ESSENTIAL QUESTION

What are the limits of reasoning and how can logical fallacies cause us to come to an unreasonable conclusion?

IMPortant definitions

• REASON: Systematic thinking; thinking using a process
• LOGICAL FALLACY: An invalid pattern of reasoning
• FALSE DILEMMA: Assuming that only two alternatives exist

THE STORY

A guard had just sat down when there was a knock at the door. A person in a uniform held up a badge and asked the guard a question. The officer replied and was duct taped and handcuffed. Carrying the artwork, the man left the building. A man is found in the building and a member of the police force is notified.

FOLLOW-UP QUESTIONS

THERE ARE THREE ANSWER CHOICES: TRUE, FALSE, AND UNCERTAIN

1. The guard was a man
2. A person appeared after the guard sat down.
3. The person who knocked at the door was a police officer
4. A question was asked and answered
5. The guard was duct taped and handcuffed
6. While paintings were removed from the building, the story does not state how many
7. After the man collected the artwork, he ran out of the building.
8. No artwork was removed from the building.
9. The story concerns a series of events in which only three persons are referred to: the guard, the person in uniform, and the member of the police force.
10. The following events in the story are true: a guard was handcuffed, a man pretended to be a police officer and stole artwork from the museum, and the police force was quickly notified.

CORRECT ANSWERS

1. Uncertain
2. Uncertain
3. Uncertain
4. True
5. Uncertain
6. Uncertain
7. Uncertain
8. False
9. Uncertain
10. Uncertain

PARTICIPANT RESULTS

• PARTICIPANT 1: 50%
• PARTICIPANT 2: 40%
• PARTICIPANT 3: 60%
• PARTICIPANT 4: 40%

ANALYSIS

Most people were not able to correctly answer many of the seemingly obvious questions correctly due to a tendency to see things in black and white, without considering that the answer might be uncertain. This shows that when we use this everyday style of reasoning, informal reasoning, it is easy to be mislead by logical fallacies such as the false dilemma. I learned from this exploration that reason as a way of knowing is not without its faults and limitations, and may not always bring you true knowledge.

PROGRESS journal

• Name: Reshmi Patel
• Group Members: Shivani, Muno, Ashmal
• Badge Leader: Shivani
• Date: 2/16/17 - 2/27/17
• Badge Title: WOK Badge: Reason
• Project Title: Reason and Its Limits: An Exploration of False Dilemma

2/16/17. The main point I would like to cover when we are exploring the Way of Knowing reason is determining whether or not an argument is valid. While reading the textbook and doing several of the examples, I realized how easy it is to make assumptions that are not actually valid reasoning. There are many logical fallacies in informal reasoning that we encounter each day, whether we realize it or not. For example, it is easy to make a hasty generalization based on insufficient evidence or pose a loaded question to someone due to a prior bias. These and the eight other “Deadly Fallacies” often prevent our arguments from being valid. Additionally, validity is important when looking at syllogisms. One good definition of validity that I think we should focus on is that “an argument is valid when it is the inescapable conclusion of the premises.” Often something seems that it is valid, simply because we know the conclusion to be true from experience or memory, but the argument itself is actually invalid. I found the concept that the premises and conclusion of an argument can be completely false based on what we know of the world, but the reasoning itself may still be valid. Another aspect of reason I think we could explore, related to validity, is looking at quantifiers such as all, some, and none, and their effect on the validity of an argument.

2/18/17. For one of my elective readings, I read the Varberg explanation of Zeno’s Paradox as well as the Lewis Carroll parody of this paradox, “What the Tortoise Said to Achilles.” In Zeno’s Paradox of Achilles and a tortoise, the tortoise is given a head start of 1 meter in a race and Achilles is twice as fast as the tortoise. In the time that Achilles runs to where the tortoise started, the tortoise moves half a meter further. In the time that Achilles moves forward that half meter, the tortoise has moved one fourth of a meter, and this pattern continues for eternity. With this logic, Achilles would never actually catch up to the tortoise, although in real life we know that it would be easy for Achilles to simply run past the tortoise in a few seconds. This kind of reasoning that seems logical but ends in an absurd conclusion is known as a paradox. I found Zeno’s paradox fascinating and drew out a picture to understand it more fully. It also led me to become more interested in paradoxes in general, so I went and read about some other reasoning paradoxes soon after. After reading the Varberg explanation, I read the Carroll parody of Zeno’s paradox. This involved a discussion between the tortoise and Achilles set after the race described in the paradox. It connected to the original parody because it was a hypothetical situation about the concept of an infinity inside of a finite set.

