The logical thinking process pdf download

Explanations and procedures for constructing the logic trees are considerably simplified. The logical thinking process referred to in the title is nothing less than a broadly applic This peerless best-seller is a hands-on, step-by-step workbook of instructions on how to create flowcharts and document work processes.

No other book even comes close in teaching practitioners these crucial techniques. The most noticeable change Cart Total: Checkout. These are big assumptions and they may very well turn out to be mistaken. Nevertheless, it is important to see that the main conclusion Obama argues for depends on these missing premises—premises that he never explicitly states in his argument.

So here is the final, reconstructed argument in standard form. The only way that the United States can adequately respond to the security threat that Assad poses is by military force. It is in the national security interests of the United States to respond adequately to any national security threat.

So while statement 11 is a premise of the main argument for the main conclusion statement 14 , statement 11 is also itself a conclusion of a subargument whose premises are statements 5, 6, 9, and And although statement 9 is a premise in that argument, it itself is a conclusion of yet another subargument whose premises are statements 1, 7 and 8. Almost any interesting argument will be complex in this way, with further subarguments in support of the premises of the main argument.

As we have seen, there is much to consider in reconstructing a complex argument. As with any skill, a true mastery of it requires lots of practice. In many ways, this is a skill that is more like an art than a science. The next chapter will introduce you to some basic formal logic, which is perhaps more like a science than an art. In chapter 1 we introduced the concept of validity and the informal test of validity.

According to that test, in order to determine whether an argument is valid we ask whether we can imagine a scenario where the premises are true and yet the conclusion is false. The informal test relies on our ability to imagine certain kinds of scenarios as well as our understanding of the statements involved in the argument.

Because not everyone has the same powers of imagination or the same understanding, this informal test of validity is neither precise nor objective. For example, while one person may be able to imagine a scenario in which the premises of an argument are true while the conclusion is false, another person may be unable to imagine such a scenario.

As a result, the argument will be classified as invalid by the first individual, but valid by the second individual. That is a problem because we would like our standard of evaluation of arguments i. What are the precise success conditions for having imagined a scenario where the premises are true and the conclusion is false? The goal of a formal method of evaluation is to eliminate any imprecision or lack of objectivity in evaluating arguments. As we will see by the end of this chapter, logicians have devised a number of formal techniques that accomplish this goal for certain classes of arguments.

What all of these formal techniques have in common is that you can apply them without really having to understand the meanings of the concepts used in the argument. Furthermore, you can apply the formal techniques without having to utilize imagination at all. Thus, the formal techniques we will survey in this chapter help address the lack of precision and objectivity inherent in the informal test of validity. In general, a formal method of evaluation is a method of evaluation of arguments that does not require one to understand the meaning of the statements involved in the argument.

By the end of this chapter, if not before, you will understand what it means to evaluate an argument by its form, rather than its content. However, I will give you a sense of what a formal method of evaluation is in a very simple case right now, to give you a foretaste of what we will be doing in this chapter. Suppose I tell you: It is sunny and warm today. This statement is a conjunction because it is a complex statement that is asserting two things: It is sunny today.

It is warm today. Here is that simple argument in standard form: 1. It is sunny today and it is warm today. Therefore, it is sunny today. But we can also see that the form of the inference is perfectly general because it would work equally well for any conjunction, not just this one. Therefore, A We can see that any argument that had this form would be a valid argument. For example, consider the statement: Kant was a deontologist and a Pietist.

Kant was a deontologist and Kant was a Pietist. Therefore, Kant was a deontologist. That is what it means for an argument to be valid in virtue of its form. In the next section we will delve into formal logic, which will involve learning a certain kind of language.

A proposition is simply what I called in section 1. Thus, for our purposes, we can treat a proposition as the same thing as a statement.

Atomic propositions are those that do not contain any truth-functional connectives. A truth-functional connective is a way of connecting propositions such that the truth value of the resulting complex proposition can be determined by the truth value of the propositions that compose it. Suppose that the floor has not been mopped but the dishes have been washed.

The reason is that a conjunction, like the one above, is only true when each conjunct i. If either one of the conjuncts is false, then the whole conjunction is false. This should be pretty obvious.

What this shows is that conjunctions are true only if both conjuncts are true. This is true of all conjunctions.

