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be able to recognize the validity of some fairly complex deductive arguments. # **Practice Problems: Recognizing Propositional Patterns Determine if each statement below —taken as a whole —is a simple statement, negation, conjunction, disjunction, or conditional. Then determine the statement’s truth value (each proper name refers to well known places; don’t assume the statement refers to l ittle-known places with names similar to better-known locations). 1. Either Nicaragua is in Central America or Germany is in Europe. 2. Both France and Paraguay are in Asia. 3. If Bolivia is in South America, then Tahiti is in the South Pacific. 4. Greenland is in the Middle East or Ukraine is in Central America. 5. It is false that Denmark is in Africa. 6. Algeria is in North America, but Guatemala is in Central America. 7. It is false that Brazil is in South America. 8. China is in Asia. 9. India is north of South Africa or it is false that the USA is south of Canada. 10. It is false that both Holland and Spain are in Central America. 11. It is not the case that either Congo or Angola is in Africa. 12. Russia is larger than Spain, if Japan is smaller than Mexico. 13. If it is false that Spain is near Portugal, then Uruguay is in South America. 14. Either Ecuador and Namibia are in Asia, or Iran is in the Middle East. 15. Both El Salvador and Venezuela are in the Western Hemisphere, or Turkey is in the Western Hemisphere. Answers: 1. Disjunction, true 2. Conjunction, false 122 3. Conditional, true 4. Disjunction, false 5. Negation, true 6. Conjunction, false 7. Negation, false 8. Simple statement, true 9. Disjunction, true 10. Negation (i.e., a negated conjunction), true 11. Negation (i.e., a negated disjunction), false 12. Conditional,
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true 13. Conditional, true 14. Disjunction, true 15. Disjunction, true # Symbolization Although we are not covering symbolic logic in Critical Thinking, it may be of interest to some students how logicians can make our lives easier by abbreviating propositional statements even further. Since we are not covering this in Critical Thinking, we’ll look at translating English into contemporary symbolic logic very quickly. Feel free to pass over this section, as it will not be required for this course. We’ll translate here simple statements, negations, conjunctions, disjunctions, and conditionals with symbols, or operators , commonly used by logicians today. English statement Translation into symbolic logic Operator Cats rule. CIt is false that cats rule. ~C tilde Cats rule and dogs drool. C • D dot Cats rule or dogs drool. C v D wedge If cats rule, then dogs drool. C D horseshoe Translation into symbolic logic makes writing and working with propositional statements much easier and quicker. English can be messy, but symbolic logic has a clarity and precision that many people enjoy. Consider the following more complex examples, where we use parentheses (and brackets and then braces, if needed) to disambiguate the statement’s meaning. If there is a need for more than one operator (as below), the main operator is the symbol that tells us what kind of statement the statement is as a whole. Thus the main operator of a negation will be the tilde, for a conjunction it’s the dot, for a disjunction it’s the wedge, and for conditionals it’s the horseshoe. To be more precise, the main operator has the largest range (or scope ), covering more of the statement than any ot her of the statement’s operators. First, let’s look at some examples of symbolic translations: 1. Al and Bob like apples, or
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Charlie does. (A • B) v C 2. Al or Bob like apples, and Charlie does. (A v B) • C 3. It is false that if Sue likes strawberries then Betty likes blueberries. ~(S B) 4. If it is false that Sue like strawberries, then Betty likes blueberries. ~S B123 5. It is not the case that either Juan or Vic likes oranges. ~(J v V) 6. Not both June and Kelly like prunes. ~(J • K) 7. If Gene is not grand, then Wally is not wonderful. ~G ~W 8. If both Lou and Don like pears, then either Sally or Tracy likes apricots. (L • D) (S v T) 9. Either Abdul likes artichokes, or if Sasha likes salmon then Tran does not like tuna. A v (S ~T) 10. If Naomi does not like nan, then Petra likes pita and Stu doesn’t like sourdough. ~N (P • ~S) The range consists of that part of the statement that the operator is acting upon (including itself). Consider the following statement: ~(N v B) AThe range of the wedge is underlined here: ~(N v B) AThe range of the tilde is underlined here: ~(N v B) AAnd here we underline the range of the horseshoe: ~(N v B) A The horseshoe’s range includes itself, plus its full antecedent (i.e., ~(N v B) ) and consequent (i.e., A). Since the horseshoe has the largest range, it’s the main operator of the full statement, and that makes the statement as a whole a conditional. Once more in life, size matters. # **Practice Problems: Main Operators Consider the ten translations above, and determine the main operator for reach. Answers: 1. wedge 6. tilde 2. dot 7. horseshoe 3. tilde 8. horseshoe
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4. horseshoe 9. wedge 5. tilde 10. horseshoe # **Practice Problems: Translating into Symbolic Logic Translate the following English statements into the language of propositional symbolic logic. Use the upper-case letters provided for simple statements. 1. Carl is from Canada and Bob is from Bolivia. (CB) 2. Paulo is not from Panama or Angie is from Argentina. (PA) 3. If Frank is from France, then Gerald is German. (FG) 4. Bart is British, and either Sandy is Spanish or Paula is Portuguese. (BSP) 5. Arnold is from Angola and Mandy is not from Mali, if Patty is from Paraguay. (AMP) 6. It is false that either Carlisle is Cuban or Tran is Tahitian, and Parisa is Peruvian. (CTP) 7. Isaac is from Israel, if it’s the case that both Huy is Hungarian and Adaishewa is not from Albania. (IHA) 8. Tuan is Thai or it is false that Murtaza is Mongolian, or Simeon is not from Sudan. (TMS) 124 9. It is false that both Terrie is not from Togo and Gamani is from Ghana, or Ben is from Benin. (TGB) 10. Julia is Jordanian, if Mark is Malaysian and Inez is not from India. (JMI) Answers: 1. C • B 6. ~(C v T) • P 2. ~P v A 7. ~(H • ~A) I3. F G 8. (T v ~M) v ~S 4. B • (S v P) 9. ~ (~T • G) v B 5. P (A • ~M) 10. (M • ~I) J # Valid Argument Patterns Now that we are familiar with the patterns of some basic propositional statements, we can begin to examine propositional argument patterns. There are a small number that are so common, they have names. Most are wonderfully intuitive and easy to see, but it takes a
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moment to slow down and develop some precision with them. Our goal is to become familiar enough with these patterns that we can reco gnize when an argument is valid. We’ll limit ourselves to becoming familiar with eight common patterns of valid inference. # Modus Ponens A simple one is called Modus Ponens , which is Latin for “the Affirming Mode.” It has the following pattern (the three dots aligned in a pyramid is a common way of indicating the conclusion of an argument): If A, then B A BThe order of the two premises does not matter, as the following is Modus Ponens, too: AIf A, then B BIt is not really possible to prove that this is a valid inference, as it’s so simple and basic. But it confuses no one. If A is true, then B has to be true; and A is true. Thus, B is guaranteed to be true. It does not matter what statements A and B stand for; if the premises are true, then the conclusion is certain. Of course, one or more of the premises might be false, but that would make the valid argument unsound. All we are doing here, though, is recognizing valid arguments to be indeed valid. Here are some examples of Modus Ponens in full English: 125 If Ichiro played for the Seattle Mariners, then Ichiro played baseball. Ichiro played for the Seattle Mariners. Thus, Ichiro played baseball. Barack Obama is the U.S. president. If Barack Obama is the U.S. president, then Barack Obama is a politician. Therefore, Barack Obama is a politician. Modus Ponens is a pattern, so technically it can be illustrated using all sorts of things besides statements or upper-case letters. For example: If #, then $ If Ψ, then Φ If ☺,
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then ☼ ◊ A B# Ψ ☺ If ◊, then □ A $ Φ ☼ □ B It’s just a pattern. # Modus Tollens Another common pattern is called Modus Tollens (Latin: “the denying mode”), and it look ssomewhat similar to Modus Ponens: If A, then B Not-B Not-A For Modus Tollens, we have a conditional ( If A, then B ), but then state that its consequent ( B) is false. From those two claims (the order in which they appear is irrelevant), we may confidently conclude that the antecedent ( A) is false. Here are some English instances of Modus Tollens: If it’s raining , then the ground is wet. The ground is not wet. Thus, it’s not raining .If Hong Kong is in Oregon, then Hong Kong is in the USA. But Hong Kong is not in the USA. Hence, Hong Kong is not in Oregon. It is false that Yogi [the cartoon bear] is a fish. If Yogi is a salmon, then Yogi is a fish. Thus, it is not the case that Yogi is a salmon. If President Barack Obama pitches for the Seattle Mariners, then he is a baseball player. But President Obama is not a baseball player. Therefore, he does not pitch for the Seattle Mariners. 126 Technically speaking, the following three valid inferences are not examples of Modus Tollens, as they do not precisely match the Modus Tollens pattern: If A, then not-B Not-R If not-O, then not-Y B If not-D, then R Y Not-A D OAgain, to be picky —and there’s little in life as picky as deductive logic— Modus Tollens makes use of two claims: one is a conditional, and the other is the negation of the consequent of that
