Importance of Questions & Understanding in Logic Course: Effective Forum Discussions, Schemes and Mind Maps of Logic

Download Importance of Questions & Understanding in Logic Course: Effective Forum Discussions and more Schemes and Mind Maps Logic in PDF only on Docsity! Chapter 7 Summary Please remember that you are not expected to be great right away on translating. However, only a few posts relevant to doing well on the main post. Much better if there were more question posts in the forums, especially on Ex. III. Too many students jumped right into the main post without asking questions first. Some asked questions but did not wait for feedback before making the main post? Usually leads to lower grades on the main post. At this stage in the semester, you need to jump in and be proactive. Reality check: Did you really do ALL the exercises? Check your answers? If not, very bad start to the symbolic logic part of the course. Even if you struggled on the main post and Ex. III, if you followed directions and did all the exercises, checked your answers, and then asked questions in the forum, it will pay off down the road. If you followed directions, you can skim and jump around below. See the frequently asked questions and main post answer. Also, be sure to see the section on advice for C8. Before we discuss C7, I would like to share with you a former student’s great comment about Chapters 1-5. If not so much relevant to the exam, at least very relevant to life. She said that the fallacy chapters actually helped her become LESS cynical. I agree it should. Contrary to what happens to most people in reading these chapters -- they become more cynical -- our goal is not cynical criticism of people in power, but forcing people to reason better. Our goal is not just to pin labels on people's arguments, but to show how the arguments could be stronger by showing how they are weak. A lot of this has to do with why I wrote Chapter 6 (optional). Exams and Grades As I hope you know, I have received all the exams, graded them, and posted results in Gradebook. The highest grade was 130/120, A++, the student had a perfect score and nailed both bonuses! The lowest score was 25/120? Go figure. I kid you not. Two other students had 120 and 121 using one of the bonuses. A commonly missed one was the question on whether we question the truth of the premises for a fallacy of relevance. No, the issue is the reasoning. Another missed one -- It is not true that arguments with all true premises and a true conclusion will never be invalid. Major point in C1 = Invalid arguments can have true premises and a true conclusion, BUT they also allow for true premises and a false conclusion. Review the QuizMe’s? Very relevant to part of the main post this week. See below. As I noted in Gradebook, if you want to talk more about the exam in detail, send me a phone number and good time to call. Otherwise, please remember that I have a phone office hour from Monday-Thursday, at 12 noon (845-9163). Friday by appointments. We can also arrange a weekend phone meeting, if you give me a good time to call and a phone number. In general, those who took full advantage of the posting forums did better. Word to the wise – same message as in the First Day, Self-check, and How To Do Well in this Course pages – if you want to do well, take full advantage of the forums and post early and often. Generally, wait for feedback and then post on the main post late in the week or at least after you receive feedback. C7-C12 will be challenging for most students and the only way to be successful that I know is to follow the steps I give you and ask lots of questions. Remember that past students have told me that the videos are very helpful now. For the exam, a few comments on important terminology: Invalid arguments never have true premises and a true conclusion?? NO, NO, NO. They allow for everything. We don’t want everything. We want only guaranteed true conclusions IF the premises are true. Only valid arguments succeed in doing that. Invalid arguments never have true premises?? NO, NO, NO. Invalid arguments can surely have true premises, but the key problem is that they do not guaranteed true conclusions even if the premises are true. If you missed these, need to review C1, but another chance also to get these concepts via pictures in C8. Chapter 7 Important question from a former student. Worth repeating since it goes with the introduction to this chapter and covers a basic theme of the UH hallmarks. Here was the exchange: “My question is about this whole concept of formulas. Is it always necessary to employ a formula to an argument when you could simply break down the argument without one? (Since you are going to anyway). I guess I am asking, why are formulas the preferred method for logicians when they eliminate the content of the argument? Doesn't this disrupt the purpose of being able to see the argument more clearly? This really intrigues me. • Then do all the exercises. • Compare your answers with those posted via the Main Page. • Ask questions in the Laulima forum about ones that you have that are different. You can also ask questions about any problems in understanding that comes up with any of the above parts. • Do the practice quiz. • Ask questions related to the main posting question. For instance, the hard one in the main translations was #3. I gave hints. If the hints were not clear, ask questions about the details. • Throughout the week read ALL the posts of other students and the responses. • LAST: Post on the main posting question after you have received feedback. (Obviously to follow this plan you cannot do a question post late in the evening on the due date.) Yes, it is a lot of work to read ALL the posts and yes it is hard to find