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		<title>The Weight of Our Assumptions About Others &#8211; 1</title>
		<link>https://fountainmagazine.com/all-issues/2020/issue-137-sep-oct-2020/the-weight-of-our-assumptions-about-others-1/</link>
		
		<dc:creator><![CDATA[Louima Cunningham]]></dc:creator>
		<pubDate>Tue, 01 Sep 2020 12:26:23 +0000</pubDate>
				<category><![CDATA[Issue 137 (Sep - Oct 2020)]]></category>
		<category><![CDATA[assumption]]></category>
		<category><![CDATA[Belief]]></category>
		<category><![CDATA[Questions & Answers]]></category>
		<category><![CDATA[shaming]]></category>
		<category><![CDATA[sin]]></category>
		<guid isPermaLink="false">http://107.21.79.195/all-issues/2020/issue-137-sep-oct-2020/the-weight-of-our-assumptions-about-others-1/</guid>

					<description><![CDATA[Question: While sayings of Prophet Muhammad, peace be upon him, counsel against condemning believers to shame, despising them, and disclosing their faults, they also enjoin not remaining silent and unresponsive before oppression and evil. How is a believer supposed to achieve this balance? Answer: In such a saying mentioned in the work of Tirmidhi, the [&#8230;]]]></description>
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<p><strong>Question: </strong>While sayings of Prophet Muhammad, peace be upon him, counsel against condemning believers to shame, despising them, and disclosing their faults, they also enjoin not remaining silent and unresponsive before oppression and evil. How is a believer supposed to achieve this balance?</p>
<p><strong>Answer: </strong>In such a saying mentioned in the work of Tirmidhi, the Messenger of God states, <em>“Whoever shames his brother for a sin will not die until he commits it also” (Tirmidhi, Sifatu’l Qiyamah, 53). Thus, he forbade shaming others and rebuking them and he pointed out what kind of a consequence awaits those who commit such a sin.</em></p>
<p><span id="more-5620"></span></p>
<h3>Not shaming anyone</h3>
<p>It is stated that a person who shames a fellow believer for an offense he did or did not commit will not die without committing it. Sometimes, this might yield a consequence as—God forbid—a problem related to the person’s spouse, daughter, son, or another next of kin. Namely, God Almighty may sometimes let that person receive the punishment of that wrong in person or sometimes by means of a family member. While people can mostly find a way out of the problems they are personally faced with, the problems their nearest relatives are faced with can overcome them.</p>
<p>Perhaps such recoil can serve as a blessing in disguise for that believer as hardship sometimes does. For example, it could bring about atonement for the person’s sin. Such distress and disgrace the person experienced in this world can serve as a means of deliverance from their relevant punishment in the next world. Namely, by forbearing a lighter form of punishment, the person can be saved from the heavier one. And sometimes, the sin committed in this world is so grave that worldly afflictions do not suffice for cleansing it. For example, considering a man who violated the rights of so many people, who threatened the safety of their lives and properties, who treated their decency like a plaything, and who is involved in the evils of unbelief, associating partners with God, and hypocrisy, the due punishment for all of these heavy wrongs he committed will only be given on the Day of Judgment.</p>
<p>We cannot surely know the Divine wisdom underlying behind what happens; God makes some suffer in this world and some in the next. If we do not wish to suffer such a disgrace neither in this world nor the next, believers being the first, we need to keep our tongue under control about others, and even revise our thoughts about them.</p>
<p>Here is evidence from the Prophet’s tradition: “Whoever can guarantee about what is between their two jaw-bones and what is between their two legs (i.e. if they protect the decency of their tongue and private parts), I guarantee Paradise for them” (Sahih al-Bukhari, Riqaq, 23). The tongue is very significant in this respect. It is easy to restrain it from the beginning. However, it becomes difficult to repair the destruction that it can cause when not controlled properly. To give a basic example, when a person shames another person on account of a wrong or sin, he needs to go and ask forgiveness from that person for having violated his rights.   </p>