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conditional; fr om these two we derive the negation of the conditional’s antecedent. For those who are beginning to like the symbolic approach, Modus Tollens looks like this symbolically: P Q ~~K ~A B K ~J ~Q L ~K ~B ~~J ~P ~L ~~A ~K Recall that there are two formal fallacies that look like Modus Ponens and Modus Tollens. Review the differences here, as two are valid lines of inference, while the other two are invalid formal fallacies. Modus Ponens ☺ Affirming the Consequent ?? Modus Tollens ☺ Denying the Antecedent ?? If P, then O If P, then O If P, then O If P, then O P O Not-O Not-P O P Not-P Not-O # Disjunctive Syllogism Disjunctive Syllogism is another common deductive pattern that produces a valid argument. A Disjunctive Syllogism is made up of two premises: a disjunction and the negation of one of the disjuncts. From those two statements we are guaranteed that the other disjunct is true. For instance: A or B Either R or Y Not-K Not-L or not-Q Not-not-not-M Not-A Not-Y K or W Not-not-L H or not-not-M B R W Not-Q HEnglish examples include: * Either Obama is a Republican or he is a Democrat. But he’s not a Republican. Thus, he’s a Democrat. * Either Lady Gaga is not a singer or she is dancer. But it is false that she is not a singer. Hence, she is dancer. 127 * I’m going to study for the test. For either I study for the test or I’ll fail the thing, and I don’t want to fail the thing. For those who are interested, Disjunctive Syllogism would look symbolically like this: P v
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O ~I ~A v ~Q ~~~~~K A v (H • M) ~P H v I ~~A ~~~~K v P ~A O H ~Q P H • M # Hypothetical Syllogism Hypothetical Syllogism is a pattern consisting of two premises, both of which are conditionals. It is required, though, that the two conditionals “match up kitty-corner.” That is, the antecedent of one must be exactly the same as the consequent of the other. If so, we can conclude with a third conditional. We argue this way all the time. For instance: If Yogi is a bear, then Yogi is a mammal. If Yogi is a mammal, then Yogi is an animal. Thus, if Yogi is a bear, then Yogi is an animal. Notice how “Yogi is a bear” matches up “kitty -corner” in the premises. The pattern would still be Hypothetical Syllogism if the premises are exchanged: If Yogi is a mammal, then Yogi is an animal. If Yogi is a bear, then Yogi is a mammal. Thus, if Yogi is a bear, then Yogi is an animal. The following are abbreviated examples of Hypothetical Syllogism: If J, then L If not-U, then K If G, then V A BIf L, then B If K, then W If not-P, then G B C If J, then B If not-U, then W If not-P, then V A C # **Practice Problems: Recognizing Propositional Patterns For each abbreviated argument below, determine if it’s a precise example of Modus Ponens, Modus Tollens, Disjunctive Syllogism, or Hypothetical Syllogism. Or is it something else? 1. If E, then K Not-K Not-E 2. J or Y Not-Y J3. If M, then V 128 If V, then J If M, then J 4. P
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If P, then D D5. If N, then O Not-N Not-O 6. Not-H H or T T7. If not-Q, then K Not-Q K8. If A, then X X A9. If not-I, then H If not-U, then not-I If not-U, then H 10. If A, then S If A, then J If S, then J Answers: 1. Modus Tollens 2. Disjunctive Syllogism 3. Hypothetical Syllogism 4. Modus Ponens 5. Something else (it’s the invalid formal fallacy Denying the Antecedent) 6. Disjunctive Syllogism 7. Modus Ponens 8. Something else (it’s the invalid formal fallacy Affirming the Consequent) 9. Hypothetical Syllogism 10. Something else (it’s an unnamed invalid inference) # Assessing Arguments Let’s now do something with our knowledge of these four propositional logic patterns. We’re going to introduce a technique called natural deduction . This technique is a way of proving that valid arguments are indeed valid. We’ll not look at the full system (you can do that in Symbolic Logic, i.e., PHIL& 120), but we’ll get a taste of it here, and focus on the basic sort of argumentation we’re likely to run into in ordinary, work aday situations. 129 We’ll here work only with valid arguments. We’ll also write them a little differently. Consider the following argument: If Angie is from Albania, then Katie is not from Kenya. Angie is indeed from Albania. Katie is from Kenya or Phillip is from the Philippines. It follows that Phillip is from the Philippines. We can abbreviate this argument as follows, lining the premises up vertically, and placing the conclusion to the right of the last premise, after a slash: 1. If A, then not-K 2. A 3. K or P / P In natural deduction we use valid patterns of logic to deduce, or infer,
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the conclusion. Recall that with valid arguments, the truth of the premises will guarantee that the conclusion is true. So, if we can “get” the conclusion from the premises, we’ll have shown that the premises guarantee the truth of the conclusion, and that the argument is valid. To do this, we look at the premises and see if we can find any logical move to make. That is, can we see the possibility of applying any of the propositional patterns we have learned so far? Yes! If we focus on lines 1 and 2, we see that they form the Modus Ponens pattern, and they give us Not-K. So let’s write that down, justifying the newly acquired statement by appealing to the lines used and the pattern (or “rule”) we used. Just so we don’t have to write down the complete name of pattern s, let’s refer to Modus Ponens as MP , to Modus Tollens as MT , to Disjunctive Syllogism as DS , and to Hypothetical Syllogism as HS .1. If A, then not-K 2. A 3. K or P / P 4. Not-K 1, 2 MP We’ve yet to get the co nclusion , so we’ve yet to prove this argument to be valid. But let’s continue. We now have four lines available to us. Do we see another pattern we can use (or an additional use of MP)? Yes! We can use lines 3 and 4 with DS to get P, our conclusion! For those who are interested, to the right is the same proof using symbolic logic (it’s not much different, just simpler). 1. If A, then not-K 1. A ~K 2. A 2. A 3. K or P / P 3. K v P / P 4. Not-K 1, 2 MP 4. ~K
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1, 2 MP 5. P 3, 4 DS 5. P 3, 4 DS Once we deduce (or “get”) the conclusion, we’ re done! We have shown that if the premises are true, then the conclusion must be true. The argument is therefore valid .130 Here’s another example that’s already abbreviated (with another example of how such a deduction would look using symbolic logic): 1. A or D 1. A v D 2. If A, then M 2. A M3. Not-M / D 3. ~M / D 4. Not-A 2, 3 MT 4. ~A 2, 3 MT 5. D 1, 4 DS 5. D 1, 4 DS We begin here by seeing that lines 3 and 4 fit the Modus Tollens pattern, so we use MT to get Not-A . That’s not the conclusion, so we trundle forward. Scanning all four lines at that point, we see that lines 1 and 4 fit the Disjunctive Syllogism pattern, so we use DS to get D, which is the conclusion. We are then finished, and we’ve shown the argument to be valid. Here’s one more example. 1. If A, then not-G 2. If not-G, then K 3. If K, then either O or B / If A, then either O or B 4. If A, then K 1, 2 HS 5. If A, then either O or B 3, 4 HS We began by seeing that lines 1 and 2 fit the Hypothetical Syllogism pattern to give us line 4: If A, then K . We then saw that the consequent of line 4 matched up with the antecedent of line 3, providing us another opportunity to use Hypothetical Syllogism, this time to give us the conclusion. Some deductions (or proofs ) take one or two steps, but others can take much
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longer. It all depends on how complex the argument is and how many patterns we have at our disposal. If we learned an infinite number of patterns, each deduction would take only one step. But who wants to learn that many patterns? If we learn only a small number of patterns, many of the deductions will be quite long and difficult. That doesn’t sound very good, ei ther. So, for our introductory purposes, we’ll learn a small number (we’ll examine only four more) and keep the deductions reasonably short. # **Practice Problems: Deductions Using the First Four Patterns Use the first four propositional patterns and natural deduction to prove the following arguments to be valid. 1. 1. If A, then if B then C 2. B 3. A / C 2. 1. D or not-H 131 2. L and K 3. If both L and K, then not-D / Not-H 3. 1. If A, then G 2. If not-A, then M 3. Not-G / M 4. 1. If D, then C 2. If it is the case that if D then N, then F 3. If C, then N / F 5. 1. Not-Q 2. If R, then Q 3. If not-R, then if A then Q / Not-A 6. 1. G, or B or M 2. Not-B 3. If A, then not-G 4. A / M 7. 1. If M, then if N then O 2. If P, then if O then S 3. M 4. P / If N, then S 8. 1. If N, then B 2. N 3. If B, then not-Q 4. Q or A / A 9. 1. G or S 2. If A, then B or M 3. Not-B 4. A 5. If M, then not-G / S 10. 1. If B, then
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Q 2. Not-A 3. Not-Q 4. If F, then A 5. F, or if not-B then D / D Answers: 1. 1. If A, then if B then C 2. B 132 3. A / C 4. If B, then C 1, 3 MP 5. C 2, 4 MP 2. 1. D or not-H 2. L and K 3. If both L and K, then not-D / Not-H 4. Not-D 2, 3 MP 5. Not-H 1, 4 DS 3. 1. If A, then G 2. If not-A, then M 3. Not-G / M 4. Not-A 1, 3 MT 5. M 2, 4 MP 4. 1. If D, then C 2. If it is the case that if D then N, then F 3. If C, then N / F 4. If D, then N 1, 3 HS 5. F 2, 4 MP 5. 1. Not-Q 2. If R, then Q 3. If not-R, then if A then Q / Not-A 4. Not-R 1, 2 MT 5. If A, then Q 3, 4 MP 6. Not-A 1, 5 MT 6. 1. G, or B or M 2. Not-B 3. If A, then not-G 4. A / M 5. Not-G 3, 4 MP 6. B or M 1, 5 DS 7. M 2, 6 DS 7. 1. If M, then if N then O 2. If P, then if O then S 3. M 4. P / If N, then S 5. If N, then O 1, 3 MP 6. If O, then S 2, 4 MP 7. If N, then S 5, 6 HS 133 8. 1. If N, then B 2. N 3. If B, then not-Q 4. Q or A / A 5. B 1, 2 MP 6. Not-Q 3, 5 MP 7. A 4, 6 DS 9. 1.