time throughout the week with our busy schedules to do the work a little at a time. But I do not know any other way for logic and math. FYI, this course will count for FS only one more time. This semester! After this semester, it is all FQ. So, if you do not want to have to take Math, best to complete this course now. That means putting in the time to do well on the rest of the course. Speaking of steps, below is a highly recommended set of steps to follow in getting through C8. It could be very traumatic if you don’t follow those steps. For most on- campus students C8 is the easiest chapter in the whole course. For online students it is one of the hardest, because you have to discipline yourself on your own to go through the steps. Notice the videos are labeled Truth Tables, Part I and Part II. Summary of key concepts in C7 Below is a summary of the terminology for this Chapter. Also in the book but some students find it easier to print out these summaries for the final exam. (Note: Microsoft has again disrupted our lives with a supposed upgrade to Word. On some new computers this page will open in Word and not in an Adobe reader. Long story but basically Microsoft is trying to destroy the Adobe Company. If when printing this summary, you get boxes where you should get our symbols, let me know asap.) negations = statements with 'not' conjunctions = statements with 'and' disjunctions = statements with 'or' conditionals = statements with 'if/then' biconditionals = statements with 'if and only if' antecedent = that part of a conditional statement in front of the () symbol consequent = that part of a conditional statement in back of the () symbol / = symbol that we use for the conclusion of an argument. (Only needed for #25, Ex III this week, but will be used for every translation in C8, C9, and C10 – all arguments.) Note the terms ‘antecedent’ and ‘consequent’ only apply to conditional (if/then) statements. Also, see below on the use again of the important terminology -- statements and arguments. Frequently Asked Questions -- Student Confusion and Suggestions Interesting comment from a former student. He noted that his head was “spinning from this new language.” The irony here is that your heads are spinning because of the English! Symbolic logic was invented to keep our minds from spinning and accurately keep track of statements that contain "not both, both not, only if, if only," etc. Again, be careful about trying to read and do all the work at one time. If you try to do all the work in a math or logic course all at once, you will significantly increase anxiety. Remember that I told everyone at the beginning of the class that the biggest problem for most students in math is that they just need "therapy." They are not just bad at math, as they rationalize to themselves. They need to understand the GAME. The game is to understand that all steps in math and logic are easy, and you need to understand to look for the easy steps and not try to jump around and do everything at once. So speaking of steps, did you use the dictionary and the associated notes in the Chapter and the C7 Supplement Lecture to do the exercises? Did you view the first video for C7 and the discussion and visuals on the dictionary? Translating is challenging, but you will make it much more challenging by trying to understand too much at one time. It is good to ask questions on "unless," "neither/nor," and "both not," “only if, and “if and only if,” as to why we have the translations that we do in the dictionary. BUT, you can get many of the exercises correct by just mimicking the dictionary. For instance, students often ask a good question about #6, Ex. II. “Children will be promoted to the next grade only if they pass the essential competency test.” Here is how to do this one without thinking too much. • We see "only if" as the key connective. So we go to #18 in the dictionary. • Then the note for #18 (C7 Lecture) says "only if = consequent." Meaning that what follows the "only if" will go in the consequent position for an ( here) statement. • So we get G  C. "competency test" follows the "only if" so C comes after the () symbol. You should be able to get that answer EVEN IF YOU DON'T UNDERSTAND WHY yet! There is a very good reason for this translation. It is not just an appeal to authority. The reason was explained in the Chapter and the first video for C7. But, to ease into this, just learn how to mimic the dictionary first. Previous student comments on strategy: "The dictionary is very helpful because at this point, I'm just trying to plug in the symbols to get a feel for all this." “I was thinking rather than using the dictionary per Professor Pine’s directions. Then I realized that I could get 90% of every exercise by just trying to find which one in the dictionary fit best.” “At first I was getting many wrong. Then after a post and Dr. Pine’s response I realized I was just going for it on each one and not using the dictionary step by step. Still had some problems but I got a lot more correct.” Yes, take the practice quiz. You should be able to get the right answers without thinking! Don’t just “go for it,” as this student noted. See the video on how to break complicated ones into parts and use the dictionary. Remember the section in the C1 Supplement Lecture -- Why Logicians Don't Think! The dictionary already represents hundreds of years of thinking on what basic expressions in language mean. It is not perfect and there are many advanced discussions still taking place on logic and My response: "This is a very important question but it may indicate that you are confused on the very important difference between STATEMENTS and ARGUMENTS. Except for #25, Ex. III all the exercises in C7 are just statements. It will