<p>We should be very careful even while giving an account of a situation.  While opening a matter to discussion, we should speak so cautiously that nobody should be harmed or hurt by our words. Otherwise, if we start talking with remarks like “such-and-such person did so, that’s why such things happened to us&#8230;” and continue our discussion always with accusations and negative assumptions, we hurt many people, violate their rights unknowingly, and pass to the next world with a very heavy burden of sins.</p>
<p>Remember that the noble Prophet stated that a person who puts a fellow believer to shame on account of a sin he committed will be doomed to commit the same sin. Can you imagine the situation of those who revile others for misdeeds and sins they did not commit? Undoubtedly, defaming innocent people with lies and libel, and making them appear guilty by means of conspiracies and set-ups, are far graver sins in the sight of God. And if the people concerned are a wide group of people, rather than a single person, if the mud and marring target to besmirch an extensive movement and to make them lose esteem, then it is not so easy for those who commit these sins to be saved. Unless each member of the group concerned forgives the violation of their rights and gives the person their blessing about it, it is not possible for those who make these remarks to be cleansed of their sins. Therefore, it is unthinkable for real believers to engage in these plots that are typical of unbelief and hypocrisy.</p>
<p>As a believer shows serious concern about protecting their own esteem and honor, they have to show the same seriousness while others are concerned. They should not harm anybody, either via their hands or tongues. By purifying their minds from polluted thoughts, they should make having positive assumptions and views about people a part of their character. Technically, the Arabic word for a believer “mu’min” refers to a trustworthy person who does not harm anybody. A believer in the real sense of the word inspires such trust to those around them that nobody feels worried about being harmed by that person. Other people neither feel any relevant panic that stems from a real or apprehended reason, nor do they fear any betrayal when they turn their back against that person. They even know that even if they do some evil that the believer will not respond to them with the same evil because believers have certain limitations they will never transgress and essential principles that they will never violate.</p>
<h3>Avoidance from spying</h3>
<p>In the sayings we stated above, the Messenger of God banned shaming believers because of certain misdeeds and sins that they had committed. We must also point out that believers have no such responsibility in Islam to go out of their way in order to learn about the vices of others. On the contrary, the Qur’an definitely forbids this with the verse, “Do not spy on (one another)…” (Hujurat 49:12).</p>
<p>People who continually busy themselves with the faults and flaws of others will suffer a “pollution” of their character and a “deformation” of their nature after some time. Once their nature has gone corrupt, they will not be obsessed only with sinful people, but they will also begin to defame innocent people too. On the other hand, if a person adopts as a character trait the virtue of not denigrating even people corrupted with sins they will constantly keep glowing and will brighten up their surroundings even in situations while some mar the reputations of others.</p>
<p>Imam Hadimi makes the following remark in his work “Bariqa”: “Even if you see a believer in a very sinful condition, do not rush to make a judgment about him. Wipe your eyes and ask yourself whether you see correctly. … If you concluded that what you saw was real, then say, ‘O God! Save him from this ugly condition and save me from committing such a sin!’ and go away.”</p>
<p>Although Imam Hadimi wishes to remind us of an important truth with these words, in my opinion the best attitude for a person who comes across such a sin is to say, “Maybe I saw mistakenly,” turn away instantly, move away from there, and not mention what he saw to anyone. God did not assign us as prosecutors for spying into other’s sins.</p>
