Wednesday, November 7, 2012
For tomorrow, toddle off to Oxford and work through this logic tutorial
on consistency and validity. Once on the site, follow the Tutorials
link, then select Tutorial One. Continue until you finish Exercise
1.4. Having completed this, consider (in writing) how the skills this
tutorial develops help you understand and tackle the puzzles and paradoxes from the previous post.
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Many of the problems were hard to decipher, but after reading through the exercises I can identify how the some of the problems were constructed. With the monkey puzzle the skill of identifying an argument’s validity is not considered because from the beginning we must understands that all of the statements are true. To calculate the length of the rope we must identify the conclusion of each argument. With the Island of knights and knaves puzzles the statement that “Knights always tell the truth. Knaves never tell the truth; any sentence uttered by a knave is false.” is a necessary truth. This is true because under the circumstances these two sentences must be true to solve the puzzle. The super bullet problem can be explained by the idea that a valid statement can have consistent premises, but an inconsistent conclusion.
ReplyDeleteI found that the first three sections were quite easy to understand and fairly standard. When I started on the fourth section (the validity of an argument), I started getting frustrated because I just couldn’t grasp the concept. Therefore, I looked up another website that explained the same material. I understood that and then found that the material made sense when I once again returned to the Oxford University website.
ReplyDeleteOne of the mistakes I kept making was mixing up the words “true” and “consistent.” Consistent simply means that they can exist at the same time. A consistent set of sentences can be true, but they can also be false. Understanding the difference between consistency, being true, valid arguments and invalid arguments helped me understand The Super Bullet problem better because the premises of The Super Bullet problem are inconsistent (there cannot a bullet and a plate equally strong at the same time). However, it is a valid argument because all arguments with inconsistent premises are valid even if the premises aren’t actually true.
Consistency also helped me with the Knights and Knaves problem. The way to solve that would be to take turns assigning the role of knight and knave to each speaker and then determining from there whether or not everyone else’s comments are consistent with the first one. If not, then I change the role and try again. I can make a true conclusion when all of the comments are consistent.
The skills this tutorial helped me develop are:
- not making assumptions when trying to determine whether or not facts and statements are consistent
- Correctly determining consistencies from inconsistencies
- Learning the difference between different types of ambiguities
- Learning the difference between a valid and an invalid argument
- Learning how inconsistent premises can still give valid arguments
The logic tutorial has helped be better understand the puzzles which allows me to tackle them in a more systematic and logical approach. The teaching from the tutorial that I was not made aware of previous to this exposure was structural ambiguity. I had not included structural ambiguity in my logic during the logic puzzles and paradoxes. I find this useful because the way you phrase something can help you to understand it.
ReplyDeleteTruth values taught me to consider beneath the assumed and see what is possible. Lexical ambiguity is to consider alternate meanings which can help me find the underlying answer to a question that may seem endless because I was misinterpreting it. Finally, I learned that for an answer to be logical does not mean for it to be physically true. An argument is valid just if its counterargument is inconsistent. An argument is valid if it is consistent. For an argument to be valid requires consistency from all premises as well as its conclusion.
Most importantly, the tutorial reintroduced the requirement of an argument having consistency and not contradicting itself. The steps of considering truth values, consistency, ambiguity, and the validity of arguments should be included because they are particularly helpful when coming to a final argument as an answer.
The tutorial was helpful but also very confusing at the same time. I learned from the different sections that when solving the puzzles from last week’s post I needed to break up the different parts into even smaller parts. By doing this it would help organize my thoughts and the parts of the puzzle. One section that was helpful was when given a piece of a puzzle you must check the validity to know whether or not you can continue solving with it making sense. A lot of the pieces of the puzzles had a lot of ambiguity in the way that it makes you question if it could be true at all.