The conjunction above has a certain form—the same form as any conjunction. We can represent that form using placeholders— lowercase letters like p and q to stand for any statement whatsoever. Thus, we represent the form of a conjunction like this: p and q Any conjunction has this same form. As before, this conjunction is true only if both conjuncts are true. In that case, while it is true that it is sunny today, it is false that it is hot today—in which case the conjunction is false.

The only way the statement would be true is if both conjuncts were true. The four basic truth-functional connectives are: conjunction, disjunction, negation, and conditional. In the remainder of this section, we will discuss only conjunction. The conjunction is true if and only if both conjuncts are true. We can represent this information using what is called a truth table.

Truth tables represent how the truth value of a complex proposition depends on the truth values of the propositions that compose it. Each of the following four rows represents a possible scenario regarding the truth of each conjunct, and there are only four possible scenarios: either p and q could both be true as in row 1 , p and q could both be false as in row 4 , p could be true while q is false row 2 , or p could be false while q is true row 3.

As we have seen, a conjunction is true if and only if both conjuncts are true. This is what the truth table represents. Since there is only one row one possible scenario in which both p and q are true i. Since in every other row at least one of the conjuncts is false, the conjunction is false in the remaining three scenarios.

At this point, some students will start to lose a handle on what we are doing with truth tables. Often, this is because one thinks the concept is much more complicated than it actually is.

For some, this may stem, in part, from a math phobia that is triggered by the use of symbolic notation. But a truth table is actually a very simple idea: it is simply a representation of the meaning of a truth-functional operator. When I say that a conjunction is true only if both conjuncts are true, that is just what the table is representing. There is nothing more to it than that.

Later on in this chapter we will use truth tables to prove whether an argument is valid or invalid. Understanding that will require more subtlety, but what I have so far introduced is not complicated at all. Nevertheless, I am still asserting two independent propositions. For example, in the conjunction: Bob brushed his teeth and got into bed There is clearly a temporal implication that Bob brushed his teeth first and then got into bed.

It might sound strange to say: Bob got into bed and brushed his teeth since this would seem to imply that Bob brushed his teeth while in bed. But each of these conjunctions would be represented in the same way by our dot connective, since the dot connective does not care about the temporal aspects of things. Bob vacuumed the floor; Sally washed the dishes. Both of these are conjunctions that are represented in the same way.

Not every conjunction is a truth-function conjunction. We can see this by considering a proposition like the following: Maya and Alice are married. If this were a truth-functional proposition, then we should be able to identify the two, independent propositions involved.

But we cannot. What would those propositions be? In contrast, the following is an example of a truth- functional conjunction: Maya and Alice are women. Unlike the previous example, in this case we can clearly identify two propositions whose truth values are independent of each other: Maya is a woman Alice is a woman Whether or not Maya is a woman is an issue that is totally independent of whether Alice is a woman and vice versa.

That is, the fact that Maya is a woman tells us nothing about whether Alice is a woman. In contrast, the fact that Maya is married to Alice implies that Alice is married to Maya.

So the way to determine whether or not a conjunction is truth-functional is to ask whether it is formed from two propositions whose truth is independent of each other. If there are two propositions whose truth is independent of each other, then the conjunction is truth-functional; if there are not two propositions whose truth is independent of each other, the conjunction is not truth-functional.

If the sentence is a truth-functional conjunction, identify the two conjuncts by writing them down. Jack and Jill are coworkers.

Tom is a fireman and a father. Ringo Starr and John Lennon were bandmates. Lucy loves steak and onion sandwiches. Cameron Dias has had several relationships, although she has never married. Bob and Sally kissed. A person who plays both mandolin and guitar is a multi- instrumentalist. No one has ever contracted rabies and lived. Jack and Jill are cowboys. Josiah is Amish; nevertheless, he is also a drug dealer.

The Tigers are the best baseball team in the state, but they are not as good as the Yankees. Bob went to the beach to enjoy some rest and relaxation.

The ring is beautiful, but expensive. It is sad, but true that many Americans do not know where their next meal will come from. Negation and disjunction In this section we will introduce the second and third truth-functional connectives: negation and disjunction.

We will start with negation, since it is the easier of the two to grasp. Negation is the truth-functional operator that switches the truth value of a proposition from false to true or from true to false.

