Creativity: Muslims are largely consumers and not producers of science and technology. Creativity requires originality. To be original they must internalize science and technology within their intellectual and cultural heritage. The failure of creativity is due to an unsuccessful grafting a European world-view onto a Muslim world-view. The European world-view is derived from over 3000 years of Greco-roman and Judeo-christian intellectual and cultural traditions. The Muslim world-view is based on the Qur'an and the sunnat. What motivates a European to creativity in science and technology can not motivate the Muslim. The motivation of the Muslim must come from within the Islamic intellectual and cultural heritage.
BASIC CONCEPTS OF KNOWLEDGE
Supremacy of knowledge, siyadat al 'ilm: The Qur'an has talked about the supreme position of knowledge. Knowledge is the basis for leadership (2:247). Those who know are grades higher than those who do not know (58:11, 139:9).
Grades/categories of knowledge: Three categories of knowledge are described. 'Ilm al yaqeen (102:3-5) is knowledge that is certain with no doubts and which represents finality. 'Ayn al yaqeen (102:7) is knowledge that is empirical but is of lesser degree than 'ilm al yaqeen since it is based on observation by human senses and intellect that are not perfect. Haqq al yaqeen (56:95, 69:51) is the the truth behind reality. All human knowledge is probabilistic and the aim of scientific research is to raise the probability of being near the truth, ilm al yaqeen, as much as possible..
Evidence-based knowledge: The Qur’an makes the case for evidence-based knowledge, hujjiyat al burhan, and always challenges those who make claims or allegations to produce their evidence (2:111). It rejects any knowledge not based on concrete evidence and proof.
Objectivity of knowledge: Islamic epistemology, nadhariyyat ma’rifiyyat Islamiyyat, is defined by objectivity. Objectivity is defined by the Qur'anic term, istiqamat, which implies staying on the path of truth and not being swayed by whims, desires, and any other human subjective tendencies or bias (41:30). Correct knowledge is the truth, haqq. Human observation and interpretation can be biased away from this truth by human desires/inclinations, hiwa al nafs (4:135).
Relativity of knowledge: The Islamic position is that there are some established truths that do not change with time or place. Other facts change when the frame of reference changes, nisbiyat al haqiqat. The concept of relativity can be also used to mean different levels of knowledge. Above every knower is someone more knowledgeable until Allah who has ultimate perfect knowledge.
Probability of knowledge: The concept of probability concretizes the limitations of human senses. Knowledge based on human senses and human intellect is approximate. The aim of scientific research is to increase the probability of truth but can not reach perfect truth. No scientific fact is absolutely right or correct. Each has a calculable probability of being correct. The higher the probability of truth the nearer knowledge is to haqq al yaqeen. The more the research effort, the nearer to the truth does the researcher get.
Sources of knowledge: Human senses are used to get knowledge from the environment (16:78, 17:36, 96:3-4). Intellect (‘aql) enables humans to understand and correctly interpret the sensory perceptions of the signs of Allah in the universe. Misuse or under-use, ta’atwil al ‘aql, are severely condemned (2:170-171).
Limitations of human knowledge: Human knowledge is limited (3:66) because of finite capacities of human senses and the intellect that interprets sensory perceptions. Only God knows the unseen that human senses can not reach, ghaib mutlaq. Humans using senses and their instrumental extension can reach some hidden things, ghaib nisbi, such as visualizing a distant island using a microscope. The whole purpose of scientific research is to roll back the field of ghaib nisbi in the present (4:34), the past (3:44), or the future (10:20).
BASIC CONCEPTS OF PROBABILITY
Definition of probability: Probability is a measure of likelihood of occurrence of an event. Probability, an intuitive concept employed in ordinary life, is systematized and quantified in statistical work to make it objective. Frequentist probability is the relative frequency of an event on repeated trials under the same conditions. It is in other words the ratio of the occurrence of an event out of all the potentially possible equally likely outcomes.
Classification of probability: Subjective (personal or intuitive) probability, referred to in common parlance as 'likely' or 'probable, is not consistently reliable. Objective or empirical probability, a quantification of chance, can be measured or can be computed. Bayesian probability combines a prior probability with new empirical data to reach a posterior probability. The prior probability can be objective or subjective. Theoretical probability, a type of objective probability knowable or calculable without experimentation, can be determined by abstract reasoning. In conditional probability, the event depends on occurrence of a previous event.