<p>It should not be forgotten that one of the Divine names is Sattar, which means “One who covers faults and sins.” It thus befalls a believer to adopt this virtue. The Messenger of God, Prophet Muhammad (pbuh), taught us that if a person covers the faults of a believer, God covers the faults of that person in this world and the next (see Sahih Muslim, Dhikr 38). Many things that will put us to shame might come up on the Day of Judgment. If we do not adopt this Divine conduct in this world, we might be put to shame in the next one. Namely, the shame with which we troubled others will come home to roost and trouble us in the next world. We should give up seeking, and exposing, the shameful sides of people. And when we do learn about them, let us not reveal them to others.</p>
<h3>Not scorning and not hurting anyone else</h3>
<p>In another saying, the Messenger of God taught us that, “It is enough of an evil (to bring perdition) for a person to hold his believing brother in contempt (and making their honor and esteem into a plaything). Namely, such an evil will make the person a loser in the next world” (Sahih Muslim, Birr 32). With the approach of Hazrati Ali, nobody should be scorned even if they subscribe to a different faith, belief system, or way of life. Some people may have certain negative attributes that we do not approve of such as unbelief, hypocrisy, and misguidance. In such a case, it is not becoming for a believer to target those people and attack them. On the contrary, what we need to do is endeavor to save those people from these evil attributes that we do not like because the Pride of Humanity (Prophet Muhammad (pbuh)) did not insult anybody throughout his life and did not hold anybody in contempt.</p>
<p>In the same way, a believer cannot revile somebody that has fallen or stumbled in a callous fashion. They cannot put the person in question to shame by speaking about their wrongdoings to others. Particularly, revealing their mistakes and sins over time in an exaggerated fashion is definitely not the attitude of a believer. What falls to a believer is respecting and protecting the reputation and honor of all other people as if they were their own. Additionally, the duty that falls to believers in the face of the misdeeds and sins of others includes trying to learn a lesson from their situation, helping them if they are able to, and imploring to God so that He does not let themselves fall into the same situation.</p>
<p>It does not befall a believer to shame or hurt a person even if they do it to them. This is not an excuse for us to act immorally. Even if they scorn us, we cannot scorn them back. Even if they shame us, we cannot shame them in return. And even if they hurt us, we cannot hurt them, for in our understanding hurting people is a stumble. Others’ hurting you is a stumble on their part. If you respond in the same way, you will have committed a stumble on your part. If you think that cursing, hurting, and rude attitude and behaviors are shameful, you should not repeat the same shameful behavior. In addition, you should not forget that showing patience in the face of other’s unjust blows, their laying shame on you, and besmirching you will act as atonement for your sins.</p>
<p>Ibrahim Hakki puts it nicely:</p>
<p><em>Do not hold anyone in contempt </em><em><br /> </em><em>Do not hurt anyone, don’t break a heart </em><em><br /> </em><em>Don&#8217;t side with your carnal side</em><em><br /> </em><em>Let us see what God will let come out<br /> Whatever He lets come out is good<br /> </em></p>
<p>Also, M. Lutfi Effendi says:</p>
<p><em>Pearls of wisdom offers the poet:</em><br /><em>&#8220;Do not be hurt,</em><br /><em> should someone hurt you.</em><br /><em> For, lesser in perfection </em><br /><em> is the one who is hurt </em><br /><em> than the one who hurts.”</em></p>
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		<title>Nasraddin Hodja&#8217;s Pot and Reductio Ad Absurdum</title>
		<link>https://fountainmagazine.com/all-issues/2014/issue-97-january-february-2014/nasraddin-hodjas-pot-and-reductio-ad-absurdum/</link>
		
		<dc:creator><![CDATA[Louima Cunningham]]></dc:creator>
		<pubDate>Wed, 01 Jan 2014 00:00:00 +0000</pubDate>
				<category><![CDATA[Issue 97 (January - February 2014)]]></category>
		<category><![CDATA[absurd]]></category>
		<category><![CDATA[absurdity]]></category>
		<category><![CDATA[absurdum]]></category>
		<category><![CDATA[assumption]]></category>
		<category><![CDATA[cephalus]]></category>
		<category><![CDATA[contradiction]]></category>
		<category><![CDATA[definition]]></category>
