Logical Theology

…considered thoughts and opinions

Archive for the month “August, 2012”

The Gambler’s Fallacy

When people gamble at a casino, they often make the mistake of assuming that some event is due to happen because of past events. Suppose that a coin is tossed 8 times, and all 8 times the coin lands tails. The probability of this occurring is 1/256 (one chance in 256 tosses). Ask yourself this question: if the coin is not fixed, is heads or tails more likely to come up?

The answer is that the odds of either heads or tails are 50/50.

The fact that the previous 8 tosses resulted in tails does not make it more likely that the next toss will be heads, assuming the coin is fair (having two different sides and equally weighted).  To think that heads is more likely to occur than tails is to commit the gambler’s fallacy.

In fact, if a coin is flipped 8 times, whatever combination of heads and tails comes up, the odds of that combination are still 1/256. It is true that if the coin is fair, the number of heads and tails will approach 50/50. However, the fact that heads came up 8 times in a row does not increase the odds of the next throw being tails. Thus, the gambler’s fallacy is committed when someone believes that after a number of lucky or unlucky events, the opposite outcome is more likely or due to occur. This overlooks the fact that there may be other factors which go into the situation. If an event is truly random, claiming that an unlikely event (good or bad, lucky or unlucky) will make a future event more likely is a fallacy.

Let’s consider the following examples:

Example 1:

Jack says, “I am going to win that 10 million-dollar lotto this month.”

Jill replies, “How do you know you will win?”

Jack responds, “Because I have been playing the lotto for twenty years straight.”

Jill replies, “You have been playing the lottery for over 20 years and have never won. Why would you be more likely to win this time?”

Jack responds, “Because after playing for so long, my odds of winning are much higher than they were in the past.”

What Jack fails to realize is that his odds of winning the lotto are exactly the same every time he plays. In essence, he believes that because he has been playing the lotto for twenty years, his chances of winning it this time are greater than those before. This is clearly not the case.  In reality, his chances of winning the lotto with a single ticket are just as small as they were every other time he played. The fact that he played for the last twenty years does not increase his chances in the present lottery.  Therefore, Jack has committed the gambler’s fallacy.

Gamblers commit this fallacy all the time. They assume that because the probabilities of something happening are low, they are going to place their bets against it happening. Thus, they assume that they are more likely to win a dice game because they have lost the previous six times. They might also assume that a roulette wheel will land on a different color because it has landed on red the previous dozen times. However, in thinking this, they have succumbed to the gambler’s fallacy. A throw of the dice is random. No matter how many times the dice are thrown, the fact that you lost six times does not increase the odds of having a favorable throw. No matter how many times the roulette wheel is spun, the odds of it landing on one color as opposed to the other are exactly the same for each spin. If it keeps landing on red, the logical conclusion is that the wheel is fixed, not that black is more likely.

Though the gambler’s fallacy gets its name from the gamblers who commit it, the gambler’s fallacy is not restricted to dice games and roulette. Many people in non-gambling situations can commit this fallacy as well.

Let’s consider another example.

Example 2:

Michael says, “I believe that the odds of the Mars rover landing on Mars are very good.”

Gloria says, “Why do you think that?”

Michael says, “Because we have lost the last 4 probes we sent there. Probability-wise, our odds are therefore greater that our mission will be successful.”

It may well be that the odds are better for this mission as opposed to the last one; however, this would be due to better science, technology, favorable conditions, and planning. While scientists can and do attempt to correct any errors and give their space missions the best chance of succeeding, if the odds of future Mars missions were increased, it would not be due to the fact that the last four missions were failures. The odds of success are not magically increased just because there have been numerous past failures. Unless technology improves, the odds for each mission’s success are exactly the same or nearly so. The fact that the last four probes were lost is not a factor in how likely it is that the current mission will succeed.

Consider one final example.

Example 3:

Jennifer says, “I do not think that you need to worry about purchasing that car.”

Florence responds, “Why not? I heard from five of my friends who bought past cars from the same company that their radiators overheated.”

Jennifer replies, “That is my point. After those failed car designs, the company is surely going to produce a good car.”

No, that is not necessarily the case. It may well be that the company has fixed the design flaws of their past car models. However, after manufacturing faulty car designs, Jennifer should insist on being given proof that the company’s current car design is not flawed.  Florence’s suggestion that because of past failures, the company is due to produce a good car design is an example of the gambler’s fallacy. The fact that the company has failed in the past does not automatically mean that are going to succeed now.

The Bottom Line: Believing that repeated lucky or unlucky events make the opposite event more likely to occur is a logical fallacy.

Straw Man Fallacy Part 2


Let us now consider how the straw man fallacy can be committed within Christian dialogue. Consider the following examples:


Example 1:

Keith says, “Personally, as a four-point Calvinist, I believe that Calvinism offers the best explanation of why people do not accept Jesus.”

Marilyn responds, “I disagree. I don’t see how anyone could possibly believe people do not have free will and are just robots under the command of God, and yet also believe that God is righteous in predetermining people to go to hell.”