In English, the negation is most naturally added just before the noun phrase that follows the linking verb like this: Dogs are not mammals. Just as we can make a true statement false by negating it, we can also make a false statement true by adding a negation. But we can make that statement true by adding a negation: Cincinnati is not the capital of Ohio There are many different ways of expressing negations in English.

There is one respect in which negation differs from the other three truth- functional connectives that we will introduce in this chapter. Unlike the other three, negation does not connect two different propositions. That is, if we know the truth value of the proposition we are negating, then we know the truth value of the resulting negated proposition.

We can represent this information in the truth table for negation. You can find the tilde on the upper left-hand side of your keyboard. What the table says is simply that if a proposition is true, then the negation of that proposition is false as in the first row of the table ; and if a proposition is false, then the negation of that proposition is true as in the second row of the table. As we have seen, it is easy to form sentences in our symbolic language using the tilde.

All we have to do is add a tilde to left-hand side of an existing sentence. In propositional logic, a constant is a capital letter that represents an atomic proposition. Think about it; you should be able to figure it out given your understanding of the truth-functional connectives, negation and conjunction. Before we can do that, however, we need to introduce our next truth-functional connective, disjunction.

What this sentence asserts is that one or the other and possibly both of these individuals tracked mud through the house. Thus, it is composed out of the following two atomic propositions: Charlie tracked mud through the house Violet tracked mud through the house If the fact is that Charlie tracked mud through the house, the statement is true. If the fact is that Violet tracked mud through the house, the statement is also true.

This statement is only false if in fact neither Charlie nor Violet tracked mud through the house. This statement would also be true even if it was both Charlie and Violet who tracked mud through the house. Think about what the slogan means. Think about the conditions under which this statement would be true. But suppose that your seatbelt is buckled, is it still possible to get a ticket as in the third scenario—row 3? Of course it is!

That is, the statement allows that it could both be true that your seatbelt is buckled and true that you get a ticket. How so? Suppose that your seatbelt is buckled but your are speeding, or your tail light is out, or you are driving under the influence of alcohol. In any of those cases, you would get a ticket even if you were wearing your seatbelt.

So the disjunction, click it or ticket, clearly allows the statement to be true even when both of the disjuncts the statements that form the disjunction are true. The only way the disjunction would be shown to be false is if when pulled over you were not wearing your seatbelt and yet did not get a ticket.

Thus, the only way for the disjunction to be false is when both of the disjuncts are false. These examples reveal a pattern: a disjunction is a truth-functional statement that is true in every instance except where both of the disjuncts are false. The following four rows represent the conditions under which the disjunction is true. As we have seen, the disjunction is true when at least one of its disjuncts is true, including when they are both true the first three rows. A disjunction is false only if both disjuncts are false last row.

However, sometimes a disjunction clearly implies that the statement is true only if either one or the other of the disjuncts is true, but not both. For example, suppose that you know that Bob placed either first or second in the race because you remember seeing a picture of him in the paper where he was standing on a podium and you know that only the top two runners in the race get to stand on the podium.

That sentence makes explicit the fact that this statement is a disjunction of two separate statements. However, it is also clear that in this case the disjunction would not be true if all the disjuncts were true, because it is not possible for all the disjuncts to be true, since Bob cannot have placed both first and second. When you believe the best interpretation of a disjunction is as an exclusive or, there are ways to represent that using a combination of the disjunction, conjunction and negation.

We will see how to represent an exclusive or in section 2. Use the suggested constants to stand for the atomic propositions. Either Bob will mop or Tom will mop. It is not sunny today. It is not the case that Bob is a burglar.

Harry is arriving either tonight or tomorrow night. Gareth does not like his name. Either it will not rain on Monday or it will not rain on Tuesday. Tom does not like cheesecake. Bob would like to have both a large cat and a small dog as a pet. Bob Saget is not actually very funny. Albert Einstein did not believe in God.

The process of translation starts with determining what the atomic propositions of the sentence are and then using the truth functional connectives to form the compound proposition. Sometimes this will be fairly straightforward and easy to figure out—especially if there is only one truth-functional operator used in the English sentence.