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G or S 2. If A, then B or M 3. Not-B 4. A 5. If M, then not-G / S 6. B or M 2, 4 MP 7. M 3, 6 DS 8. Not-G 5, 7 MP 9. S 1, 8 DS 10. 1. If B, then Q 2. Not-A 3. Not-Q 4. If F, then A 5. F, or if not-B then D / D 6. Not-B 1, 3 MT 7. Not-F 2, 4 MT 8. If not-B, then D 5, 7 DS 9. D 6, 8 MP # Simplification We’ll now look at four more propositional patterns. Two are super easy, one is weird, and one is a mild pain in the neck. Simplification (abbreviated as Simp ) is one of the easy ones. What Simplification says is if a conjunction is true, then each conjunct is true by itself. This is another case where talking about it makes it sound more complicated than it is. Here’s what Simplification can do: Mark is a medic and Mark is an athlete. Thus, Mark is a medic. Or Mark is a medic and Mark is an athlete. Thus, Mark is an athlete. Obviously, if Mark is both a medic and an athlete, then he’s a medic…or an athlete. 134 The pattern is so simple that it’s hard to come up with a variety of illustrations of its use. But here are some: A and G A and G Not-T and K Not-R and either H or E L, and B and W A G Not-T H or E B and W If you have a conjunction, you can think of the two conjuncts as two pieces of ripe fruit ready to be plucked. Simplification makes a somewhat complex conjunction simpler by reducing it to
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one of its conjuncts. Simplification can now be added to our growing list of patterns used in natural deduction. 1. A and G 1. N or J 2. If A, then G / G 2. Not-N and G 3. A 1 Simp 3. If J, then Q / Q 4. G 2, 3 MP 4. Not-N 2 Simp 5. J 1, 4 DS 6. Q 3, 5 MP # Conjunction Conjunction is another easy pattern to recognize. Conjunction ( Conj for short) says that if you know any two statements to be true, then they are both true. That may seem way too obvious, but it’s an important pattern in logic. Here’s how it can work: * Canada is north of the USA. The USA is north of Mexico. Thus, Canada is north of the USA, and the USA is north of Mexico. * Theresa is tall. Theresa is a logician. Thus, Theresa is tall and Theresa is a logician. * Theresa is tall. Theresa is a logician. Thus, Theresa is a logician and Theresa is tall. We might abbreviate the second argument above this way: TL T and L The individual statements can be simple or compound (with a complex symbolic example thrown in for those relishing such things): K or B If J, then Y A • (B v ~O) If G, then B If not-P, then D ~H L K or B, and if G then B If J then Y, and if not-P then D [A • (B v ~O)] • (~H L) Here are two natural deduction proofs using Conjunction: 1. If both A and B, then C 1. K and G 135 2. A 2. Not-L and E / K and not-L 3. B / B and C
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3. K 1 Simp 4. A and B 2, 3 Conj 4. Not-L 2 Simp 5. C 1, 4 MP 5. K and not-L 3, 4 Conj 6. B and C 3, 5 Conj # Addition This pattern may feel like cheating. Addition allows you to take any complete statement, and add any other statement to it to make a disjunction. Examples include: A G U If P, then N Not-Y A or B G or not-G U or U If P then N, or not-J Not-Y or E In English, this might look like this: Dogs are animals. Thus, dogs are animals or whales fly though the air with pink wings. As long as the first statement is true (and it is here), then it really does not matter what statement (true or false) we add to it; the disjunction as a whole will be true. Here are examples of using Addition ( Add for short) in natural deduction. 1. K 1. If A, then B 2. If either K or G, then P / P 2. A / B or W 3. K or G 1 Add 3. B 1, 2 MP 4. P 2, 3 MP 4. B or W 3 Add 1. Not-J 1. ~K • Z 2. If either not-J or not-M, then Q 2. (~K v R) ~O 3. If Q, then P / P, or both Y and E 3. O v (K v H) / (H v I) v ~P 4. Not-J or not-M 1 Add 4. ~K 1 Simp 5. Q 2, 4 MP 5. ~K v R 4 Add 6. P 3, 5 MP 6. ~O 2, 5 MT 7. P, or both Y and E 6 Add 7. K v H 3, 6
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DS 8. H 4, 7 DS 9. H v I 8 Add 10. (H v I) v ~P 9 Add # Constructive Dilemma Well, one had to be the worst, and here it may be: Constructive Dilemma (CD for short). This pattern appeals to three statements to make an inference. Two are conditionals, and one is a disjunction made up of the antecedents of the two conditionals. What we can infer from this mess is another disjunction made up of the consequents of the two conditionals. Maybe looking 136 at some abbreviated examples will make more sense than verbally trying to describe it (the order of the three premises is irrelevant, of course). Let’s also give those growing nu mber of symbolic logic fans a peek at how Constructive Dilemma can look. If P, then Q Not-L or G P QIf R, then S If not-L, then D R SP or R If G, then not-K P v R Q or S D or not-K Q v S Perhaps two English examples might help? If I eat go od food, then I’ll be healthy. If Joe studies tonight, then he’ll pass the test. If I eat junk food, I’ll be unhealthy. If Joe plays games tonight, then he’ll have fun. Either I’ ll eat good food or junk food. Joe is either going to study or play games tonight. Thus, I’ll e ither be healthy or unhealthy. Thus, Joe will either pass the test or have fun. Here’s how Construct ive Dilemma might show up in a natural deduction proof: 1. If K then Y, and if J then B 1. If M, then B 2. K or J / Y or B 2. M or H 3. If K, then Y 1 Simp 3. If
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H, then Q 4. If J, then B 1 Simp 4. If B or Q, then A and E / E or W 5. Y or B 2, 3, 4 CD 5. B or Q 1, 2, 3 CD 6. A and E 4, 5 MP 7. E 6 Simp 8. E or W 7 Add # **Practice Problems: Natural Deduction Use the eight propositional patterns and natural deduction to prove that each of the following arguments is valid. [We’ll give the last beefy problem to those who have embraced th e optional joys of symbolic logic.] 1. 1. Not-Z, and either H or W 2. If H, then Y 3. If W, then Z / Y or Z 2. 1. A and not-P 2. B and J / A and J 3. 1. L and Q 2. K and not-W 3. If both Q and K, then D / D 4. 1. If M then B, and P 2. If S, then I 137 3. S or M / I or P 5. 1. A 2. If either A or B, then S / S 6. 1. Not-G 2. G or not-D 3. If F, then D / Not-F 7. 1. T, and M or S 2. If T, then not-M / T and S 8. 1. If not-A, then B 2. Not-A or D 3. If D, then H / B or H, or not-M 9. 1. Not-B 2. H 3. If both not-B and H, then either B or N / N 10. 1. If A, then G 2. If it’s the case that if A then not-R, then it’s the case that if F then G 3. If G, then not-R / If F, then not-R 11. 1. If B then G, and F 2. M
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and S, and if A then D 3. B or A / G or D 12. 1. E and F 2. S 3. If both S and F, then H / H or not-F 13. 1. If L, then J 2. Not-J 3. L or O 4. If O, then either J or M / M and not-J, or J 14. 1. It is false that either A or B 2. A / Z 15. 1. A 2. S 3. If both A and S, then P / P and S 16. 1. Not-D and R 138 2. D or L 3. If L, then S / S and R, or not-L 17. 1. If G, then H 2. Not-H and M 3. If both not-G and M, then either H or P / P 18. 1. If R then S, and if S then not-D 2. If it’s the case that if R then not-D, then R 3. D, or if S then M / If R then M, or if M then R 19. 1. A and not-C 2. If A, then C or not-D 3. If F, then D / Not-F or not-A, and A 20. 1. Not-A and not-I 2. If not-Q, then A 3. If not-A, then X 4. If both X and not-not-Q, then K / K and not-I 21. 1. (R • P) (Q v I) 2. (~Q v A) R3. (~Q v J) P 4. ~Q • N / [I • (~Q v A)] v (P I) Answers: 1. 1. Not-Z, and H or W 2. If H, then Y 3. If W, then Z / Y or Z 4. H or W 1 Simp 5. Y or Z 2, 3, 4 CD 2. 1. A and not-P 2.
