First, we should emphasize that Prof. Zewail’s statements resonate very well with what famous scholar Ibn-al Haytham said 10 centuries ago:

“The seeker after truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. Thus the job of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.”

Every human being is given the ability to think. That is what makes all the progress of humanity possible. When we think we process the information we receive based on what we already know and we usually make judgments. Nobody can deny that all humans go through this process many times every day. But we can question the outcome of our thinking process, that is, our judgments. Many times, we can be wrong in our judgments, and this is where “critical” thinking might help.

Today, most people learn how to think systematically at schools, particularly during university education. In fact, according to Derek Bok, the former president of Harvard University, faculty members in the US almost unanimously agree that “teaching critical thinking” is the principal aim for undergraduate education. Although many have great conviction that critical thinking is very important, there is no universal definition for it. The American Philosophical Association gives the following definition:

“Purposeful, self-regulatory judgment which results in interpretation, analysis, evaluation and inference as well as explanation of the evidential, conceptual and methodological considerations on which a judgment is based.”

Based on this definition and what we quoted from Ibn-al Haytham, we can identify the following points about critical thinking:

1) When you read or hear a statement, do not accept it without question.

2) Try to find other information that can support or disprove the statement, try to come up with ways to demonstrate validity or falsehood of the statement, and test the statement.

3) As you perform your critical examination, be aware of your own deficiencies as a human. Consider your own biases, numerous possibilities of making mistakes in your judgments, or prejudices you can assume without knowing.

4) Be aware of the method you use for evaluating a claim, and think about both its strengths and weaknesses.

Critical thinking, if we develop the habit of performing it, can help us every day. Consider how you receive information in the twenty-first century. Typically, you read a newspaper or watch news on TV. If you just accept what you hear and see, then you can sometimes be manipulated or fooled. In an ideal world we can assume that objective presentation of news is possible. In the real world, however, those who transfer news bits to the population are also humans who are prone to similar biases. Many times a newspaper or a TV station represents certain values, ideologies, or supports some political positions. Besides, news reporting is so much commercialized that news editors and reporters also think about how to attract readers, and might use catchy words deliberately. Therefore, everyone should ask questions, clarify certain interpretations, and need to fight their own biases before reaching conclusions whenever they encounter a media report. An increased number of critical thinkers will help create a healthy debate about controversial issues.

We can expand this critical approach with respect to news media to our formal education experiences. At schools, our teachers deliver new information every day. We also read our textbooks. Typical student tendency might be to just accept what they hear and what they read, though this may depend on the student’s intellectual development and the culture of the society. If we perform critical thinking in the classroom and while reading textbooks, we can grow intellectually much more than otherwise. We can retain what we learn more easily. In addition, the purpose of schools and universities is to prepare us for life. We all know that in real life problems are never well defined, and most of the time you cannot readily find an authoritative figure or a manual to consult. Therefore, it is imperative that we teach students to question what they hear and what they read. In order to encourage students to perform more critical thinking in the classroom, however, we might need to find alternative modes of teaching and move away from conventional method of active teacher – passive students.

Although we must strive to teach critical thinking, we should also recognize the fact that there are roughly three distinct phases in our lives with respect to thinking, and not everyone is in the same phase at a given time. When we are young we usually think that every question has a certain answer, and it is just a matter of finding the authority who can give that answer. As we grow up, however, we realize that sometimes many authoritative figures may disagree. This observation may make one a relativist; that is, we might start thinking that depending on who you ask the answer varies, and it is all relative. As we further grow in our intellectual development, we usually notice that although people disagree on certain topics, we should always make some decisions, and some points of view have more support than others. By performing critical thinking we can filter out less reliable information, and come to better conclusions. In some complex cases, however, we might realize that there is no single correct judgment, and circumstances might lead us down different paths.

In the context of these three different phases, we can safely claim that on the average you expect the ability to think critically improve, as we get older. Elementary school children are most likely to think that there is a correct answer to every question. In middle and high school, many students will realize that there may be different answers to the same question depending on whom you ask. By the time of their graduation we expect university students to learn how to critically evaluate information. This final outcome, though very significant for a healthy society, highly depends on our teaching strategies. That is, if rote memorization is more valued than critical evaluation, then university graduates might stay as naive relativists or even worse.

Critical thinking is extremely crucial to separate the truth from myth. A well known example is about our brains. In many societies, it is said that people typically use about 10% of their brain, and geniuses like Einstein are able to use more of their brains. Some questions to ask are as follows:

1) What does it mean to use 10% of the brain?

2) Who provides this information? Is s/he a neuroscientist?

3) How do people measure brain usage?

4) Einstein lived long time ago. Did they measure his brain activity the same way as the control group to conclude that he used more of his brain?