However, many sentences will contain more than one truth-functional operator. Here is an example: Bob will not go to class but will play video games. What are the atomic propositions contained in this English sentence? So if the first statement is a negation, what is the non- negated, atomic statement? That is, it is asserting both of these statements. For example: Bob will not both go to class and play video games. Notice that whereas the earlier sentence asserted that Bob will not go to class, this sentence does not.

Rather, it asserts that Bob will not do both things i. Using the same translations as before, how would we translate this sentence? It should be clear that we cannot use the same translation as before since these two sentences are not saying the same thing.

Thus, our translation must be different. Parentheses are using in formal logic to show groupings. When using multiple operators, you must learn to distinguish which operator is the main operator.

The main operator of a sentence is the one that ranges over influences the whole sentence. In this case, the main operator is the negation, since it influences the truth value of all the rest of the sentence. We can see the need for parentheses in distinguishing these two different translations. Without the use of parentheses, we would have no way to distinguish these two sentences, which clearly have different meanings.

Here is a different example where we must utilize parentheses: Noelle will either feed the dogs or clean her room, but she will not do the dishes. Can you tell how many atomic propositions this sentence contains? Notice that the sentence is definitely not asserting that each of these statements is true. Rather, what we have to do is use these atomic propositions to capture the meaning of the original English sentence using only our truth-functional operators. In this sentence we will actually use all three truth-functional operators disjunction, conjunction, negation.

A well-formed formula is a sentence in our symbolic language that has exactly one interpretation or meaning. However, the translation we have given is ambiguous between two different meanings. It could mean that Noelle will feed the dogs or Noelle will clean her room and not do the dishes.

That statement would be true if Noelle fed the dogs and also did the dishes. The result is that those groupings are connected by a disjunction, which is the main operator of the sentence. But the original sentence could also mean that Noelle will feed the dogs or clean her room and Noelle will not wash the dishes. In contrast with our earlier interpretation, this interpretation would be false if Noelle fed the dogs and did the dishes, since this interpretation asserts that Noelle will not do the dishes as part of a conjunction.

These two grouping are then connected by a conjunction, which is the main operator of this complex sentence. The fact that our initial attempt at the translation without using parentheses yielded an ambiguous sentence shows the need for parentheses to disambiguate the different possibilities. Since our formal language aims at eliminating all ambiguity, we must choose one of the two groupings as the translation of our original English sentence.

So, which grouping accurately captures the original sentence? It is the second translation that accurately captures the meaning of the original English sentence. That sentence clearly asserts that Noelle will not do the dishes and that is what our second translation says. In contrast, the first translation is a sentence that could be true even if Noelle did do the dishes. Given our understanding of the original English sentence, it should not be true under those circumstances since it clearly asserts that Noelle will not do the dishes.

So how can we use the truth functional operators to connect these atomic propositions together to yield a sentence that captures the meaning of the original English sentence?

Again, it is the main operator because it groups together the two main sentence groupings. Consider the sentence: Tom will not wash the dishes and will not help prepare dinner; however, he will vacuum the floor or cut the grass. Step 2: Pick a unique constant to stand for each atomic proposition. Step 3: If the sentence contains more than two atomic propositions, determine which atomic propositions are grouped together and which truth-functional operator connects them.

Step 4: Determine what the main operator of the sentence is i. Step 5: Once your translation is complete, read it back and see if it accurately captures what the original English sentence conveys. Try using these steps to create your own translations of the sentences in exercise 10 below. Exercise Translate the following English sentences into our symbolic language using any of the three truth functional operators i.

Use the constants at the end of each sentence to represent the atomic propositions they are obviously meant for. After you have translated the sentence, identify which truth- functional connective is the main operator of the sentence. Note: not every sentence requires parentheses; a sentence requires parentheses only if it contains more than two atomic propositions. Bob does not know how to fly an airplane or pilot a ship, but he does know how to ride a motorcycle.

Tom does not know how to swim or how to ride a horse. Theresa writes poems, not novels. Bob does not like Sally or Felicia, but he does like Alice. Cricket is not widely played in the United States, but both football and baseball are.

