Better Reasoning X: Double Negation and Mid-Term
As this is tenth post in the Better Reasoning series, it is worth pausing a moment and taking stock. One thing that comes to mind is that there is one valid inference rule that has not yet been covered. This is the rule known as Double Negation. Using the conventions adopted earlier, the two forms of this rule can be represented as follows;
P,
Thus,
Not not P.
Not not P,
Thus,
P.
The idea behind this rule is reasonably intuitive. If someone is described as being 'not unhappy', we know that the speaker means to imply that the person is actually happy. That is to say, we a familiar with cases where two negatives lead to a positive. Conversely, we know that a positive is equivalent to a double negative. For example, if a garbage can is smelly, we know that it is not unsmelly!
One reason for mentioning this rule is that, although it is pretty intuitive, when reasoning, it is useful to have an explicit rule to appeal to, rather than relying on brute intuition, as intuition can go wrong at times. Thus, the rule is worth discussing here, for the sake of completeness. Another reason for bringing up the double negation rule is that it is needed for a certain on-line exercise.
In many classes at Universities that teach better reasoning skills, it is often traditional to have assignments that are graded, or periodic examinations. Thus, it would be nice to have something similar available with this series of posts. It turns out that there is a test readily available on-line.
Before proceeding to the on-line test though, it would be useful to offer some study tips. The test does not cover all the topics discussed in this series. However, it does test the material covered in Better Reasoning IV and Better Reasoning V which both covered the valid argument forms. Prior taking the test, it might be a good idea to review these two posts.
When you feel ready for the challenge of the test, the test can be accessed at,
Better Reasoning On-Line Mid-Term Exam.
Some of the terminology may not be familiar, but the basic logical concepts that have been covered here are the same. Ideally, a person should score a minimum of eight out of ten. Of course ten out of ten would be better, but there are a couple of question that go beyond the material covered here. Should you get a question wrong, read the explanation and try an understand where you made a mistake. Good luck!
The CP
P,
Thus,
Not not P.
Not not P,
Thus,
P.
The idea behind this rule is reasonably intuitive. If someone is described as being 'not unhappy', we know that the speaker means to imply that the person is actually happy. That is to say, we a familiar with cases where two negatives lead to a positive. Conversely, we know that a positive is equivalent to a double negative. For example, if a garbage can is smelly, we know that it is not unsmelly!
One reason for mentioning this rule is that, although it is pretty intuitive, when reasoning, it is useful to have an explicit rule to appeal to, rather than relying on brute intuition, as intuition can go wrong at times. Thus, the rule is worth discussing here, for the sake of completeness. Another reason for bringing up the double negation rule is that it is needed for a certain on-line exercise.
In many classes at Universities that teach better reasoning skills, it is often traditional to have assignments that are graded, or periodic examinations. Thus, it would be nice to have something similar available with this series of posts. It turns out that there is a test readily available on-line.
Before proceeding to the on-line test though, it would be useful to offer some study tips. The test does not cover all the topics discussed in this series. However, it does test the material covered in Better Reasoning IV and Better Reasoning V which both covered the valid argument forms. Prior taking the test, it might be a good idea to review these two posts.
When you feel ready for the challenge of the test, the test can be accessed at,
Better Reasoning On-Line Mid-Term Exam.
Some of the terminology may not be familiar, but the basic logical concepts that have been covered here are the same. Ideally, a person should score a minimum of eight out of ten. Of course ten out of ten would be better, but there are a couple of question that go beyond the material covered here. Should you get a question wrong, read the explanation and try an understand where you made a mistake. Good luck!
The CP
Labels: Better Reasoning
posted by The Combat Philosopher at 3:10 PM
2 Comments:
It's interesting that in many languages (including Middle English and early modern English), double negatives intensify the negativity rather than negating it. I think that might mean that the logical/mathematical model is less intuitive than modern English speakers might think, no?
Hi Bardic,
You have a fair point. In my neck of the woods we see something similar when people call something "bad bad" to indicate that it is very bad. I'm not sure why logic goes with the reversable negation version. However, as this is a comment, it does bring to mind my one linguistics kind of joke.
So, a rather senior professor is teaching a class on the way negative terms work. The class is made up of the usual kind of students, including the one bored looking disaffected student who is sitting at the back. As the professor is concluding his lecture, he remarks that "...although in some cases, two negative terms may yield a positive, there is no case where two posutive terms will yield a negative!"
At this point, the student at the back puts up his hand and says, "yeh, right."
I like it.
The CP
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