When we search for answers to these questions, we typically find that there is no basis for this claim. It does not mean much. Maybe the statement originally meant that many do not use their brain’s full potential, which might be true. But, when the statement is compared to what we know about brain science, then it becomes a myth.

While everyone and every profession benefits from critical thinking, some jobs require critical thinking more than others. Scientists, for example, have an obligation to be extremely critical of others’ work. Let us remember that Ahmad Zewail and Ibn-al Haytham are both scientists. In science, there is a process called “peer review,” which is extremely useful. Any research carried out becomes scientific knowledge after it is submitted to the critical reviews of other scientists in the field. Any contribution submitted to a scientific journal is tested for correctness and originality. At the end of the critical review, the reviewers submit a report to the editors of the journal, who then make a decision. Many times the authors of the article are asked questions or are asked to make modifications, to which they may respond. In short, we can safely state that a scientist must be a critical thinker, or otherwise s/he cannot perform his or her research duties, and s/he is prone to become a repeater of someone else’s ideas, and may go awry at times.

From what we explained so far, it is probably obvious that we need some background knowledge about a subject in order to become a real critical thinker. It is clear that if someone knows nothing about urban planning, for example, it is very hard for him to critically examine any work on urban planning. This straightforward observation suggests that most people cannot be critical thinkers even if they want to be. Fortunately, this conclusion is only partially true because critical thinking is not a single discrete outcome but rather a continuum. Although knowledge of a topic makes us better thinkers in a field, there are always some minimal questions one can ask. For example, there is a controversial topic and someone makes some crucial statements about it. Even if you don’t know about the topic, you can ask whether the speaker is an expert on the topic or not. Or you can ask about what kind of evidence he is using. Does the evidence presented come from a reliable source? Why may this person take this side of the argument, but not other alternatives? Are there any other alternative approaches to the same issue? That is, at minimum, the answers to these questions can help us develop sound judgment.

A great case in which many feel lost is the global warming debate. By doing a simple web search on global warming you can find articles both supporting and denying human-caused global warming. But which point of view should you believe? Although there is consensus that global warming is happening, there is disagreement about whether it is caused by our technological conveniences, or whether it is just a result of natural temperature fluctuations in geological time scales (hundreds of thousands of years).

Indeed, the question “which point of view should you believe?” may not be the correct question. Instead, perhaps we should ask why people feverishly debate about this issue. Why do people care a lot about various aspects of global warming and atmospheric science research? A little investigation shows that there is a lot at stake. Accepting that excessive use of energy by humans, which leads to increase in carbon dioxide levels in the atmosphere, causes global warming has many economic, political, and social consequences. If you agree that man-made global warming can trigger many other events which can eventually make the climate on the Earth fall off-balance, then it follows that many people in the world must change their lifestyles, and this may also mean that some big companies must make changes which may hurt their profits, or that some governments might not use certain political leverage in international relations.

Obviously, it will not be easy to accept such findings, even if they come from some prominent scientists. There are, in fact, scientists on both sides of the aisle. This is because atmospheric science is extremely complex, and even with our best computers modeling the changes in the atmosphere it remains a very hard task. Further investigation also shows that there are different types of evidence people use. Some point to reports prepared with sponsorship from some governments or companies. Some expand on disagreements among scientists, and conclude that no action is needed until all the claims are proven. As we mention above, there are also scientific articles published in “peer-reviewed” journals. The Intergovernmental Panel on Climate Change (IPCC) puts out consensus statements. In short, it is a complex issue, and the credibility of evidence varies. We leave further investigation on climate change to practice critical thinking to the interested reader.

Critical thinking requires effort, sometimes a lot of effort. Lazy personalities and those who do not like to engage their mental abilities are less likely to perform critical thinking. In this regard, critical thinking is also very different from rote criticism. Rote criticism does not require much effort; typically the statements of the person performing the critique do not have a sound basis. While critical thinking is necessary for a healthy society to clarify especially certain controversial topics, mere criticism of one another can be a means to create unnecessary enmity among individuals.

Critical thinking does not mean that we need to become a skeptic and reject everything. In fact, descriptions of critical thinking involve paying special attention to certain criteria and standards. In practice, if one does not have any reference it becomes very hard to move forward in thought. What needs to be emphasized is that the world is not black and white. It displays a vast variety of colors. We can give more weight to certain colors than to others. What we cannot claim is that there is a single color, and all others are false. We can certainly have certain beliefs, paradigms, and values. These may become the basis for some of the criteria and standards against which we evaluate new information. At times, great events and findings might force us to evaluate certain paradigms we take for granted, too. However, such sharp turns do not happen frequently in the life of an individual or society.