Lansing is east of Grand Rapids but west of Detroit. A, J, E Children should be seen, but not heard. Carla will not have both cake and ice cream. Carla will have neither cake nor ice cream. There are four possible scenarios, and the statement would be true in every one except the first scenario: Carla has cake Carla has ice cream False Carla has cake Carla does not have ice cream True Carla does not have cake Carla has ice cream True Carla does not have cake Carla does not have ice cream True To say that Carla will not have both cake and ice cream allows that she can have one or the other just not both.

It also allows that she can have neither as in the fourth scenario. The negation applies to everything inside the parentheses—i. Thus, again we see the importance of parentheses in our symbolic language. Earlier in section 2. Recall our example: Bob placed either first or second in the race. Using the wedge, we get: FvS However, since the wedge is interpreted as an inclusive or, this statement would allow that Bob got both first and second in the race, which is not possible.

So we need to be able to say that although Bob placed either first or second, he did not place both first and second. So, to be absolutely clear, we are asserting two things: Bob placed either first or second.

This statement might be true if, for example, Carla was on a diet and was sticking to her diet. Using the same method I introduced earlier, we can ask under what conditions the statement would be true or false. Exercise For each of the following, write out what atomic proposition each constant stands for. Then translate the sentences using the constants you have defined. Finally, after you have translated the sentence, identify which truth-functional connective is the main operator of the sentence.

Coral is not both a plant and an animal. Although protozoa and chimpanzees are both eukaryotes, they are not both animals. There are four atomic propositions here; just use A, B, C, and D for each different proposition. Neither chimpanzees nor protozoa are prokaryotes. China has not signed the Kyoto Protocol and neither has the United States. Peter Jennings is either a liar or has a really bad memory.

Peter Jennings is neither a liar nor has a really bad memory. Peter Jennings is both a liar and has a really bad memory. Peter Jennings is not both a liar and a person with a really bad memory.

L, M C, M Mother Theresa may be a saint. Even so, she has not been canonized yet by the Catholic Church. S, C Methods Citations. Results Citations. Topics from this paper. Mental Processes Problem solving Rewrite programming. Trees plant Diagram Evaporation. Citation Type. Has PDF. Publication Type. More Filters. Maturity Models for Systems Thinking.

Recent decades have seen a rapid increase in the complexity of goods, products, and services that society has come to demand. By now it should be clear that the Logical Thinking Process is a system-level problem-solving tool. In other words, we can decide to change those things on our own. Span of control varies for each individual, but it has one common characteristic for everybody: it's extremely limited. It doesn't matter if you're the President of the United States or a company employee - most of what you must deal with on a daily basis is beyond your unilateral control.

Sphere of Influence Sphere of influence is an arbitrary perimeter enclosing those aspects of our lives that we can influence to some degree , even if we can't exercise unilateral control over them. The sphere of influence obviously is substantially larger than the span of control.

Follow the cause-and-effect chain wherever it may lead Use it [sphere of influence] to help you decide for which problems you can reasonably expect effective results and for which attack might be futile. Sometimes people confuse cause and effect with correlation.

It's important to understand the difference between the two, because CRTs with correlations embedded in them are likely to be invalid: They may isolate the wrong root causes, which could cost you time, energy, and resources in trying to solve the wrong problem The difference between correlation and cause and effect is essentially the difference between ho w and why Without knowing why, you'll never know what makes the correlation exist. This means you'll never be sure whether the correlations depends on other variables you haven't identified.

In a problem analysis situation, this could cause you to focus on the wrong problem. It also means that you won't be able to effectively predict future instances of the correlation, because you'll never know whether a key variable is present or not. What is an undesirable effect? Essentially, it's the most prominent indication you have that something might be amiss in a system. An UDE is something that really exists; something that is negative compared with the system's goal, critical success factors, or necessary conditions You might be aware of several UDEs.

Or you might just notice one. In a complex system, there will probably be several. But you can start a CRT with as few as one. UDEs are only the most visible results of much more complex interactions and processes, but like a gopher hole in a perfectly manicured lawn, they're the "gateway" to finding the real underlying problem.

If you choose the wrong gateway, you won't find the right problem In building a Current Reality Tree, we work our way from UDEs back through the chain of cause and effect to root causes.

The root cause is the beginning of the cause-effect relationship. There may be several intermediate effects and causes between the root cause and the UDE But when you've worked your way down to a cause and you just can't go any farther, you're at a root cause There's no point in working on something over which you don't have at least some influence.