Marilyn is essentially arguing that it seems very difficult to reconcile the belief that people do not have free will with the belief that God is just in choosing who will be saved and who will be damned.  While this is a real problem for those who hold both views, and those who believe these views need to offer a response to this criticism, Marilyn has not demonstrated that this is in fact what Keith believes. Modern Calvinists do not all agree on the same beliefs. There are many different groups within Calvinism, and they do not all agree on everything. Though Keith should have been clearer about his beliefs, unless Marilyn can demonstrate that her comments accurately reflect Keith’s beliefs, she has committed the straw man fallacy.  Marilyn should have asked Keith to more clearly explain his beliefs before she judged them. Had she given him an opportunity to elaborate on his statement, she would have been able to offer a better response to Keith’s beliefs.

Example 2:

Nate says, “In my opinion, Church X is overly concerned with secondary issues. They are right to hold some beliefs strongly, but I believe they are wrong not to allow any dissent on a great number of minor issues.”

Bob replies, “I disagree. Church X is right to take a strong stand against those who hold wrong beliefs.  People need to be taught the truth and not allowed to spread falsehoods.”

Taking a strong stand against the teaching of falsehood and insisting that people are taught the truth is a good thing. However, while what Bob said is true, he did not address Nate’s position. Nate was arguing that Church X was overly “concerned with secondary issues” and needed to allow people to hold different views on subjects which are not essential beliefs.  Nate even said that he felt it is right to hold some beliefs strongly.  Bob ignored Nate’s position, and decided to talk about taking a strong stand against the teaching of falsehoods, implying that everything Church X teaches is an essential doctrine.  But even if he could demonstrate this, which he did not, he would not have offered a proper response to Nate’s argument. Nate was talking about non-essential beliefs, not those beliefs which are essential to the Church.  Arguing that all of the church’s beliefs are essential does not refute the argument that there needs to be room for dissent and disagreement over secondary issues.  Since Bob said he disagreed with Nate’s position, he needs to provide a response to it. Instead of properly responding to Nate, Bob only set up and knocked down a straw man.

THE BOTTOM LINE: While straw man arguments can adequately refute the position they actually address, using them against an argument they do not refute is a logical fallacy.


Straw Man Fallacy

When someone is engaged in a debate with another person, it is important for both to fairly represent each other’s positions. When an opponent’s position is misrepresented and then rejected, the straw man fallacy has been committed.  This fallacy gets its name from the fact that just as a straw man is easier to knock down than a real human, a misrepresented argument is easier to reject than a strong argument. This fallacy can be committed in a variety of ways, including distorting an opponent’s argument and quoting someone out of context.  However the fallacy is committed, it essentially involves substituting a weaker argument in place of the initial argument, refuting the weaker argument, and then concluding that the initial argument has been refuted.  The reality is that only the weaker, distorted argument was refuted.  Consider the following examples:

Example 1: 

Rebecca says, “I think our current tax system is messed up and needs to be changed. The current system is supposed to require the wealthy to pay more in taxes than the poor.  However, the ultra rich have ways to get around these laws, and as a result, they can avoid paying higher taxes.  So in reality, our tax system is one in which both the ultra rich and the poor pay low taxes while the middle class is heavily taxed.  Because of this, I think we need a better tax system.”

Sarah responds, “How can you say that?!!  Any alternative taxation method will cause the poor to suffer a much higher tax rate.”

There are multiple fallacies in Sarah’s response, but for now let’s just address the straw man fallacy.  Rebecca was not arguing that the current tax system needs to be jettisoned and replaced with a different tax system.  All that Rebecca was arguing was that the current tax system had serious problems and needed to be changed. By using the phrase “alternative taxation method” Sarah has distorted Rebecca’s argument and set up a straw man. What if Rebecca actually favored taxing the wealthy more than the poor, and wanted the current tax system to be changed so that the ultra rich couldn’t escape having to pay taxes and the middle class ended up paying less?

Example 2:

Robert says, “I think that we should legalize marijuana and heavily regulate and tax it like alcohol and tobacco.” 

Kyle says, “Yes I agree, let’s legalize dangerous drugs, give people easy access to them, allow the criminals to win and drugs to proliferate through our society, as they surely will if pot is legalized.”

As with Example 1, there are multiple mistakes in logic here, which is to be expected when dealing with straw man fallacies.  In fact, there are two straw man fallacies in Kyle’s response.

First, the straw man fallacy is committed by Kyle using the phrase “dangerous drugs.” This distorts and rewords Roberts’s argument that marijuana should be legalized, taxed, and regulated, so that it is easier to refute. It is illogical because Robert was only talking about legalizing marijuana, not all drugs. In addition, Kyle has misrepresented Roberts argument by stating that legalizing marijuana would “give people easy access to them.”  However, Robert was arguing for the opposite – that marijuana should be heavily regulated.

To better see why Kyle’s statement is fallacious, let us change the example in the following way:

Robert says, “I think that we should legalize alcohol and end prohibition. Alcohol should not be illegal. Rather, it should be heavily taxed and regulated, like tobacco.”