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B and J / A and J 3. A 1 Simp 4. J 2 Simp 5. A and J 3, 4 Conj 3. 1. L and Q 2. K and not-W 3. If both Q and K, then D / D 4. Q 1 Simp 5. K 2 Simp 6. Q and K 4, 5 Conj 7. D 3, 6 MP 139 4. 1. If M then B, and P 2. If S, then I 3. S or M / I or B 4. If M, then B 1 Simp 5. I or P 2, 3, 4 CD 5. 1. A 2. If either A or B, then S / S 3. A or B 1 Add 4. S 2, 3 MP 6. 1. Not-G 2. G or not-D 3. If F, then D / Not-F 4. Not-D 1, 2 DS 5. Not-F 3, 4 MT 7. 1. T, and M or S 2. If T, then not-M / T and S 3. T 1 Simp 4. M or S 1 Simp 5. Not-M 2, 3 MP 6. S 4, 5 DS 7. T and S 3, 6 Conj 8. 1. If not-A, then B 2. Not-A or D 3. If D, then H / B or H, or not-M 4. B or H 1, 2, 3 CD 5. B or H, or not-M 4 Add 9. 1. Not-B 2. H 3. If both not-B and H, then either B or N / N 4. Not-B and H 1, 2 Conj 5. B or N 3, 4 MP 6. N 1, 5 DS 10. 1. If A, then G 2. If it’s the case that if A then not-R, then it’s the case that if F then G 3. If G, then not-R / If F, then not-R 4. If
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A, then not-R 1, 3 HS 5. If F, then G 2, 4 MP 6. If F, then not-R 3, 5 HS 140 11. 1. If B then G, and F 2. M and S, and if A then D 3. B or A / G or D 4. If B, then G 1 Simp 5. If A, then D 2 Simp 6. G or D 3, 4, 5 CD 12. 1. E and F 2. S 3. If both S and F, then H / H or not-F 4. F 1 Simp 5. S and F 2, 4 Conj 6. H 3, 5 MP 7. H or not-F 6 Add 13. 1. If L, then J 2. Not-J 3. L or O 4. If O, then either J or M / M and not-J, or J 5. Not-L 1, 2 MT 6. O 3, 5 DS 7. J or M 4, 6 MP 8. M 2, 7 DS 9. M and not-J 2, 8 Conj 10. M and not-J, or J 9 Add 14. 1. It is false that either A or B 2. A / Z 3. A or B 2 Add 4. A or B, or Z 3 Add 5. Z 1, 4 DS 15. 1. A 2. S 3. If both A and S, then P / P and S 4. A and S 1, 2 Conj 5. P 3, 4 MP 6. P and S 2, 5 Conj 16. 1. Not-D and R 2. D or L 3. If L, then S / S and R, or not-L 4. Not-D 1 Simp 5. L 2, 4 DS 141 6. S 3, 5 MP 7. R 1 Simp 8. S and R 6, 7 Conj 9. S and R, or not-L 8 Add 17. 1. If
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G, then H 2. Not-H and M 3. If both not-G and M, then either H or P / P 4. Not-H 2 Simp 5. Not-G 1, 4 MT 6. M 2 Simp 7. Not-G and M 5, 6 Conj 8. H or P 3, 7 MP 9. P 4, 8 DS 18. 1. If R then S, and if S then not-D 2. If it’s the case that if R then not-D, then R 3. D, or if S then M / If R then M, or if M then R 4. If R, then S 1 Simp 5. If S, then not-D 1 Simp 6. If R, then not-D 4, 5 HS 7. R 2, 6 MP 8. Not-D 6, 7 MP 9. If S, then M 3, 8 DS 10. If R, then M 4, 9 HS 11. If R then M, or if M then R 10 Add 19. 1. A and not-C 2. If A, then C or not-D 3. If F, then D / Not-F or not-A, and A 4. A 1 Simp 5. C or not-D 2, 4 MP 6. Not-C 1 Simp 7. Not-D 5, 6 DS 8. Not-F 3, 7 MT 9. Not-F or not-A 8 Add 10. Not-F or not-A, and A 4, 9 Conj 20. 1. Not-A and not-I 2. If not-Q, then A 3. If not-A, then X 4. If both X and not-not-Q, then K / K and not-I 5. Not-A 1 Simp 6. X 3, 5 MP 7. Not-not-Q 2, 5 MT 142 8. X and not-not-Q 6, 7 Conj 9. K 4, 8 MP 10. Not-I 1 Simp 11. K and not-I 9, 10 Conj 21. 1. (R • P) (Q v I) 2. (~Q v A) R3. (~Q v J) P 4.
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~Q • N / [I • (~Q v A)] v (P I) 5. ~Q 4 Simp 6. ~Q v A 5 Add 7. ~Q v J 5 Add 8. R 2, 6 MP 9. P 3, 7 MP 10. R • P 8, 9 Conj 11. Q v I 1, 10 MP 12. I 5, 11 DS 13. I • (~Q v A) 6, 12 Conj 14. [I • (~Q v A)] v (P I) 13 Add 143 # Chapter 11: Causal Arguments We have looked briefly at causal arguments twice in this text. We first met them as a pattern of inductive argumentation. Secondly, we saw them in False Cause and Slippery Slope informal fallacies. Now it’s time to look at causal argumentation more closely, and to see how one might reason well in drawing a conclusion about the cause of an event. # Necessary and Sufficient Causes First, we need to be aware of some different kinds of spatio-temporal causation. Philosophers and scientists often appeal to two kinds of causes in particular: necessary and sufficient. A necessary cause is a state of affairs that is needed for another state of affairs to take place. Without the necessary cause, the second event will not take place. For instance, oxygen is necessary (i.e., needed) for a match to catch fire, but it is not sufficient. The match can be surrounded by oxygen, but still not catch fire. However, the match needs oxygen to catch fire. Other examples of necessary causes include the following: * Water is a necessary cause of plant health. * Force is needed for a coiled spring to be lengthened. * Paint is needed for an artist to paint a portrait. * Laborers are needed for farm crops to be harvested. * Fertilization is necessary
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for pregnancy to occur. * People need air to live. * Having power will cause a radio to play. A sufficient cause is a state of affairs that is enough for another state of affairs to take place. There may be more than one factor that can cause an event to take place, but a sufficient cause is one of them. If a man is thirsty, water is usually enough to quench his thirst. He does not need water, as other liquids might do the job. Water is thus a sufficient —but not a necessary —cause for quenching a man’s thirst. Other examples of sufficient causes include: * Placing a loaf of bread in one’s home freezer will cause that loaf of bread to freeze. * Heating a pot of broth on a very hot stove is sufficient to boil the broth. * Exercising more and eating less is enough to lose weight. * Breaking a leg playing football is enough to make someone injured. * Eating cheesecake will give most logic instructors pleasure. * Having a billion dollars causes a person to be financially rich. * Dropping a radio from a high-flying airplane will cause the radio to break. * Lack of gasoline is a sufficient cause of a car not running. If a causal relation is claimed —as in “C causes E”— then ask if C is needed or merely enough for E to take place. If the former, then C is a necessary cause of E; if the latter, then C is a sufficient cause of E. 144 Some causes are both necessary and sufficient for something to obtain (that is, to be the case as an event, occurrence, or state of affairs). For example, a logic instructor might say, “Our only course assignments are three tests.