		<category><![CDATA[initial]]></category>
		<category><![CDATA[justice]]></category>
		<category><![CDATA[leads]]></category>
		<category><![CDATA[method]]></category>
		<category><![CDATA[Nasraddin Hodja]]></category>
		<category><![CDATA[neighbor]]></category>
		<category><![CDATA[person]]></category>
		<category><![CDATA[Perspectives]]></category>
		<category><![CDATA[pot]]></category>
		<category><![CDATA[proof]]></category>
		<category><![CDATA[reductio]]></category>
		<category><![CDATA[shows]]></category>
		<category><![CDATA[socratic]]></category>
		<category><![CDATA[Socratic Method]]></category>
		<category><![CDATA[unacceptable]]></category>
		<guid isPermaLink="false">http://107.21.79.195/all-issues/2014/issue-97-january-february-2014/nasraddin-hodjas-pot-and-reductio-ad-absurdum/</guid>

					<description><![CDATA[From a children’s tale to Socrates and the Qur’an, the need for logic and sound reasoning is universal. Nasraddin Hodja is a well-known folktale character in the Middle East. He is famous for his wit, which is apparent in the wisdom-filled stories that have been ascribed to him for eight centuries. Although Hodja was not [&#8230;]]]></description>
										<content:encoded><![CDATA[<blockquote>
<p><em>From a children’s tale to Socrates and the Qur’an, the need for logic and sound reasoning is universal.</em></p>
</blockquote>
<p>Nasraddin Hodja is a well-known folktale character in the Middle East. He is famous for his wit, which is apparent in the wisdom-filled stories that have been ascribed to him for eight centuries. Although Hodja was not a philosopher, many of his tales contain elements that demonstrate philosophical concepts and principles. As an example, the story of Hodja’s pot neatly exercises a fundamental philosophical method, i.e. the Socratic method or <em>reductio ad absurdum</em>. This story, though apparently simple and funny, has a deep philosophical dimension and teaches us the Socratic method in a very accessible way. The story goes as follows:</p>
<p>One day, Nasraddin Hodja borrowed a pot from his neighbor. After he had finished using it, he took it back to the neighbor with a smaller pot put inside it. When the neighbor saw the smaller pot, he was surprised. </p>
<p>“What is that?” he asked. </p>
<p>“Well, said  Hodja, when I borrowed your pot it was pregnant and it gave birth.” </p>
<p>The man smiled and accepted both pots.</p>
<p>A few days later, Hodja borrowed the pot again but this time he did not return it. The neighbor was rather cross. He went to Hodja and asked, “What about my pot?” </p>
<p>“I am very sorry,” said Hodja, “but it died.” </p>
<p>“Don&#8217;t make jokes with me,” replied the neighbor. “How can a pot die?” </p>
<p>“If you believe that it brought a child into the world,” said Hodja, “why can&#8217;t you believe that it died?”  </p>
<p>In this story, Nasraddin Hodja suggests that his neighbor’s behavior of accepting the smaller pot is improper, by indicating an absurd consequence of his behavior, namely that a pot can die if it can give birth. This method is commonly used in philosophical argumentation since the Ancient Greeks. We can see similar examples in Plato’s dialogues. For example, in the Republic, Cephalus defines justice as speaking the truth and paying the debt. However, Socrates shows that this definition logically leads to some absurd consequences. Let us assume that somebody lends us arms when his mind is right, but wants them back later when he lost his mind. According to Cephalus’ definition of justice, we should give the arms to that insane and crazy person since they are not ours but his. Yet, no one would approve such an act. Once Cephalus encounters this counterexample, he understands that his initial definition has some problems; he approves Socrates’ point and tries to modify his idea of justice. Thus, the dialogue continues. Different definitions are introduced and checked by this method.</p>
<p>We can display the logical structure of the Socratic method in the following way. In a conversation, somebody holds an assumption, and makes a definition or claims something. The other person shows that this assumption, definition, or claim leads to an absurdity. For this reason, this method is also called <em>reductio ad absurdum</em>, i.e. reducing to absurdity. Since the initial assumption leads to something unacceptable, it is unacceptable as well by logical inference. Then the person who held that assumption is forced to abandon or modify it. See Table 1 for a comparison of these examples.</p>