In conclusion, critical thinking skills are essential for everybody. We should be aware of our own shortcomings, biases, prejudgments, as well as the sources, agendas, worldviews, paradigms and the information channels we use when we process new information. Critical thinking cannot be done instantly; it requires effort and courage to come face-to-face with one’s own errors. Teaching critical thinking is not instant, either. Formal and informal education institutions must strive to develop critical thinking skills in students, and such an endeavor might require modification of our approach to teaching. In the final evaluation, it is extremely crucial that we take the necessary steps to increase the number of critical thinkers in the world for the benefit of all humankind.

Dr. Ertan Salik is an Assistant Prof. of Physics at California State Polytechnic Univ, Pomona. As well as teaching and conducting physics research Dr. Salik is currently involved in many education programs.

Notes

1. The Fountain magazine, interview with Ahmad Zewail by Nuh Gedik, Jan-Feb 2009, issue 67.
2. Steffens, Bradley. Ibn-al Haytham: First Scientist, Morgan Reynolds Publishing. Also see Book Review in The Fountain Magazine, issue 63, May-June 2008.
3. Bok, Derek. Our Underachieving Colleges, Princeton Univ Press, 2006.
4. Critical Thinking: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction, American Philosophical Association Report, 1990.
5. IPCC consensus statements can be downloaded from http://www.ipcc.ch/.

Given the emphasis by the Qur’an on logical reasoning, it is understood that its audience (all of mankind) is expected to have a basic understanding of logical principles. It is our purpose in this article to go over a few basic principles of logic and give examples of how they are used in the Qur’an.

Logical principle 1: Proof by contradiction. An important aspect of logic concerns methods of proving or disproving statements. This is one of the basic principles of proving statements, and it is commonly used to prove mathematical statements. To show that a statement is true using this principle, suppose its negation is true, that is, that the statement itself is false. If you can then obtain a contradiction, something that is clearly false, this shows that the original statement is true. We shall illustrate this principle with an example. The reason we choose this example is that it is a classical result in mathematics, and the argument is beautiful. According to Hardy, this is an example of a first-class theorem about a significant mathematical fact (“a real mathematical theorem”) that is accessible to a general, educated audience (Hardy, 1967). There is a fundamental theorem in number theory which says that “there are infinitely many prime numbers.”1 There are many other proofs of this theorem but the most elementary and elegant proof is given by Euclid and it is by contradiction. Hardy claims that “both the statement and the proof can be mastered in an hour by an intelligent reader, however slender his mathematical equipment” (Hardy, 1967). Here is that proof: Suppose there is only a finite number of primes. Call them p1 , p2 , … pn. Now, consider the number N = p1 , p2 , … pn +1. Clearly, N is not equal to any of the primes in the list. Therefore, N itself is not a prime, and hence N must be divisible by one of the primes p1 , p2 , … pn (this is by “the fundamental theorem of arithmetic” which states that every integer greater than 1 can be written as a product of prime numbers). However, that is not the case: when N is divided by each one of pi there is a remainder of 1. This is a contradiction, and it arises from the assumption that there are only finitely many primes. Hence, the assumption cannot be true, and we conclude that there are infinitely many primes.

Proof by contradiction, or reductio ad absurdum in Latin, is one of the mathematician’s finest tools. There are many examples of theorems in mathematics where the simplest proof is by reductio ad absurdum. Another classical example is to show that √ is not a rational number (Hardy, 1967).

Now, we would like to give examples from the Qur’an where this logical principle is used. Consider the verse: “Had there been in the heavens and the earth any deities other than God, both would certainly fallen into ruin” (Anbiya 21:22). Here the argument is: suppose there were gods other than God. Then the earth and the heaven could not maintain their order (because the powers and wills of different gods would interfere with each other). Since this is clearly not the case (because we see perfect order in the universe), this contradicts the logical consequence of the initial assumption. Therefore, the initial assumption (i.e., there are more than one god) is wrong.

For another example, let us consider the verse: “Do they not contemplate the Qur’an? Had it been from any other than God, they would surely have found in it much inconsistency” (Nisa 4:82). Here the statement to be proven is “The Qur’an is the word of God, and it is from God.” To prove this statement by reductio ad absurdum, suppose for a moment the opposite statement is true, that is, that the Qur’an is not from God. A logical consequence of this assumption would be it is the word of a human being, but then there would be inconsistencies in it because the Qur’an talks about such great matters that if a human being had written it he would have made mistakes and inconsistent statements (for more on this point see Unal, 2007, page 228, and Nursi). However, we see no such statements in the Qur’an, thus contradicting the initial assumption. Therefore the Qur’an is the word of God.