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To get an A in this course, you will need to get an A on those three tests. Moreover, getting an A on those three tests is enough to guarantee that you ’d get an A in the course, regardless of what else you may or may not do here. ” This instructor is outlining the necessary and sufficient causes for getting an A in his class. Getting As on all three tests is — he claims —both needed and enough to get an A for the course. The topic of causality can be vastly complex, and philosophers, scientists, doctors, and others are still looking into it. A paleontologist may want to know what caused a dinosaur to die; an epidemiologist may want to know what is causing a skin irritation; a sociologist may want to know what causes a culture to adopt a ritual; an environmental activist may want to know how best to cause people to use automobiles less. Some of this discussion hinges on what we mean by cause . Necessary and sufficient causes are often relevant, but a full discussion can hardly stop there. Contributory causes may be neither necessary nor sufficient, but causally relevant to a state of affairs obtaining. For instance, eating leafy greens —nutritionists tell us —in some sense causes bodily health. Yet leafy greens are not necessary for such health (there are people in the world who are healthy but who have no or little access to leafy greens), nor are they sufficient (you can have all the leafy greens imaginable, but still be unhealthy because you lack other important foods). Australian philosopher J. L. Mackie (1917 –1981) provides a more complex analysis of causation. In The Cement of the Universe: A Study of Causation (Oxford: Oxford University Press, 1980) he refers
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to INUS conditions . Mackie argues that what most of us have referred to as necessary or sufficient causes are often a combination, or plurality, of causes. An effect, he holds, can be produced by a variety of distinct groups of factors. Each group is sufficient to cause the effect, but no particular group is itself necessary to do so. Normal events like a house catching fire, the initiation of a street riot, the learning of a new language, or the hitting of a baseball with a bat involve complex causal relations. An event E is caused not by one specific event A, but more likely by a group of conjoined events A+B+C+D. But, Mackie continues, E might also have been caused by a different set of conjoined causal factors: G+H+I or H+A+K+L. One can be guilty of the informal fallacy of False Cause if one “oversimplifies” a complex causal relationship issue by saying that E was caused by one specific causal factor (e.g., A). Mackie refers to each individual factor of any group of causal factors as an INUS condition for E. The acronym refers to his description of an INUS condition as an insufficient but nonredundant part of an unnecessary but sufficient condition for E. He illustrates his meaning with a house fire caused (in part) by a short circuit. The short circuit is insufficient by itself, since it alone would not have started the fire. The short circuit was nonredundant (or needed) in the group of causal factors, however, as without it, the other factors would not have been enough to initiate the fire. The set of factors that includes the short circuit is together sufficient to start the fire, but unnecessary , as some other group of factors (e.g., ones involving lightning or an arsonist) could
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account for the blaze. 145 Classes in Metaphysics (the philosophical study of the ultimate nature of reality) and Philosophy of Science are probably the best places to tackle the intricate field of causation fully. For our purposes here, we’ll limit our inquiry to necessary and sufficient causes. # **Practice Problems: Necessary and Sufficient Causes Are the following causes necessary only, sufficient only, both necessary and sufficient, or neither necessary nor sufficient for the state of affairs noted to obtain? Imagine ordinary circumstances for each case. 1. A large rock thrown through a window causes the window to break. 2. Diesel fuel causes Bob’s diesel truck to run. 3. Hitting someone’s leg with a small marshmallow causes her leg to be injured. 4. Getting the stomach flu causes one to feel poorly. 5. A rise in temperature will cause the mercury to rise in a thermometer. 6. Covering a campfire with dirt will cause it to go out. 7. Natural or artificial sunlight will cause photosynthesis to take place in plants. 8. Placing blue litmus paper in acid will cause the paper to turn red. 9. An ordinary lamp must have a bulb for the light to shine. 10. Eating five large hamburgers will cause a hungry person to feel full. Answers: 1. Sufficient only 6. Sufficient only 2. Necessary only 7. Necessary only 3. Neither necessary nor sufficient 8. Both necessary and sufficient 4. Sufficient only 9. Necessary only 5. Both necessary and sufficient 10. Sufficient only # Mill’s Methods John Stuart Mill (1806-1873) was an important British philosopher famous for his books Utilitarianism (1861; read in many college Ethics classes) and On Liberty (1859; read in many Social Philosophy classes). He also wrote a book on logic: System of Logic, Ratiocinative and Inductive (1843; rarely read in logic classes
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today). The part of this logic book that logicians continue to draw upon is Mill’s discussion of causal arguments. Although Mill’s analysis has been improved upon, most logic and critical thinking textbooks produced today give credit to Mill by presenting “Mill’s Methods.” Tho se “methods” are five ways by which we can argue that C is a cause of E. As it turns out, Mill did not really discover anything; ordinary people like your auto mechanic and doctor use these lines of reasoning all the time to try to determine the cause of your engine or stomach trouble. Most of this will seem like perfectly common sense, and it is. We’ll just be making our reasoning about causation a little more precise. # Method of Agreement 146 Imagine that five students leave the school cafeteria one day, and all immediately begin to get physically, grossly sick, seemingly from something they ate. Given the high quality and social consciousness of the food offered at our cafeteria, this may be hard to imagine, but give it a try nonetheless. You are a doctor assigned to determine the likely cause of the public malady. A janitor is waiting in the wings, mop and pail in hand, to see if additional students become ill. What would you do? The first and obvious response is to ask each of the five students what he or she had just eaten. You are hoping that there is a food item they each ate. Let’s imagine this is what you found out: Al ate potato chips and french fries. Barbara ate french fries, a taco, and a donut. Charlie ate pizza, a corn dog, and stole some of Ba rbara’s f rench fries. Debbie mixed her french fries in a side of gravy. Ellen is a vegetarian and
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ate only french fries, a donut, and potato chips. What is the likely cause of the illness? French fries! Why? Because it is the one food that all five students ate, or agreed upon. It is the one factor in agreement among all the various foods they ate that woeful afternoon. It’s not, of cour se, guaranteed that it was the french fries that caused the illness (it might have been the plates the fries were served on), but this is inductive reasoning, and guaranteed conclusions are not expected. Still, the fries are the likely suspect, and further inquiry or testing should be directed their way. We can create a table to visually show the data collected. Place the various cases to the left of the table, and on top of the table place the various possible causes of the phenomenon in question (i.e., the illness). At the top right we’ll note the phenomenon in question. For convention’s sake, we’ll use an x for when the cause obtains, and a dash for when it does not. Potato chips French fries Taco Donut Pizza Corn dog Gravy Became ill Al x x - - - - - xBarbara - x x x - - - xCharlie - x - - x x x xDebbie - x - - - - x xEllen x x - x - - - xIt is only the french fries column that agrees perfectly with the column under the phenomenon in question. It’s possible that Al had an allergic reaction to the potato chips he ate, and each of the others responded individually and uniquely to some food or combination of foods they ingested, but the likely cause of the group’s illness was the one thing they all ate in common: the fries. It 147 looks
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like, moreover, that eating the fries was needed for them to get sick. Donuts were not needed, for instance, because Al, Debbie, and Charlie got sick without eating them. French fries were thus likely a necessary cause for these five students becoming ill in this manner this day. We can go so far as to say that if the Method of Agreement gives clear results, it can point to a necessary (but not sufficient) cause of an event. The Method of Agreement works particularly well in hindsight, or retrospectively. If we have a group of events and want to know their cause, we can go back, so to speak, and try to determine what causes obtained for each of them. The Method of Agreement works better if there are more examples of things experiencing the phenomenon in question. So, if ten students got sick this woe begotten day, and all ten ate f rench fries, then we’d have stronger reason to believe i t was indeed the fries that caused the illness. If we had only two students who became ill, and fries were the only thing they both had eaten, we could still conclude it was probably the fries that were the problem, but the argument would be weaker. Ideall y, we’ll have at least three cases to compare —with more being better —when appealing to the Method of Agreement. Anything less than three will make for a fairly weak inference; it would not be enough for us to see a solid pattern. # Method of Difference Another line of causal reasoning is called the Method of Difference . Whereas the Method of Agreement is usually retrospective (i.e., looking back for a cause of an effect that already took place), the Method of Difference is usually forward looking and
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more controlled. In the Method of Difference, we take two things and make sure they are exactly the same in all relevant respects, except for one key difference. If one thing experiences the phenomenon in question and the other doesn’t, then that one key difference is likely the cause of the phenomenon. For instance, let’s say you want to determine whether Kwik -Gro fertilizer stimulates plant growth. We might take two plants of the same variety, age, and health, and place them in similar pots, using similar soil. We give them exactly the same amount of sunlight, air circulation, and water. Everything is controlled to be the same, except we feed Plant A with Kwik-Gro, but do not give the amendment to Plant B. If Plant A grows significantly more vigorously than Plant B, we are justified in concluding that Kwik-Gro fertilizer is the cause of the extra growth. Note that we can do this test in parallel, taking 200 similar plants and treating them all exactly the same, except we give Kwik-Gro to 100 plants but not to the others. This is using the Method of Difference in a 100-pair series. Such duplication of the method helps avoid unexpected differences in the plants, soils, water, air, or other factors. If 90 percent of the plants treated with Kwik-Gro showed substantial increase in growth, and none of those not treated with Kwik-Gro did, then we could say that there was approximately a 90 percent chance that Kwik-Gro will assist growth. Testing with more pairs of plants or finding a higher percentage in the results will make our conclusion stronger. The Method of Difference works well on inanimate objects and plants, but is morally problematic when used on sentient animals; it’s even more problematic when used on humans. 148 Humans are
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highly complex creatures, and no two are close to being exactly alike. Rats from the same parents, houseflies, and other simpler critters can be enough alike so that we can readily limit the test to one controlled difference in an experiment. Humans are too complex, and additional differences become apparent and undercut the conclusion that the one intended difference is the cause of the phenomenon in question. Also, it is often immoral to control humans to such an extent that only one difference is allowed. It would take caging a pair of humans and forcing upon them the same food, water, air, social companionship, freedom, rational discourse, etcetera to attempt the use of Method of Difference. The Nazis did this with unwilling humans, and the world still refuses to make use of the findings. We can set up a chart for the Method of Difference: 1 pint tap water / day Southern exposure to sun Soil XKwik-Gro Variety of plant 1week old at start Healthy at start Constant air circulatio n Extra growth Plant Ax x x x x x x x xPlant Bx x x - x x x x -This chart shows that the two plants were the same —as best as we could determine —in all relevant ways except that one received Kwik-Gro and the other did not. The one that received Kwik-Gro experienced extra growth; the other did not. Since Kwik-Gro was the only known relevant difference, we can conclude that it likely is the direct cause of the extra growth. The results of the Method of Difference can be the inverse of this, though. Instead of the one subject that has the difference experiencing the phenomenon in question, it could be that the subject failing to have the differing trait experiences the phenomenon in question.