2/21/17. Today, I furthered my knowledge of reason by looking at the ways in which all types of reason can be uncertain. Before discussing and learning about reason in this class, I thought of reason as something infallible, meaning that if you reasoned correctly it would always bring you to the truth. However, I two main things that prove this assumption false, the first being that a conclusion is only as true as its premises and the second that often reasoning that seems correct actually contains logical fallacies, such as hasty generalizations or circular reasoning. I feel that we are very prepared for our Badge Project and have a good plan to complete and present it by Thursday. Today, we wrote the story based on the Storycorps interview, keeping in mind that it is important to keep it vague and somewhat uncertain. We then wrote out ten statements about the story that seem obviously true or false at first glance, but are actually mostly uncertain. Before Thursday, we will each find a participant for the study and add the results to the presentation.

2/23/17. After presenting today, we realized that while our ideas were good, our presentation itself was all over the place. We spent so much time writing the story and questions, and putting together the activity, that we did not actually practice the presentation much at all. I rehearsed my part of the presentation and my group members may have done the same, but we did not rehearse it all together to make sure that what we were saying individually fit as a group. Therefore, when we presented, we all discussed different things and the presentation as a whole didn’t really come together. We all had different ideas when it came to presenting the project and because of our lack of teamwork, we were not able to present these ideas well together. Additionally, some of the other members were not as actively involved, and instead of trying to get them involved, I just did more of the work myself. This meant that when it came time to present, half of our group did not know much about the project or interpreted it differently, so the cohesiveness of the presentation was severely lacking. When re redid the project as a video, first we went over as a group, exactly what we did for the project and how it connected to reason. Then, we discussed our different viewpoints on it before starting to record. I think this was much more effective and our video recording turned out much more coherent and cohesive than the original presentation, with the same basic concept.

2/24/17. We ended up changing the logical fallacy we focused on in the redo presentation. At first, we thought that the logical fallacy that was occurring in the reasoning was hasty generalization because the participants were answering questions and making assumptions based on too little information. While this

extension proposal

I propose that the following article about the Monty Hall problem should be added to the list of elective readings: http://www.montyhallproblem.com/

I believe that this would be a valuable addition to the elective readings because it shows how there can be multiple patterns of reasoning, that all seem logical, but can bring you to different conclusions, which may or may not be correct.

The premise of this problem is the following: "You are given the opportunity to select one closed door of three, behind one of which there is a prize. The other two doors hide “goats” (or some other such “non-prize”), or nothing at all. Once you have made your selection, Monty Hall will open one of the remaining doors, revealing that it does not contain the prize. He then asks you if you would like to switch your selection to the other unopened door, or stay with your original choice. Should you switch?"

The reasoning that most people follow when first being given this problem is thinking only of the fact that there are two possibilities left, a goat and the prize. Thus, the probability that the prize is behind each of the two doors should be 1/2 and it does not matter whether or not you switch. However, this method of reasoning leaves out some crucial information we are provided with. The door that is opened does not have a prize. Since there was originally a 1/3 chance that the door you picked had the prize, there was a 2/3 chance that the prize was in one of the other two doors and not in your door. So, now that one door that does not have the prize has been completely eliminated, there is a 1/3 chance that your door has the prize and 2/3 chance that the other door has the prize. Thus, you should always switch.

I liked this explanation in particular because it includes the following explanation of the problem, an exaggeration that I find makes it much easier to understand: "Imagine that there were a million doors. After you have chosen your door, Monty opens all but one of the remaining doors, showing you that they are “losers.” It's obvious that your first choice is wildly unlikely to have been right. And isn't it obvious that of the other 999,999 doors that you didn't choose, the one door he avoided opening is wildly likely to be the one with the prize?"