The final example we would like to give related to this principle is expressed in the verse: “If you are in doubt about the Divine authorship of what We have sent down our servant (Muhammad) then produce just a sura (chapter) like it and call for help to all your supporters” (Baqara 2:23). Here the statement to be proven is the same as the one in the previous example. The argument goes like this: If it was possible for anybody other than God to produce the Qur’an, you should be able to make something like it with all of your supporters, if not an entire book, just a chapter of it. The Qur’an presents disbelievers with a challenge. However, they have not been able to meet the challenge. They chose to fight with the sword because fighting with words was not possible. Therefore the assumption that “the Qur’an could have been written by a human” is wrong.

Logical principle 2: The next principle we would like to discuss is the equivalence of an implication to its contrapositive. A statement of the form “If P, then Q” is called an implication. In such an implication P is called the premise, or the hypothesis and Q is called the conclusion. Such a statement asserts that whenever P is true (or satisfied) then Q is guaranteed to be true. However, if/when P is not true, it does not say anything about the truth value of Q. An example of an implication from daily life is: “If it is rainy, then it is cloudy.” Here the premise is “it is rainy” and the conclusion is “it is cloudy.” Another example would be: “If you are in New York City, then you are in the US.” A mathematical example is: “if a number n is divisible by 6, then it is even.” An implication can also be read as “P implies Q,” or written “P => Q.” The contrapositive of an implication “if P then Q” is “if not Q then not P.” For example, the contrapositive of the first implication above is “if it is not cloudy then it is not rainy,” of the second one, “if you are not in the US, then you are not in NY city,” and of the third one, “if n is odd (not even) then n is not divisible by 6.”

Here are two examples from the Qur’an where we can apply this principle. The first one is the verse we discussed above: “If you are in doubt about the Divine authorship of what We have sent down our servant (Muhammad) then produce just a sura like it and call for help to all your supporters.” We can rephrase this statement as “if the Qur’an is not the word of God, then humans can produce a like of it,” and its contrapositive is “if humans cannot produce something similar to the Qur’an, then it is the word of God.” Remember that these two statements are logically equivalent. Now, we know that humans cannot produce anything comparable to the Qur’an despite much effort and motivation, therefore it follows that it is the word of God.

The second example we want to consider is the verse: “Say (to them, O Messenger) if you indeed love God, then follow me, so that God will love you and forgive your sins” (Al Imran 3:31). The contrapositive of this statement can be stated as (slightly simplified) “if you are not following his messenger, then you really do not love God.” So, we obtain a clear measure of whether one really loves God or not. Following the Prophet is a necessary condition to attain the love of God.

Logical principle 3: The final principle we discuss is false implies anything. This is actually a special case of an implication of the form “P implies Q.” Recall that such a statement asserts that whenever P is true, Q is also true, so P promises Q. However, if P is not true then it does not claim anything about Q; it may or may not be true. For example, if it is not rainy then it may or may not be cloudy. An implication is false when P is true yet Q is false. Intuitively, we can think of this as breaking a promise. The question arises as to what the truth value of an implication should be when the premise P is false. It is accepted that the implication will be true in this case, because when the premise is false, the conclusion is totally irrelevant. This is called “false implies anything.” One can make any conclusion whatsoever based on a false premise, but it really does not mean anything. For example, the statements “if 2+2=5, then there are only finitely many primes,” and “if the world is flat, then there are no wars in the world” are both true statements. These statements are true but they really do not have any substance. They are true by a convention in logic. The important point one needs to pay attention to is this: Once you believe a premise that is not true, it is possible to make any conclusion you want and the whole argument looks right. However, such an argument is quite meaningless. So one needs to examine very carefully what is being assumed in a logical argument.

One example we want to consider from the Qur’an related to this principle is the verse: “Those who deny Our Revelations and turn arrogantly from them-for them, the gates of Heaven will not be opened and they will not enter Paradise unless a camel can pass through the eye of a needle” (A’raf 7:40). With a little simplification, we can rephrase this verse as “if a camel passes through the eye of a needle, then disbelievers will enter Paradise.” Since the premise is false (obviously, a camel cannot pass through the eye of a needle), this implication is true. However, this is not good news for disbelievers because the truth of this implication has nothing to do with the truth of its conclusion. This again shows the point: One needs to examine logical arguments carefully. What looks true or convincing formally and on the surface may not mean anything in reality if it is based on a false premise.

Nuh Aydin is an associate professor of Mathematics at Kenyon College, in Ohio, USA.

Notes

1. A positive integer n that is greater than 1 is called a prime if its only positive divisors are 1 and n. 1 is not considered to be a prime. Thus the sequence of prime numbers is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29…

References

• Hardy, G. H. A Mathematician’s Apology, Cambridge University Press, 1967.
• Nursi, Bediuzzaman Said. The Words (translation), The Twenty-Fifth Word, Available online at http://en.nurglobal.net/modules/mastop_publish/?tac=The_Twenty-Fifth_Word
• Unal, Ali. The Qur’an with Annotated Interpretation in Modern English, The Light Inc., 2007.