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For instance, suppose that two people (we can use people if we take moral considerations seriously) with similar tendencies for headaches are —as far as we can tell —the same in every relevant respect, except that for two weeks we give one daily doses of pain reliever Z. As it turns out, the person who takes Z does not get headaches over this time period, while the other person does get the regular headaches. Since pain reliever Z was the only known relevant difference, we can conclude that taking Z helps people from getting (at least those kinds of) headaches. Food Drink Exercise Social life Work pressure Relaxation and recreation Pain reliever Z Headaches Subject Ax x x x x x x -149 Subject B x x x x x x - x Here the Method of Difference is working in an inverse manner, but it shows what is enough to prevent headaches. We can also note that pain reliever Z may not be necessary to stop headaches; pain reliever Y or a good neck massage might work well, too. Still, Z appears to be sufficient to do the job. So, to speak more generally, the Method of Difference —when the results are clear —can provide a sufficient cause for a phenomenon in question. Thus, the Method of Difference differs from the Method of Agreement in a variety of ways. The Method of Agreement looks backwards at what already happened, and tries to discover the cause of that event. The Method of Difference is usually looking forward at what will cause a specified phenomenon. The Method of Agreement works best appealing to three or more cases, while the Method of Difference works with two (or a multiple series of two). The Method of Agreement is often not controlled (since it
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is usually retrospective), while the Method of Difference is almost always highly controlled to ensure only one relevant difference. Finally, the Method of Agreement —if the results are clear —can point to a necessary cause, while the Method of Difference —if the results are clear —can point to a sufficient cause. # Joint Method The Joint Method of Agreement and Difference —or more simply, the Joint Method —looks to be a bit like a combination of the Method of Agreement and the Method of Difference. It ’s a broader ranging line of reasoning than either by itself, but it might be better understood as an expansion on the Method of Agreement. Whereas the Method of Agreement looks at a group of events (or individuals, or states of affairs) that exhibit some specific phenomenon (e.g., five students getting sick from eating food in the school cafeteria), the Joint Method takes into consideration both those who exhibit the phenomenon and those who don’t (or at least multiple instances of each). Consider the following dining fiasco: Andy, Bella, Chikka, David, Ellen, Fred entered the Chunk-O-Cheese Pizzeria together in seemingly fine health, and ate dinner there. Soon afterwards, Bella, David, and Ellen became quite ill, apparently from something they ate. Andy had taken Critical Thinking at Bellevue College, so he knew to ask what each had eaten. He even drew up a table showing the information he collected: Spaghetti Cheese pizza Pepperoni pizza House salad w/ ranch dressing House salad w/ Italian dressing Got sick Andy x x x - x -Bella - - - x - x150 Chikka x - - - x - David x x - x - x Ellen - x - x x x Fred x - x - x - What is the likely cause of the illness?
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The ranch dressing! Everyone who got sick ate the ranch dressing, and no one who did not get sick ate it. It appears —we can conclude inductively —that the ranch dressing was enough to make Bella, David, and Ellen sick (because anyone who ate it got sick), and it was also (among the foods they ate) needed to make them sick (because nothing else seemed to make anyone sick). Thus —speaking more generally —the Joint Method can point to a necessary and sufficient cause of a specified phenomenon when the results are clear. That is, if the occurrence of the phenomenon agrees perfectly with the occurrence of a specific causal factor, then the method can provide a necessary cause. If the lack of occurrence of the phenomenon matches up with a lack of occurrence of the same causal factor, then the Joint Method can provide a sufficient cause. The Joint Method as used here cannot prove deductively that the ranch dressing is the culprit, for it may be that each of the three ailing diners has a unique disposition toward various foods, and it was just dumb luck that they each ate something that did not sit well with him or her. Still, given the information we now have, the restaurant manager has good reason to take a careful look at the ranch dressing. If she had little by way of moral scruples, she might give samples to a variety of other customers, and refuse to serve it to a variety of others. If all those who eat it get sick, and none of the others do, she’d be using the Joint Method further to provide added evidence for the ranch dressing’s gastrointestinal turpitude. If the restaurant manager was an inquisitive moral monster, she might kidnap two people of similar
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genetic structure and heritage, confine them in similar cages, provide them the same water, food, air, light, and other bodily needs, and force only one to ingest a house-salad portion of ranch dressing. H ere she’s using the Method of Difference to help confirm the conclusion derived from use of the Joint Method. If the dressing-eater gets sick, but the other caged soul does not, then that gives her added reason to believe that something about the ranch dressing is causing the illness. The Joint Method, like the Method of Agreement, may also be used retrospectively. Here, however, we have access to people who got sick and people who did not get sick. Therein we find the added strength to this line of reason ing. Ideally, you’ll have at least two cases that exhibit the phenomenon in question (e.g., getting sick) and two that do not. Anything less will make for an ill-defined pattern and a fairly weak argument. Obviously, the more you have of each, the stronger the argument can be, all else being equal. # Concomitant Variation 151 The following two kinds of causal reasoning are quite different from the previous three. Concomitant Variation appeals to the related correlation of two rates of change, and concludes that there is a causal relationship between them. Examples are easy to find: Your grandfather gives you some vinyl records and an old LP stereo system. It’s so old, that all the letters and numbers have been worn off the knobs. By trial and error you figure out how to turn the stereo on, and throw on a near-mint-condition copy of Meet The Beatles . When “I Want to Hold Your Hand” comes on, you want to raise the volume to decibels that could neuter frogs at 100 yards. But you don’t
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know which knob will do the tr ick. You take hold of one, and at the rate at which you turn it you hear the volume of T he Beatles’ lilting refrains rise. As you turn the knob back the other direction, the song fades in volume. You conclude that you have found the cause of the volume level; that is, you’ve found the volume knob. Or, you are a precocious, inquisitive, and logically-minded four-year-old child. You are sitting in the front seat of your mother’s idling car (she’s away for the moment to deliver a Senate document to her Justic e Committee secretary). You don’t know how to drive, but are aware that the vehicle has the capacity to go quickly. Pushing aside “Re -elect Senator Sunny Shine” flyers from the driver’s seat, you start playing around with pedals on the floor, and note that as you press one, the car begins to move. As you press it further, the car accelerates and moves faster. When you press the pedal to the floor, you whisk across the parking lot, slamming into other cars, barely missing the now-terrified ambassador from Estonia. You let up on the pedal, and the car slows to a halt. You logically conclude that you have discovered the cause of the car’s acceleration and rate of speed. You have just used the method of Concomitant Variation. In both examples above, the concomitant (i.e., naturally accompanying, associated, attendant) variation is direct, or parallel. As one thing goes up, the other thing goes up. As one thing goes down, the other goes down. Sometimes the relationship may be inverse, as when one thing goes down, the other thing goes up. For instance, as employment rates go up, crime goes down. This indicates that there is a likely causal
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connection between crime and employment rates. It is beyond the method of Concomitant Variation, however, to determine which is causing which. Is it the drop in crime that is causing the rise in employment rates, or is it the rise in employment rates that is causing the drop in crime? Common sense or further inquiry is needed to make that determination. More complex cases of concomitant variation occur when, for instance, one rate of change is fairly steady, while another rate of change is different (either directly or inversely). For instance, imagine events A are changing at the rate of 1 unit per day: 0, 1, 2, 3, 4, 5, 6…. Let’ s say events B are also ascending (or descending) but more slowly, but at a different rate: 0, 0.5, 1, 1.5, 2, 2.5, 3…. There still is concomitant variation, as when A goes up one unit, B goes up half a unit. Since the rate of change (though different) appears to be related, we are justified in (at least tentatively) concluding that one set of events is causally related to the other set. But consider this. It oddly is the case in the larger of U.S. cities that as the crime rate goes up, so too does the amount of ice cream eaten; and as ice cream is eaten less often, the crime rate drops. Concomitant Variation indicates that ice-cream-eating is causally related to crime. We thus 152 should ban all ice cream! Well, no. We might first ask which way the causal relation goes. Does eating ice cream cause crime, or does crime cause the eating of ice cream? Neither option seems to make much sense, so we need to look further. It won’t take us long to consider a third factor: rising temperatures. As temperatures rise,
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so too does the eating of ice cream and social irritation and its attendant crime. It’s the rise in temperature that drives up both crime rates and people’s readiness to indulge in the butterfat-laden delights of vanilla, chocolate, or strawberry ice cream. Concomitant Variation can point to a causal relation, but reason and further inquiry often need to kick in afterwards to draw specific conclusions about what causes what. Also, Concomitant Variation by itself does nothing to indicate if the cause is necessary or sufficient. # Method of Residues In our introductory exploration of causal reasoning, we’ll look at one more method: the Method of Residues. This method works by determining that a specific state (or states) of affairs is caused by a fixed number of causes. After accounting for each individual cause’s specific effect, we conclude the remaining (or residual) effect is caused by the remaining cause. Although the Method of Residues can help establish a cause, it does not do much to determine if that cause is necessary, sufficient, both, or neither. The pattern of the Method of Residues looks something like this: A and B and C in some way cause effects X and Y and Z. A causes X. B causes Y. Thus, it is likely that C causes Z (the residue, or what’s left o ver of the total set of effects). Here ’s an example. A logic instructor at a community college is beset by ten of his female peers. They all claim he ’s smart, handsome, and witty, and want to go on dates with him. The instructor determines that this unsolicited attention is due to a combination of his good looks, his wealth from the huge amount of money he makes teaching in the State of Washington, and his fancy new Subaru.