Types of events considered in probability studies: Mutually exclusive events are those that can not occur together like being dead and being alive. Independent events can occur simultaneously because the occurrence of one does not affect the occurrence of the other.
Uses of probability in decision-making: Bayes’ theorem is the basis of probabilistic decision-making. In the real world the investigator has some prior belief before starting a new experiment. The experimental evidence just changes the degree of prior belief. Thus the posterior probability is a function of both the prior and experimental data.
Uses of probability in statistical inference: Statistical inference is probabilistic and quantifies the probability of wrong or correct conclusions about the null hypothesis. Probability measures quantify the degree of uncertainty in biological measurements. It also links sample statistics to population parameters if the random samples are used.
METHODOLOGY
Concepts in probability were analyzed by comparison with Islamic concepts. Islamic concepts and examples were from the Qur'an and the 6 authentic books of hadith. Probability concepts were from elementary course material for first year medical students. The following methods of comparison were used: the method of agreement, tawafuq; the method of disagreement, tabayun; the method of similitude, tashabuh; and the method of apposition, taqabul. The rationale or explanation for each correlation found was made.
RESULTS
The results of the analysis are shown in the table below:
Probability Concept | Corresponding Islamic concept(s) or example |
Empirical basis Objectivity/fair trial Subjective bias Predictability Evidence-based knowledge | Istiqamat Hiwa al nafs & dhann Sunan al llaah Hujjiyat al burhan |
Events Mutually exclusive Independent Sufficient number of trials Conditionality | Sifaat al llaah Thawab al alkhirat Dawaam al a'mal/khawatim al amal Shart |
Decision/inference Consultation Prior & posterior probability | Istikharat Abubakr al Siddiq |
Certainty & doubt Certainty Doubt Prediction Gambler's fallacy Relativity/probability of knowledge Gray areas | Yaqeen Shakk Ghaib Tanjiim, tatayur Nisbiyat al ma'arifat Shubuhaat |
Objectivity or fair trials was correlated with istiqamat, following and sticking to the path of truth.. Subjective bias, the opposite of objectivity, was correlated with hiwa al nafs which is following the emotional or other irrational or passionate inclinations of the heart. Predictability and consistency reflect the existence of sunan al llaah, fixed laws that define rational relations among phenomena. Evidence based knowledge was correlated with hujjiyat al burhan, a concept that implies among other things that evidence is the criterion that separates truth from untruth. No definitive computations of probability can be made without carrying out a sufficient number of trials. Thus adequate probability trials was correlated with dawaam al 'amal, constancy of work and khawatim al a'maal, seeing a task through its end. Any intermediate conclusions or impressions could be proved wrong by later events. Conditionality was correlated with shart, a highly developed and specialized concept in Islamic jurispudence. Consultation for decision-making with istikharat, certainty with yaqeen; doubt with shakk; gambler's fallacy with tanjiim; relativity/probability of knowledge with nisbiyat al ma'arifat, and gray zones shubuhaat. Examples of mutually exclusive events were found in divine attributes that could not co-exist with human attributes. Personal accountability and reward or punishment of each individual without regard to any other was found to exemplify independence of events. Abubakr al Siddiq was an example of how a strong prior belief in the honesty of Muhammad made him quickly believe the message and became a very strong believer
DISCUSSION
EMPIRICISM
Order and laws of the universe: There are three conceptual bases for the probability theory: physical signs of Allah, ayat; physical laws of the universe, sunan al llaah fi al kawn; and causality, sababiyat. The three concepts have an underlying and generalizing concept of order in the universe, nidhaam al kawn (2:22, 2:164, 3:27, 3;190-191). All matter, energy and events are signs of Allah (4:153). The signs, found in the cosmos (16:65-69, 2:164) and humans (16:4-8) are the basis for human thought, tafakkur (3:191); knowledge, ilm (6:37); certainty, yaqeen (51:20); and action, 'amal. All phenomena in the universe follow physical laws that are characterized by stability, thabat al sunan (17:77, 33:62, 35:43, 48:23). The laws exist for fixed unchanging relationships as well as dynamic relations, sunan al llaah fi al taghyir (6:89, 8:53, 13;11, 47:38). The purpose of scientific research is to discover these laws and use them to manipulate the environment for the service of humans. Thus empirical probability is a reflection of such laws. The fact that tossing a coin 100 times will come out heads 50% of the time is following the laws and is not a chance occurrence; it is a reflection of a fundamental law of nature about the behavior of a fair coin on repeated tossing. Other examples of the sunan are the existence of causality, parity, variance in natural phenomena, and lessons from past experience of past human generations (3:137).