<h4>Table 1</h4>
<table>
<tbody>
<tr>
<td width="197">
<p><strong>Socratic Method</strong></p>
</td>
<td width="197">
<p><strong>Hodja’s example of pot</strong></p>
</td>
<td width="197">
<p><strong>Plato’s example of justice</strong></p>
</td>
</tr>
<tr>
<td width="197">
<p>X  holds an assumption.</p>
</td>
<td width="197">
<p>The neighbor accepts that a pot can give birth to another pot.</p>
</td>
<td width="197">
<p>Cephalus defines justice as speaking the truth and paying the debt.</p>
</td>
</tr>
<tr>
<td width="197">
<p>Y shows that X leads to an absurdity.</p>
</td>
<td width="197">
<p>Hodja shows that a pot can die on the basis of this assumption.</p>
</td>
<td width="197">
<p>Socrates shows a counterexample to this definition, which is absurd.</p>
</td>
</tr>
<tr>
<td width="197">
<p>Absurdities cannot be accepted.</p>
</td>
<td width="197">
<p>The neighbor admits the absurdity of the death of a pot.</p>
</td>
<td width="197">
<p>Counterexample: returning the arms to an insane person since they belong to him.</p>
</td>
</tr>
<tr>
<td width="197">
<p>Thus, assumptions that lead to absurdities are unacceptable.</p>
</td>
<td width="197">
<p>Hodja points out then that the neighbor’s initial claim is also absurd.</p>
</td>
<td width="197">
<p>Cephalus admits that this conclusion is unacceptable and abandons his initial definition.</p>
</td>
</tr>
</tbody>
</table>
<p>The Socratic method is one of the basic methods that we use in reasoning. We use it in daily life, in sciences, and in any area where we engage in rational thinking. The strictest kind of absurdity is a contradiction, i.e. accepting and denying the exactly same thing under the same conditions. Because of this, logicians and mathematicians call the Socratic method, “the indirect proof,” or “proof by contradiction.” See the appendix for an example of the proof by contradiction in mathematics.</p>
<p>Interestingly enough, we also see this method in the holy books. For example, the Qur’an frequently suggests people use their rationality and carefully think about the universe. It is remarkable that, in the Qur’an, we find arguments that rely on the <em>reductio ad absurdum</em> method. For example, let us consider the following verse: “But the fact is that had there been in the heavens and the earth any deities other than God, both (of those realms) would certainly have fallen into ruin. All-Glorified God is, the Lord of the Supreme Throne, in that He is absolutely above all that they attribute to Him” (21:22). This verse proposes that one must have observed disorder in the universe if that person associated partners with God’s activity in the universe. Since this is not what we observe, the initial assumption is incorrect. This example shows that the Qur’an addresses the rationality of human beings, and suggests actively using that faculty.</p>
<p>As we have seen, deriving absurd consequences from an assumption and denying it on the basis of those absurdities is a common and fundamental way of reasoning that is exercised in many different areas and aspects of human life. It is called by different names over history, namely “the Socratic method,” “reductio ad absurdum,” or “proof by contradiction.” Yet, the basic idea behind these technical terms is the same. Most of us probably exercise this method without thinking about it.</p>
<h3><strong>Appendix</strong></h3>
<p>Theorem: The number that is equal to itself, when added to itself, is zero.</p>
<p>Prove that for any x, x is a number; if x +x = x, then x=0.</p>
<ol>
<li>x+x=x (assumption for conditional/direct proof)</li>
<li>x is not equal to 0. (Assumption for indirect proof/<em>reductio ad absurdum</em>)</li>
<li>x+x=2x (by addition)</li>
<li>x=2x (since “x+x” is common for both the 1<sup>st</sup> and 3<sup>rd</sup> steps, by the principle of transitivity)</li>
<li>1=2 (cancel x’s) –Contradiction</li>
<li>x=0. (The assumption that leads to the contradiction in the 5<sup>th</sup> step must be false. Therefore, it is false that x is not equal to 0. Thus, x=0 is true.) Indirect proof is complete.</li>
<li>If x+x=x, then x=0. (Conditional proof is complete)</li>
</ol>
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		<title>Some Logical Principles in the Qur&#8217;an</title>
		<link>https://fountainmagazine.com/all-issues/2008/issue-65-september-october-2008/some-logical-principles-in-the-quran/</link>
		