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Curious as to how many are interested in his dashing good looks, he borrows a friend ’s beater Dodge Dart and puts the word out that he no longer drives a hot Subaru wagon. Five of the women originally interested in him no longer even return his school-related emails. He then spreads the rumor that he has and will continue to donate half his pay to feeding starving whales off the coast of Mauritania, and two more once adulating peers drop off his radar screen altogether, never to be heard from again, except at longwinded division meetings. The logic instructor concludes that the remaining three peers are likely attracted to him due to his striking visage. The Method of Residues may also appeal to percentages, arguing —for instance —that because Cause A produces 10 percent of a set of effects, Cause B produces 15 percent of those effects, and Cause D produces 50 percent of the effects, it follows that Cause E probably causes 25 percent (the remaining residue) of the effects. For instance, imagine that Tiago has a chilly draft in his home’s living room. He has determined that there are three causes of the draft: air coming in under his front door, a broken window, and 153 an open damper in his fireplace. Tiago closes the damper and 30 percent of the draft is stopped. He fixes his window, and that stops 20 percent of the original draft. Tiago concludes that the un-insulated door is allowing 50 percent of the original draft. That 50 percent is the residue of the effect (i.e., the original draft) left over after accounting for the other two causes. And here’s yet another example of using the Method o f Residues. Sarah runs a grocery store and wants to slow down the shoplifting
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occurring there. She can afford only to pay for added security at one portion of the store’s opening hours. So she carefully records all the stock, and determines that 10 percent of the theft is done in the mornings, and 15 percent of the thefts take place in the afternoons. She concludes that 75 percent of the thefts occur in the evening hours, and hires Buckkitt Security to patrol the store then. # **Practice Problems: Causal Arguments Answer the questions that follow each scenario below. 1. Sunny Shine decides that for this year’s World Naked Gardening Day (held the first Saturday of each May) she would finally determine what effect Kwik-Gro fertilizer has on her primroses. She has two rows of these plants, each acquired from the same stock of primroses sold at the same store, and bought on the same day. She gives them all the same amount of water; the sunlight is the same for each row; the soil is the same. Dressed appropriately for the day, she applies Kwik-Gro to one row, but not to the other. The row receiving Kwik-Gro soon dries up and dies, leaving a grub-infested, gooey mess where once were thriving primroses. Shine concludes that Kwik-Gro kills primroses. Which of Mill’s m ethods is Shine using? Which kind of cause is Kwik-Gro in killing Shine’s plants: necessary, sufficient, both, or neither? 2. Pastor Bustle believes his church needs more funds so that he can give himself a raise in pay for preaching. He speculates that the length of his Sunday morning sermons is affecting the number of parishioners willing to tithe regularly to his church. For one month he preaches for 15 minutes. The next month he preaches for 30 minutes. The next month he preaches for 45 minutes. And finally, he preaches
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for 60 minutes each Sunday of a month. He notes that the longer he preaches, the less money comes in. He concludes that to get more money, he must shorten his sermon time. Which method is Bustle using? 3. Professor Kim wants to know what is a likely cause of student success (in terms of grades) in his Social Philosophy graduate seminar. He makes inquiries of his five students, and discovers that Angie reads anime comic novels regularly and studies each night for one hour; Bernardo studies only once a week for hours, is the only one to use flash cards, and drinks Red Bull before coming to class each day; Charisa does yoga before every class, but never studies, and reads anime comic novels regularly; Drew can’t read, never studies, but does yoga before class with Charisa, and drinks Red Bull immediately afterwards; Ewan and Bernardo believe that reading is a sign of capitulation to intolerant power structures and refuse to do it; Angie, Charisa, and Ewan are all raw vegans who drink only water or freshly squeezed juice; Angie, Bernardo, and Ewan all think yoga is for sissies and scorn any suggestion that they should practice it; and Ewan studies each night for an hour. Only Angie and Ewan are getting high grades in Kim’s seminar. Draw a table showing the information Kim has collected. Given this information, what is the 154 likely cause of receiving high grades in Kim’s seminar? What kind of cause (if determinable) is this (e.g., necessary, sufficient, both, neither)? Which method is Kim using? 4. Bob Shine likes horse racing, and given recent misfortunes at his architectural firm, wants to make some extra money. He finds the jockeys for the last three winning horses and bribes them into giving him some information to
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help him on future bets. All I Want to Be ate only oats the morning before the race, was never whipped by her jockey, and had Led Zeppelin played in her stall before the race. Badly in Need ate no oats before the race, had Barry Manilow played in her stall before the race, and was ne ver whipped during the race. Only Can’t Bear to Lose and All I Want to Be received injections of horse steroids before the race. The jockey for Can’t Bear to Lose is opposed to all forms of harm to animals, refuses to uses whips, feeds his horse only oats, and has him listen to Led Zeppelin before races. Draw a table to show the information Shine received. Based on this information, what is the likely cause of these horses winning their races? Is the cause necessary, sufficient, both, or neither? Which method is Shine using? 5. Doctor Nan Kompos Mentis has good reason to believe that the swelling of Ellen Veegon’s limbs is due to three foods she eats each day —raw peanuts, tofu, and kale —and wants to know how much of a problem the kale in particular is causing. Mentis has Veegon stop eating peanuts, and the swelling goes down by half. Mentis then has Veegon also stop eating tofu, and the swelling drops down by half again. Mentis concludes that the kale is causing 25 percent of the original swelling. What method is Mentis using? 6. Given the table below, what is the likely cause of Z? What method is being used? Is the cause necessary, sufficient, both, or neither? A B C D E F G Z Case 1 x x x x x x x xCase 2 x x - x x x x - 7. Given the
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table below, what is the likely cause of Y? What method is being used? Is the cause necessary, sufficient, both, or neither? A B C D E F G H Y Case 1 x x x x x x - x xCase 2 x - - x x - - x xCase 3 x x - x - - x - xCase 4 - x x x x - - - x8. Given the table below, what is the likely cause of W? What method is being used? Is the cause necessary, sufficient, both, or neither? A B C D E F G H W155 Case 1 x - x - x - x - x Case 2 x x - x - - x - x Case 3 - - - - - x x x - Case 4 x x - - - x - x x Case 5 - x - - x - x - - Case 6 - - - x - - - - - Case 7 - x x x - - - - - 9. Given the table below, what is the likely cause of V? What method is being used? Is the cause necessary, sufficient, both, or neither? (This is a more challenging problem.) A B C D E F G H V Case 1 x - - x x x x x xCase 2 x x x x x x x x -Case 3 x x - x x - x x xCase 4 x x x x x x - x -Case 5 x x x x x x - x -Case 6 - - - x - x x x xCase 7 x x x - x x x x x 10. Given the table below, what is
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the likely cause of U? What method is being used? Is the cause necessary, sufficient, both, or neither? (This is a similarly more challenging problem.) A B C D E F G H U Case 1 x x - - x - x x xCase 2 - x - x x - - - xCase 3 x - - - - x - x xCase 4 x x x x - x x x -Case 5 x x - - - x x - -Case 6 x x x x - x - x -156 11. The morally-challenged manager of the Chunk-O-Cheese Pizzeria thinks her ranch dressing is causing an outbreak of illness among her customers. She kidnaps five adults presently dining in her establishment, and in th e restaurant’s basement forces each to eat some of the dressing. One kidnapped customer is fed one tablespoon of dressing, the second is fed two tablespoons, the third three tablespoons, the fourth four, and the fifth five. The ones who eat more of the dre ssing get sicker than the ones who eat less. “Eureka!” she cries. “I’ve now confirmed that it’s the ranch dressing causing the illness!” Which method is the manager using? 12. Bob Shine’s accountant says his architectural company is losing money to theft, and that the thefts are limited to employees stealing office supplies, employees using company gasoline to drive to Reno for weekends, and employees using company vouchers for private dinners. Bob cancels all food vouchers and locks up the company gas tanks. Monetary loss due to stealing drops 75 percent. He concludes that 25 percent of the employ theft was from stealing office supplies. Which method is Shine using? 13. The cook at Joe’s Café wants to experiment with his meatloaf. He makes two batches, cooking
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both at the same temperature in the same oven and for the same length of time. The recipes are exactly the same except that he adds a quarter cup of bourbon to one batch. Everyone in the cafe likes the bourbon meatloaf better, and Joe concludes that bourbon makes his original recipe more popular. Which method is Joe using? Is the bourbon a necessary cause, sufficient cause, both, or neither? 14. Albert drank five Scotch and sodas, and got drunk. Barney drank five bourbon and sodas, and got drunk. Charlene drank five gin and sodas, and got drunk. Doris drank five rum and sodas, and got drunk. Tiago is watching all of this and concluded that soda causes people to get drunk. Which method is Tiago attempting to use (albeit, not very well)? 15. What might a logical and informed person do to show Tiago (from Problem #14) that his conclusion is mistaken and that the alcohol in the drinks caused the people to get drunk? Answers: 1. Method of Difference; sufficient cause. 2. Concomitant Variation. 3. Reads anime comic novels Studies each night for 1 hour Studies once per week for hours Uses flash cards Drinks Red Bull Does yoga Get high grades Angie x x - - - - xBernardo - - x x x - -Charisa x - - - - x -Drew - - - - x x -157 Ewan - x - - - - x Studying each night for one hour is the likely cause of the high grades; necessary and sufficient cause; Joint Method. 4. Ate oats Ate hay Not whipped Led Zeppelin Barry Manilow Horse steroids Won a race All I Want to Be x - x x - x xBadly in Need - x x - x - x Can’t Bear