Causality: The concept of causality, sababiyyat, underlies most knowledge obtained by empirical observation. Simply stated this concept asserts that there is a material cause for every physical event that a human observes (18:84-85). Rules of causality must be followed or respected ittibau al sabab (18:84-89). In many cases humans are not aware of the causal relation but they can not deny its existence. They can discover the causes by empirical research. Empirical evidence never conclusively discovers causal relations but we can calculate the probability of truth of any relationship that is found. The higher this probability the more likely is the causal relation.
Concept of probability and pre-destination: The concept of pure chance is not absolutely true from a tauhidi perspective. All events are pre-destined by Allah who fixed the physical natural laws, sunan al llaah. The consistency and predictability of probability events (theoretical and empirical) is based on sunan. The consistency on which probabilities and predictions are based is because there are underlying sunan. The first creation was the pen that wrote down all what would happen (KS 449). The human's life, death, and all earthly endeavors are in the hands of Allah (KS 433). Even the fault of Adam and Hawa was part of pre-destination (KS 434). Pre-destination is involved in medicine; every disease has a cure (KS 338). Pathogenesis, therapy, and prevention of disease are all part of the same pre-destination
Objectivity: The Qur'anic term istiqamat refers to objectivity which is the opposite of bias. Istiqamat is required in everything including measurement (17:35, 26:182). Bias arises in speculation not based on facts, dhann or waham (4:157, 6:116, 6:148). Subjective probability may have an empirical basis being part of previous experience that has been distorted by time of other human weaknesses. Human reason, ra'ay, has good and bad aspects. It is condemned (KS 244) and even forbidden (KS 245) when it is a cause of deviation from objectivity. Theoretical probability has an empirical basis. The human intellect need not carry out an experiment to work out certain logical relationships and predict events.
Empirical evidence: The story of Ibrahim (2:260) illustrates the significance of evidence-based empirical knowledge. Ibrahim knew and believed from revealed knowledge that Allah resurrects the dead. He, however, asked Allah to show him how the dead were resurrected not out of weak faith but because being human be could understand and internalize knowledge that comes from empirical observation. Allah ordered him to carry out an experiment and to observe the phenomenon of resurrection for himself. Thus empirical knowledge extended and reaffirmed revealed knowledge.
EVENTS/TRIALS
Intentionality: Human actions are intentional but human will is limited. Divine will is not limited in any way. The term inshallah is one of the commonest heart from the lips of Muslims. Inshallah expresses the intention to do something and is a sort of probability statement that most likely the intention will be fulfilled. However a human does not full will; not all what humans want will happen. That is why a rider 'if God wishes' is used. Computation and interpretations of probabilities of human actions is based on the premise that human action is purposive and is not pure hazard. The Prophet taught that all human activity is considered according to its intention (KS p. 93). Any action that has no intention is considered void.
Prediction of the unseen ('ilm al ghaib): Probability can enable prediction of future events. This is based on empirical experience of past events and does not in any way pretend to reveal the unseen. Absolute knowledge of the unseen remains the prerogative of Allah alone. It is He alone who has Ilm al ghaib (2:216).
Sufficient number of trials: Two hadiths of the prophet indicate the importance of doing sufficient work or making enough trials before reaching any conclusions. The physical laws apply when a trial is repeated a sufficient number of time. They do not apply very accurately to one trial or a few trials. The first hadith is that all work is judged by its last stages, al a'amal bi al khawatim (KS p. 93). This indicates that a job must be followed through its conclusions before any judgments are made. The second hadith states that the best of work is what is constant even if little (KS p. 94) again emphasizing the importance of a sufficient period of performance or trial before reaching any conclusions.
Joint probability: The prophet taught that a hypocrite has three signs (KS 521): telling lies in conversation, cheating when trusted, and abusing when quarrelling. If a person has one of them he is not considered a hypocrite but is said to have a tendency to hypocrisy. However if a person has all of them then he is a true hypocrite. Thus the joint probability of three events is very low and is found in those few who are truly hypocrites.
Conditional probability: Conditionality, 'ilm al shurut, is a specialized sub-discipline of Islamic law. It helps the Muslim student understand and appreciate conditional probability. Ablution is a condition for validity of salat. Light is a condition for vision (2:17, 2:20). Each event has some conditions attached to it.