Kyle says, “Yes I agree, let’s legalize this dangerous substance, allow criminals like Al Capone to win, and allow alcohol to proliferate through our society and lead to moral decline.”

In this case, the straw man would be committed by labeling alcohol a “dangerous substance”, thus distorting and rewording Roberts’s argument and making it easier to reject. After all, it is more difficult to defend legalizing a “dangerous substance” than legalizing alcohol.

Example 3:

Gloria says, “I personally think that people should not be required to get marriage licenses. A license is a permission slip to do something. Why should people have to get the government’s permission to marry whomever they wish? Marriage is a natural right that all human beings share. Our government used to prohibit inter-racial marriages. Wouldn’t it be better for people to have the freedom to marry whomever they want without governmental interference?”

Jason says, “That is a ridiculous idea!!! If the government was not involved in marriage, priests could refuse to marry people of other religions and lifestyles. We need the government’s involvement to prevent that from happening.”

Jason has distorted Gloria’s position from people not being required to get marriage licenses to the government not being involved in marriage at all.  Gloria didn’t say anything about the government not having anything to do with marriage whatsoever.  She was only arguing that people should not need the government’s permission in order to marry, because in her opinion, marriage is a natural right and also because past governments have abused their authority over marriage. She was not arguing that governments should not have anything to do with marriage, such as having different tax laws concerning married couples. Therefore, Jason has committed the straw man fallacy.

In addition, one wonders whether Jason is fully aware of the implications of his statement. He essentially said that the government should be able to force priests to marry people, even if it is against their moral beliefs. While many would agree that it would be wrong for a priest to refuse to marry a Buddhist couple, would they say the same thing about a priest refusing to marry an adult to a child? Should the government be able to force priests and pastors to marry adults to children? I think not. So then, perhaps it would be wiser to not give the government such power.

Keep in mind that straw man fallacies can be committed unintentionally. Many times people are not even aware that they are committing the straw man fallacy. This can be caused by people using an argument that they heard someone else use, without critically evaluating the argument. 

The bottom line:

We need to be discerning and critically evaluate the arguments that we and others make, so that we can avoid this common fallacy.


Tu Quoque Fallacy Part 2

Let us now look at a few examples of how the Tu Quoque fallacy can be committed within Christian dialogue:

Example 1: 

Michael says, “Mr. Smith claims that he is not an Anglican, nor does he wish to become one, for he does not agree with Anglican doctrine.  But wait a minute!  Didn’t Mr. Smith give a substantial donation to an Anglican church last year?  So he disagrees with Anglican doctrine and yet hypocritically supports an Anglican church with his finances. He certainly is inconsistent.”

While it may seem that Mr. Smith’s actions are hypocritical, the fact that a year has gone by since he donated the money to the church gives him more than enough time to change his mind. Even if he really did believe in Anglican doctrine a year ago, the fact that he has since changed his mind does not make him hypocritical.  However, let us suppose that he has always disagreed with Anglican doctrine, even when he supported the church with his finances. Would that make him a hypocrite?  Perhaps, but not necessarily.  If Mr. Smith gave his money to the church because the church was taking the money and using it to help people, such as feeding the poor and homeless and/or helping people get free from drug addiction, then he was not necessarily agreeing with the church’s doctrine.  He was simply supporting a good work.

Example 2: 

Jill says, “You should not go to my church because what they teach is wrong.  They are very dogmatic and rude towards those who disagree with them.”

Jennifer replies, “How can you say that??! You have been going to that church for 20 years and you still attend.” 

By Jill’s suggestion that Jennifer avoid the church which she herself still attends, it is tempting to conclude that Jill is being hypocritical. However, this may not necessarily be the case.  Perhaps Jill attends the church, not because she agrees with their doctrine, but because all her family and friends go there. She may in fact disagree with the church’s doctrine, but not want to sever her family relationships. While we may believe that she should still find a new church more in line with the doctrine she accepts, the fact that she continues to attend the church does not necessarily make her hypocritical.  In addition, even if she was being hypocritical, that alone does not make her statements about the church’s doctrine and atmosphere false.

Example 3: 

Stephen says, “I just finished listening to a lecture by professor Little. It is his opinion that the doctrine of the Trinity is mistaken.  I felt he has some good arguments to support his conclusions. What do you think about his beliefs?

Jason replies, “Professor Little is a serial adulterer who has been married four times and is not even married to the two women he lives with currently. Therefore, I reject his belief that trinitarianism is mistaken.”

While most would agree that it is not good that Professor Little has behaved the way he has, his personal misdeeds and failings have no bearing on whether his argument is true or false. If Jason is going to reject professor Little’s arguments, he must do so with good arguments of his own.  Rejecting professor Little’s position due to his personal faults is committing the Tu Quoque fallacy.

The Bottom Line:  Hypocrisy and inconsistency do not automatically negate an argument someone is making.  To assert that it does is a logical fallacy.

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