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Our last chapter. Congratulations for making it this far. You should read this chapter carefully and think mostly about the philosophical questions it raises about the foundations of logic. You should also attempt to see how big philosophical decisions have huge practical effects in technology and product development. The next time you see an advertisement for sales at Shirokiya look for a rice cooker with fuzzy logic programming! In addition to the reading you should do the exercises just to get a feel for the difference between a multivalued logic and the two-valued logic of propositional logic covered in chapters 7-10. You could at least do the *-exercises and then check your answers in the back of the chapter. Notice also that you only have to do one posting for this week, although it should be a short essay that demonstrates that you understand the basic points in Chapter 12. To help you better understand this chapter, let's go back to truth tables (Chapter 8). What you should understand by now is that the decisions we make at the most elementary level about what is true or false have vast ramifications "up the line" so to speak until it effects one's entire world view. Consider a simple truth table commitment for a conjunction in Western logic: A B A ·
B
Suppose a toddler was learning from her mother the meaning of "and." She hears her mother say, "Tomorrow will be a very important day for you. It is your birthday. We are going to invite your two best friends from your preschool. Alice and Barbara are coming to your party." Notice that in Western logic this last statement is just true or false. There are no shades of gray. The result is the same (false) if either Alice or Barbara do not come for some reason (lines 2 and 3), and if both Alice and Barbara don't come (line 4). But a supporter of the need for more precise shades of gray reasoning would step in here and say this is obviously wrong from the child's point of view. The child would be much more disappointed if line 4 occurred than if lines 2 or 3 occurred. At least she has one of her friends at the party if lines 2 or 3 occurred. So, if the child is much more disappointed in line 4, shouldn't line four be considered MORE FALSE!? Shouldn't our logic allow for degrees of truth? Let's consider the truth table above in more detail. As page 395 shows even fuzzy logic would not be able to say that one line is more false than another. But if we change the situation a little, you should be able to understand how fuzzy logic handles more precisely some very real life situations. Notice that when we say that Alice or Barbara "attends" the little girl's party that this is potentially a fuzzy concept. Suppose the mothers of Alice and Barbara tell the little girl's mother that they will be very busy that day and are not sure they can make it, but they are pretty sure they can stop by for at least a little while. So you see from the little girl's point of view "attends" is not a black and white (true or false) event. What if one girl comes for only fifteen minutes and the other comes for the full time? Or some other variation of times? This will make a big difference from the little girl's perspective for how much truth is in the statement "Alice and Barbara are coming to your party." So, here is how a fuzzy logic truth table might look. If we assume the party is three hours long and we break the party up into 15-minute segments, we would have a table that looked like this. A B Result 0
0
0
In other words, fifteen (15) minutes of attendance would be only .08 true out of 180 (3 hours) of possible attendance, ninety (90) minutes would be .50 true, and so on. Only when either girl attended zero (0) minutes or the full three hours (180) minutes would the situation be fully ("crisply") false or true. Next any combination of different attendance values would be calculated based on the rule on page 395. So if A = 30 minutes (.16) and B = 150 (.83), the truth value for A · B would be .16. From the little girl's perspective the conjunction statement would not be fully true. In fact, it would only be a little bit true. What you should see after reading Chapter 12 is that adding degrees-of-truth-reasoning to the very foundations of logic has a drastic effect on all the other rules of logic. All the rules we have learned become applicable to only extreme cases -- cases of complete truth or complete falsehood. Even deductive validity and invalidity become more like the distinction we made in Chapter 3 between "strong inductive" and "weak inductive" arguments. A fuzzy valid argument can "blend into" an invalid deductive argument. The huge issue all this raises is, "What is the status of logic?" The fancy way philosophers ask the question is, "What is the ontological status of logic and mathematics?" Are they just rules we make up like that of a game (e.g.. basketball)? Are they simply part of a cultural view of reality? Or, are they some kind of absolutes that the universe obeys, like the law of gravity? Are they simply rules used by the human mind? Are they rules in the mind of God? From the perspective of these questions, your final exam should be a piece of cake! Good luck, and thanks for taking the course. If you enjoyed this course and/or enjoy thinking about big questions such as the above, you might be interested in another online course Philosophy 120: Science, Technology, and Values. It is offered as an E-focus (ethics) and WI (writing-intensive) course. The syllabus is at: Philosophy 120 Syllabus -- online You can find the book at: Science and the Human Prospect Aloha, Ron Ronald C. Pine |