		<dc:creator><![CDATA[Louima Cunningham]]></dc:creator>
		<pubDate>Mon, 01 Sep 2008 00:00:00 +0000</pubDate>
				<category><![CDATA[Issue 65 (September - October 2008)]]></category>
		<category><![CDATA[argument]]></category>
		<category><![CDATA[assumption]]></category>
		<category><![CDATA[conclusion]]></category>
		<category><![CDATA[false]]></category>
		<category><![CDATA[god]]></category>
		<category><![CDATA[hardy]]></category>
		<category><![CDATA[implication]]></category>
		<category><![CDATA[logical]]></category>
		<category><![CDATA[Perspectives]]></category>
		<category><![CDATA[premise]]></category>
		<category><![CDATA[prime]]></category>
		<category><![CDATA[primes]]></category>
		<category><![CDATA[principle]]></category>
		<category><![CDATA[proof]]></category>
		<category><![CDATA[qur’an]]></category>
		<category><![CDATA[statement]]></category>
		<category><![CDATA[statements]]></category>
		<category><![CDATA[true]]></category>
		<category><![CDATA[verse]]></category>
		<category><![CDATA[word]]></category>
		<guid isPermaLink="false">http://107.21.79.195/all-issues/2008/issue-65-september-october-2008/some-logical-principles-in-the-quran/</guid>

					<description><![CDATA[When we read the Qur’an, we notice that it appeals to human reasoning and invites us to reason. Among many verses in this regard, consider these: “How little you reflect” (A’raf 7:3), “God sets those who do not use their reason in a mire of uncleanness” (Yunus 10:100), “And in the alteration of night and [&#8230;]]]></description>
										<content:encoded><![CDATA[<p>When we read the Qur’an, we notice that it appeals to human reasoning and invites us to reason. Among many verses in this regard, consider these: “How little you reflect” (A’raf 7:3), “God sets those who do not use their reason in a mire of uncleanness” (Yunus 10:100), “And in the alteration of night and day, and in the provision (rain) God sends down from the sky and reviving thereby the earth after its death, and His turning about of the winds there are clear signs for a people who are able to reason” (Jathiya 45:5). “…We set out in detail the signs for people who will reason and understand” (Rum 30:28). According to the Qur’an, using reason is a necessary condition for humans to attain belief in God. One of the arguments disbelievers use to justify their rejection of tawhid (belief in the oneness of God) is that they found their ancestors worshipping idols. The Qur’an challenges this argument and invites them to think for themselves: “When he [Abraham] said to his father and his people: ‘What is it that you worship?’ they said, ‘We worship idols; and we are ever devoted to them.’ Abraham said: ‘Do they hear you when you invoke them? Or do they benefit you or harm you?’ They replied: ‘But we found our forefathers doing the same.’ Abraham said: ‘So, have you considered what you have been worshipping?’” (Shuara 26:70-75). Prophet Abraham, peace be upon him, is an example of a person who rejects his father’s beliefs when he realizes that what he was doing did not make any sense, and did not stand up against logical reasoning.</p>
<p><span id="more-941"></span></p>
<p>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.</p>
<p><b>Logical principle 1: </b> 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.</p>
<p>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 &amp;#8730; is not a rational number (Hardy, 1967).</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p><b> Logical principle 2: </b> 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 =&gt; 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.”</p>
<p>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.</p>
<p>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.</p>
<p><b>Logical principle 3: </b> 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.</p>
<p>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.</p>
<p><em>Nuh Aydin is an associate professor of Mathematics at Kenyon College, in Ohio, USA.</em></p>
<h3><b>Notes</b></h3>
<ol>
<li>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…</li>
</ol>
<h3><b>References</b></h3>
<ul>
<li>Hardy, G. H. A Mathematician’s Apology, Cambridge University Press, 1967.</li>
<li>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</li>
<li>Unal, Ali. The Qur’an with Annotated Interpretation in Modern English, The Light Inc., 2007.</li>
</ul>
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