cause lots of problems later if students don’t know the difference between statements and arguments." If you don't understand the difference between translating statements and translating arguments, you should use the C8 forum to let us know. Compare Exercise III in C7 with Exercise IV in C8. All the translations exercises from now on will be of arguments (C8, C9, and C10). For arguments, the very first step is to find the conclusion as started doing in C2. Then identify the premises. And then translate each statement. You will have both types on the final exam." If you don't know the difference between statements and arguments, be sure to read pages 327-328 very carefully. It means you missed a crucial distinction back in Chapter 1 and this lack of understanding the basics will cause lots of problems later. Please note there is / in #25. For the forum, you can use just (/) in the forum to indicate the conclusion of an argument because our bulletin board program will not transfer this symbol from Word. So, notice the answer for #25: 1. ~G  ~(A v B) 2. G  (H  C) 3. (H • E)  ~C 4. B  (H • E) / ~B Above is how we translate an entire argument. This argument has four premises and a conclusion indicated by / Main Posting Exercise Admittedly some of these were hard for an early stage. I hope everyone took the Practice Quiz first. If you did well on the Practice Quiz, you are doing ok for this stage. Here are the answers to the main posting question. As noted above, best to ask questions first, especially on Ex. III. Some students said they were confused on #3 on the main post. Yes, hard one, but one just like this in Ex. III to ask questions about? 1. A  ~(B v C) or A  (~B • ~C) To get this one correct, we see if/then so we use  as he major connective. Then we see “neither/nor,” so we use # 15 in the dictionary. 2. S  ~R To get this one right, you should have used #18 in the dictionary. Some students did not translate the "not." That is the way some students read. They don't pay attention to detail. Notice that we have this translation by following the note in the Supplement Lecture for "only if." "We don’t have an economic recession" follows the "only if," so ~R comes after the () symbol. S  ~R and ~R  S are not correct. The original said "only if," not "if and only if." 3. (C  M) • ~(M  C) or (C  M) • (M • ~C) The hardest one. This one was intended to challenge you a little and underscore the importance of taking complex statements in steps. Some students had half of it right. Here you needed to combine the insights from doing #7, Ex. II (a necessary condition), or #10, Ex. I, and #18, Ex. III (a negation of a sufficient condition) to give you the foundation for getting this one right. Even better is #16, Ex. III. It is important to study and think about some of the wrong answers. M is necessary for C = (C  M) But = • M is not sufficient for C = It is not true that M is sufficient for C = ~(M  C) ~M  C No, this says, "If we don't have a strong military presence in Southeast Asia, then we will be successful in dealing with China’s growing power." A very different statement than denying that M is a sufficient condition. Students often have ~T  V for #18, Ex. III. No, that says "if the premises are not true in an argument, then the argument is valid." Consider the difference between: ~(F  C) and ~F  C If F = a student passed the final exam, and C = a student passes the course, then the first sentence makes sense. It says that it is not true that passing the final exam is sufficient for passing the course. True, we have more than just this exam. But the second one, although it makes sense grammatically, no instructor in his or her right mind would ever say this = If you fail the final exam, you will pass the course!! The parentheses make a huge difference. Some students will have (M • ~C) for the second half. Believe it or not, that is correct! If M is not sufficient for C, then M can happen but not C. But notice that is the result of thinking and not just using the dictionary. Very good, but harder than necessary. 4. ~T  ~V False. Bonus (complete answer): This statement is incorrect because it is possible for invalid arguments to have true premises and valid arguments to contain false premises. (Chapter 1) Having false premises in an argument is not sufficient or conditional to having an invalid argument. Valid arguments allow for all possibilities of T and F, except one – they do not allow for all true premises and a false conclusion. So, if the premises are not true of a valid argument, the conclusion can still be true or false. If you are still struggling with these C1 concepts, we have another chance to understand them now, and via pictures with truth tables. Compare this answer with #18, Ex. III, ~(T  V). Number 18 is true. Yes, it is not true that having true premises automatically means an argument is valid. Invalid arguments can also have true premises. You should compare carefully what you posted with the above answers. Ask follow-up questions in the C8 forum, if you don’t see if yours were right (equivalent) or wrong. For the last one above, for those who may still be saying or thinking, "If the premises are true, then an argument is valid," and/or, "If the premises are false, then the argument is invalid" you are showing that you still don't understand that there is a difference between the reasoning of an argument and its content. Remember the example of a computer in Chapter 1. A computer can be given all false information to process, but if functioning properly, it will still be logical and give a valid conclusion. Also, please look again at Example 1-2 (C1) and the discussion on the south-of example in C1. Reviewing the valid-invalid tutorial for C1 should also help when we get to C8.