ReplyDeleteI learned that there could always be a conclusion whether or not it is how the author wanted it or not. It just needs to make sense to the “solver”. However with that may come a long list of inconsistencies that will throw you right back off the track you were on. I know that the next time I will have to solve puzzles, I’ll stop and think about how I need to begin the problem without jumping to conclusions and giving up. Patience will be the greatest help, and breaking things into smaller parts that will help me make more sense of what I have in front of me.
ReplyDeleteThis tutorial helped me to understand the meaning of a sentence and the relationship between the sentences better. It started with consistency of a sentence, which seemed a little confusing to me at first. After I read through the examples, I knew more about the meaning of consistency, and how it can affect the meaning of the sentence. For example, “Peter believes that David has three daughters and four sons, and he (David) has six children in all” is contradictory to itself. Although the name David is consistent, the information about him in the sentence is inconsistent. The second section led to the question of ambiguity based on the use of words or the structure in the sentence. Sometimes, I could understand one meaning of the sentence better than the other because that’s the way people normally use it for. For instance, “John likes swimming more than Peter”. Usually when people say that, they mean that John’s preference of swimming is more than that of Peter. However, in the structure it is stated, I could also understand it as John likes the sport swimming better than the person Peter. Based on the structure of the sentence that was written, either way might be correct if I took literally. It was the start of the confusion, and the reader has to guess the meaning in their own way. The third section talked about the relationship between the premises and conclusion. In order to get what the conclusion is, I had to understand the logic in the sentences, and what led to what. They were like the reasons and the result; in order to find the result, I must know the reasons, and whether or not they were consistent. I didn’t understand the fourth section completely, but it taught me to think widely, not be restricted in the sense that I’ve got used to believe before. Logic doesn’t mean restriction, but means to use evidence to back up the idea. Every idea can be true if the evidence is valid. Every word can have different meanings, and different structures can indicate different meanings. They are either done by mistake or done by purpose. If they are done by purpose, the author usually wants to imply another significance behind it. This often shows up in paradox and puzzles because when I thought about puzzles for the previous post, there are usually many possibilities that I needed to concern based on the literal meaning of the text. The tutorial broadened my mind, and let me think about the possibilities that I thought were impossible. I can pay more attention to the sentence itself, and how its structure may impact on its meaning. It also taught me that logic is based on reasoning, and how I can build on my own thinking to be able to think logically.
The skills in this tutorial were helpful in developing methods to tackle to puzzles and paradoxes in the previous post by stating criteria. Although confusing at times the statements of “rules” allowed for me to organize and come to a conclusion instead of just blankly jumping to any conclusion or none at all. The distinction between consistency and inconsistency along with the true and false conclusions of either. With these rules the puzzles would be easier to understand and organize because now I am not as willing to trust everything that I see. I will more likely go through a analyze every sentence structure to make sure that every piece of information is decoded and correct.
ReplyDeleteNo matter what the situation there will always be a conclusion, whether or not it is just a matter of opinion is a different story. Every person has the right to believe what they wish to believe, especially if the matter is controversial. Whether or not the statement is consistent or inconsistent or the conclusion false, true or a necessary truth.
This tutorial was a godsend, and while some of them didn't directly apply to the logic puzzles we worked on, they still were really useful in cleaning my brain of all the extra confusion accumulated while trying to solve the puzzles. It helped organize my thoughts. Some of them took a few tries to wrap my head around them, such a s the last one which discussed validity. to be honest,I'm pretty sure i still don't quite understand. the other ones, however, were quite straightforward and were applicable not only to the logic puzzles but to life in general. If one or more of the premises of a conclusion is false, than the conclusion is not necessarily true. That just makes sense! It also seems like something which should have been obvious to me, but apparently it was not so now when i revisit the logic puzzles I can focus on analyzing the sentences, creating true premises and reaching true conclusions. This is so applicable. I know i already said this, but it seems to me that this is where logic overlaps with real life. In my previous post about the puzzles, I wasn't sure how logical any of the puzzles really were. Now I understand that the logic comes in how you solve it and not just the specific situation.
ReplyDelete