Logical Theology

…considered thoughts and opinions

Archive for the category “Critical Thinking”

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.


Openness Part 2

Now that we understand the importance of being teachable, let us consider how this works within Christianity. Should Christians be open to changing their minds?

My answer is absolutely yes.

Keep in mind that no one Christian or Christian denomination has perfect doctrine in every area. Even the Apostle Paul said that “all our knowledge is fragmentary” and “I know in part” (1 Corinthians 13:9, 12). In light of this, it follows that Christians could believe things that are mistaken.  Therefore they should be open to considering the opinions of others and accepting them if they can be proven true.

This should not come as a shock, because theology itself is a human endeavor to properly interpret the Bible.  Since humans make mistakes, it follows that Christian beliefs and doctrines can also be mistaken. Because of this, Christians should willingly subject their beliefs to scrutiny and testing, and accept that which can stand up under testing (1 Thessalonians 5:21).

Unfortunately, not everyone is willing to do this. Consider the following two examples:

Example 1: 

Robert says, “Personally, I believe that suffering can in fact be beneficial and that the more recent Christian interpretations on suffering are mistaken.” 

Rachel responds, “I have read many books from many authors defending your position, and all their arguments have been exhaustively refuted. In addition, this position would seem to imply many negative things about the character of God. Therefore, I am not interested in hearing another defense of your position.”

There are multiple problems with Rachel’s statement. First, she wrongly assumes that Robert can not add anything new to the discussion because of the fact that (in her opinion) many authors have not succeeded in defending Robert’s position. She is also committing the appeal to consequences fallacy, which is committed when someone assumes that the positive or negative consequences of a belief render it true or false.  In this case, Rachel is saying that Robert’s position is false because, if it were true, it would imply that God possess negative characteristics. This is a fallacy because simply stating that negative consequences would result from a belief being true does not, in and of itself, refute the belief.  As can be seen, Rachel’s unwillingness to consider Robert’s position has resulted in logical fallacies. One wonders whether Rachel really did fairly consider the arguments of the many authors which she claims to have read. If she did not, it doesn’t necessarily make her position false, but it does mean that she does not know how to give an adequate response to those who disagree with her position.

Example 2:

Bob says, “Personally, I do not believe in the resurrection of Jesus, for I don’t believe in the possibility of miracles.  In my opinion, God cannot violate the fixed laws of nature, making miracles impossible. I further believe that my position is supported by strong evidence. Are you interested in hearing why I believe this?”

Susan responds, “While I respect your right to believe what you do, I do not wish to hear your case. I have already made up my mind about what to believe. The Bible says that Jesus was resurrected, and that is good enough for me.”

While we can give Susan credit for being blunt and honest, as opposed to trying to hide her beliefs, the fact remains that she has not presented a strong argument for her position. Susan did not present a specific response to Bob’s argument, nor was she willing to do so.  It can be tempting for Christians to refuse to look at arguments that challenges their core beliefs. However, when someone presents an argument against your beliefs, your response should not be to refuse to evaluate the argument.  Rather, you should take your beliefs, and the beliefs of those who disagree with you, and test them.  If you refuse to do so and insist that you do not need to look at what challenges you, then you are implying that it is impossible or unnecessary to test your beliefs.  If Christian beliefs are untestable, then how can that be reconciled with 1 Thessalonians 5:21 which says, “Test everything that is said and hold on to the good.” This obviously implies that we should test our interpretations of the Bible. 

If you believe that Christian doctrine does not need to be subjected to testing, then you are essentially saying that people should accept without examination the opinions of  “authorities.”  This point of view is why Susan did not bother to respond to Bob’s arguments. On the other hand, if you attempt to respond to skeptics or those with different doctrinal positions, you are assuming that Christianity can be tested and confirmed. And if Christian beliefs can be confirmed, then it is possible that they can be disproved.

The Bottom Line:  Christians should be willing to look at other points of view, put their beliefs to the test, and learn how to effectively respond to those who disagree with them.


Openness Part 1

At this point, let’s take a break from the list of logical fallacies and spend a little time talking about why people commit them.

Granted, many people have not been taught how to think critically. It is far more difficult to avoid fallacious reasoning and logical fallacies if you are not even aware of what they are and the need to avoid them. This problem can be corrected through education. However, there is another more significant problem which can not be eliminated by education alone.

This problem occurs when one is simply not teachable.

Everyone has their opinions and believes that they have good reasons for the opinions they hold. Yet while some are open to considering differing points of view, there are others that simply are not. When someone is not open to changing their mind, it can often result in that individual not taking their opponent’s argument seriously.

After all, if someone has already made up his mind and will not consider changing it, he may not go to the trouble of offering good reasons for rejecting someone else’s position.  It is important to give good reasons for one’s beliefs and opinions. If a person won’t consider the possibility that he could be wrong, that person may not even be motivated to learn how to defend his own beliefs.  Being overly-confident in one’s position therefore could lead to logical fallacies.  On the other hand, someone who is open to changing their mind will be willing to look at what challenges them. 

Most people are not going to state bluntly that they won’t even consider the possibility that they could be mistaken, and more often, they will make statements that imply that they are not willing to change their minds. Consider the following two examples:

Example 1: 

Sara says, “I think that Tom has a good argument in favor of limited government as opposed to big government. We need to listen to and evaluate what Tom says.” 

Jack responds, “Look, Tom is a Republican. We are Democrats and have always been Democrats, as were our parents and grandparents. What could we possibly learn from the Republicans?”

In this example, it is apparent that Jack believes he has nothing to learn from Republicans. Jack’s statement is another way of saying that he is not open to considering the possibility that a Republican may believe something correct, and that he himself might believe something that is incorrect.  Thus, it should come as no surprise that his statement is a classical appeal to tradition fallacy—that is, saying something is true because many have always believed it to be true.

To see this how this works in religious circles, substitute Catholics for Republicans and Baptists for Democrats. In this case, Jack would be saying that Baptists have already got the correct beliefs and that those beliefs have passed the test of time to the point that Baptists have nothing at all to learn from Catholics. Not being willing to change one’s mind indeed can make one more likely to commit logical fallacies.

Example 2:

Mitch says, “I think there are good philosophical and scientific arguments in support of the theory that there are multiple universes. I know those who believe otherwise have their reasons, but I think the philosophical and scientific arguments in support of multiple universes are much more powerful.” 

Barbara says, “I don’t want to discuss this. I have heard all of these arguments before, and they have all been rebutted. I certainly am not very interested in hearing them again.”

The problem here is that Barbara mistakenly thinks that because the previous arguments in favor of multiple universes have been rebutted, she does not need to take give the theory any more consideration. Barbara seems to have closed her mind to new input. However, the fact remains that history has shown that many scientific theories initially were not accepted but later were embraced.

Take heliocentrism and continental drift as two examples. In the time of Plato, it was a given that geocentrism was true. Likewise, scientists at one point believed that the theory of continental drift was incredible. Nevertheless, both heliocentrism and continental drift were later proven true. So is it a mistake to refuse to look at and consider new scientific data because past arguments for a theory have been refuted. The same can be said for philosophical arguments.

Ultimately, being closed to new input is a mistake because if someone holds a belief that is, in fact, true, then their belief can always survive criticism and scrutiny. When someone is unwilling to subject their beliefs to scrutiny and to consider the possibility that they could be mistaken, it is difficult to have an open dialogue with them.

The bottom line here is that we must all be open to changing our minds.

Post Navigation