Mutually exclusive events: The Prophet said that no two religions will meet in the Arabian peninsular ie it is exclusively for Islam (KS 238). He also mentioned two characteristics can not be found in a hypocrite (KS 521). Attributes of Allah can nor co-exist with their opposites among human attributes. Thus the following attributes can not co-exist: knowledge, 'ilm & ignorance, jahal; ability, qudrat & failure, ajz; truth, haqq & falsehood, batil (2:42); good, khayr & bad, sharr (3:180).
Spatio-temporal considerations: Some times and places have a higher likelihood of some events than others. Friday is a special day. There is a special time on Friday when the likelihood of answering supplications is highest (KS 156). Answering of a supplication in Makka is more likely than any other place on earth.
DECISION-MAKING
Consultation: The prophet taught the importance and manner of istikharat (KS p. 75). The concept of istikharat in my mind is preparing the mind to consult its data-bank to built a more credible prior before making a major decision. This is facilitated by the calmness that follows ablution, prayer, and supplication to Allah for guidance in decision making.
Games of chance: Games of chance and gambling like maysar and qimaar (KS 96) were forbidden by Islamic law. They are not a reflection of true probability because as mentioned before the laws of sunan work on repeated trials and not on one trial. These games in addition involve material loss to others who can not control their greed and addiction. They also involve material gain for some without hard work.
Speculation: Islamic law forbids speculation in trade because it assumes probabilities that can not be predicted with any certainty and may lead to loss and suffering. Sale of unripe fruits on a tree is forbidden (KS p. 131) because it is impossible to know in advance what the produce will be. The problem with usury, riba, is fixing probability of profit in advance to the disadvantage of one party.
Divination and fortune-telling: The Prophet said that the fortune teller, munajjim, is a liar even if he guesses the truth. Fortune-telling was forbidden (KS p. 143) in all its forms including tatayyur (7:131, 27:47, 36:18-19).
A priori and a posteriori probability: Humans use prior probabilities more than they realize. Abubakr automatically believed the mission of Muhammad because of prior beliefs about his character and honesty. He believed Muhammad when others disbelieved (KS p. 52). The prophet also first called on the Quraish to believe him by invoking his character and credibility. Omar's opinions were later confirmed by the Qur'an (KS 397).
Statistical inference and the scientific method: statistical inference provides probability, as p-value, for truth of the null hypothesis. The conclusions of the statistical tests are relative since the perfect truth is unknowable. That is why we never talk of accepting any hypothesis the most that can be said is rejection or non-rejection of the hypothesis leaving open the possibility of different findings in future experiments. Thus all inferential conclusions are relativistic, akin to relativity of the good (nisbiyat al khayr 2:216). The aim is to get as near as possible to certainty, 'Ilm al yaqeen (2:260, 5:113, 20:135, 78:4-5) by repeated experimentation.
CERTAINTY and DOUBT:
Doubt: Doubt is the antithesis of certainty and knowledge. Because human knowledge can never be perfect, doubts always occur. The Qur'an has mentioned several cases of doubting. Ibrahim did ask Allah to show him the phenomenon of resurrection. This was not because Ibrahim doubted resurrection (KS p. 47) but was a reflection of the innate human intellectual desire to see empirical proof. Ibrahim's mind was settled, tama'ninat, after Allah showed him the empirical proof (2:260). Shaitan achieves him aim of confusing humans by creating doubts in their minds about certainties. Shaitan can even create doubt in the mind of the person praying about the number of prostrations completed (KS p. 49). It is forbidden to fast a doubtful day, yawm al shakk, at the start of Ramadhan (KS 252).
The gray areas and probability of truth: The allowed, halal, is clear and the forbidden, haram, is clear and between them are unclear things, shubuhaat (KS 201). Muslims are encouraged to avoid the doubtful things because their probability of being wrong is high.
Suspicion, suu al dhann: Any ideas or conclusions based on suspicions without facts are considered a sin and were severely condemned by the Qur'an (49:12). Suspicions arise when facts are known only partially and an extrapolation is made on the assumption of the probability that the partial facts represent the complete picture.
CONCLUSIONS
The paper has shown that it is possible to use Islamic concepts and examples in teaching probability.
References:
Holy Qur'an (verse and surat numbers indicated)
Iftaah Kunuuz al sunat (KS with the page number)
Kasule, Omar Hasan: The Nature of Knowledge. Paper presented at a workshop on Islamic Education. Capetown, South Africa. February 1999.
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