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to Lose x - x - x x xNot being whipped by the jockey is the likely cause of the wins; necessary cause; Method of Agreement. 5. Method of Residues. 6. The likely cause of Z is C; Method of Difference; sufficient cause. 7. The likely cause of Y is D; Method of Agreement; necessary cause. 8. The likely cause of W is A; Joint Method; necessary and sufficient cause. 9. We’re clearly not using Concomitant Variation or Method of Residues. That leaves the first three methods. But it’s not Method of Difference, because there are not two cases being compared in which they are exactly the same except for one difference. If we were using the Method of Agreement, then all the cases would experience the phenomenon in question (i.e., V). So we are using the Joint Method, which makes sense since we are appealing to three or more each of cases that did and did not experience V. No causal factor (i.e., A-H) matches perfectly with the phenomenon in question, but factor G matches the best, so it is the most likely cause among these eight factors. Where G is experienced, V is uniformly experienced, too, so G “agrees” with H, thus providing a necessary cause. But the failure to experience G does not match up perfectly with the failure to experience V, so G does not quite provide a sufficient cause. This is a case of using the Joint Method, but it is not giving us everything we would like from it. 10. The likely cause of U is E; Joint Method; sufficient (but not necessary) cause. 11. Concomitant Variation. 12. Method of Residues. 13. Method of Difference; sufficient cause. 14. Method of Agreement. Obviously, though, it’s not the soda that causes people to get drunk, but
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the Method of Agreement alone cannot tell us this. Now go to Problem #15. 15. One way to do this is to use the Joint Method. Have a variety of people drink a variety of liquids (five glasses each), some containing alcohol, while other drinks do not. If our hypothesis is correct (i.e., that the alcohol is the one and only cause of the people getting drunk), then all people guzzling drinks with alcohol will get drunk, and none of the people sipping alcohol-free 158 drinks will get drunk. The Method of Difference might be helpful, too. We can get a series of pairs of people of roughly the same height, body mass, gender, and age (factors that may play a role in how easily one gets drunk), and give half of them five drinks with alcohol, and have half of them five drinks exactly the same except without alcohol. If the alcohol drinkers get drunk and the others do not, then it looks like alcohol is a sufficient cause for getting drunk (i.e., from this information, it is possible still that some other drug can make people drunk, too). 159 # Chapter 12: Hypotheses We often face philosophically interesting questions, those whose proposed answers thoughtful and informed people are debating. Whether murdering people to steal their money is morally right or wrong is not philosophically interesting in this sense. All reasonable and informed people agree that it’s wrong. Why it’s w rong is philosophically interesting, though, because there remains thoughtful, informed debate on that more basic issue. Of continued philosophical interest include questions such as, “Is euthanasia always morally wrong?” “How did the dinosaurs die?” “Was O. J. Simpson guilty of murder?” “How should teachers respond to student cheating?” “Does God exist?” “What role does race play in U.S.
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politics today?” “Should baristas be able to serve lattes buck naked?” There are intelligent, informed people still disagreeing on such matters. If there are two proposed theories —or hypotheses —answering a question, and one of them has a clear preponderance of evidence or good argumentation on its side, then rational people should embrace that better-supported theory. Having a clear superiority of evidence does not guarantee that one answer, theory, or hypothesis true, but as rational beings, we want —and probably should —embrace the view that is most justified or warranted. But what should we do if there are multiple opposing answers to an important question, and each answer lacks any clear evidence, or any clear preponderance of evidence? What if each answer is equal in terms of evidence and support? It may be that we could ignore the situation, and put the question “on a shelf,” so to speak, not worrying about it until more evidence comes in directing us to embrace rationally one over the other. But sometimes the question is vital enough that we need to move forward and work with a viewpoint. Guessing or simply going for the answer that “feels” right will hardly do for rational people, at least if there is more that can be said in favor of one hypothesis over another. Fortunately, there is a set of principles that can help in this regard, and before giving in to guesswork or personal, arbitrarily biased feelings, these principles are worth considering. They form criteria articulating what we’d want out of any well functioning hypothesis, that is, out of any viable answer to a puzzling question. An hypothesis is a proposed answer to a puzzling question. If a police detective finds a dead man with a knife in his back, the puzzling problem might be
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“Who killed the man?” or “Why was this man killed?” An archeologist might ask at an excavation site, “Why and how did this group of people construct this stone building?” A medical researcher might ask, “What can cure this particular form of cancer?” A philosopher might ask, “What is the ultimate nature of who we are?” A theologian might ask, “Why would an all -good God allow evil in th e world?” All are philosophically interesting questions, and multiple hypotheses have been offered for each. Sometimes empirical evidence or logical analysis shows an hypothesis to be unworthy of serious consideration. Sometimes, however, two or more hypotheses have just as much —or just as little —evidence backing them up, and it’s not clear which one (or ones) is true. What we might do in such bothersome situations is consider what we want out of an hypothesis. There are certain character traits that an ideal hypothesis will have, just like there are ideal character traits a hammer will have. If you are in need of a hammer, but don’t know at this point 160 which kind you need (small or large, framing, ball-peen, claw and nail, dead-blow, sledge, masonry, or rock pick), you at least want a hammer that does the job of a hammer. If you had to select a hammer for some use, but did not know what kind to use, and had to choose from a poorly crafted masonry hammer or a superbly crafted claw and nail hammer, you’d be ad vised to select the latter, better constructed tool. It may turn out that it’s not the best hammer for the job, but for the moment, you are rational in tentatively embracing the better crafted hammer. This embracing of a hammer or hypotheses is tentative and non-dogmatic, as being
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well-crafted provides no evidence that it’s the best hammer for the job or the correct answer to your puzzling question. Still, we may need a working hypothesis to march forward to do medical research, or to inquire further into the philosophic question at hand, or to guide the police detective in searching for a killer. If evidence or arguments turn up that make our hypothesis look bad, then we are ready to give it up, as we’ve not committed ourselves too strongly to it; we are e mbracing it only tentatively, until more information comes in. We’ll consider five criteria for superior hypotheses. If we find ourselves with two hypotheses to choose from, and if we are in need of adopting an hypothesis to move forward to do the work we need to do, then we will be advised to adopt tentatively the hypothesis that meets these criteria the best. This is not, however, an argument for the truth of the hypothesis. The “better crafted” hypothesis may still be incorrect, and the one with virtually no evidence and lacking in some important character traits may still be the true one, but we can use the appeal to these principles to say that one hypothesis is better —as an hypothesis —than the other, and that warrants us in tentatively working with it for the time being. We’ll need to wait until new evidence or argumentation comes in to justify our saying that the hypothesis is actually true. # Criteria for Hypotheses An ideal hypothesis will have five character traits. The hypothesis will exhibit: Explanatory power External consistency Internal consistency Fruitfulness Simplicity If we are considering two hypotheses, one may look good regarding a couple criteria, while the other may look good in reference to two or three others. There is no
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way to quantify precisely how well one hypothesis meets these criteria when compared to another. We need to consider each hypothesis, and then make a judgment as to which one overall —and all else being equal —functions best as an hypothesis. We’ll then tentatively e mbrace that one. # Explanatory Power The purpose of an hypothesis is to provide an answer to a potentially puzzling question. If the hypothesis doesn’t do that, it’s not functioning very well. Let’s say that Bob stubs his toe on the 161 bedpost one night, and wonders why that happened. He might hypothesize that God caused it to happen. As an hypothesis, this doesn’t explain much. It doesn’t explain why God wanted Bob to stub his toe, or how God caused the event to take place. It may be true that God exists and caused Bob to stub his toe, but a thinking person will likely —all else being equal —be inclined to look for another theory that provides a more detailed explanatory answer. What we want out of hypotheses is as much relevant information as possible. If the question pertains to the cause of a mysterious event, ideally we’d like the hypothesis to tell us what happened, what caused it to happen, why it happened the way it did, how it happened, and to do so for as many of the details of the event as possible. Moreover, an ideal hypothesis will do all this with clarity, detail, and precision. Of course, that may be too much to ask for in certain situations, but if we have two purported answers to a question and the first hypothesis answers more of the question and in greater detail than the second, then all else being equal the first is the better hypothesis. Consider a medical researcher
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who seeks the cause of a form of paralysis. Hypothesis A says the illness is caused by breathing polluted air. Hypothesis B says that drinking tap water from rusty pipes over the course of one year will damage nerves, cause tingling in the extremities initially, and eventually produce paralysis. Hypothesis B answers more of the question than Hypothesis A, and does so with far more detail. If the evidence and argumentation for A is equal to that of B, then because B has more explanatory power than A, we should prefer it over A…at least tentatively. We must keep in mind that just because an hypothesis provides broad-ranging and detailed answers to a question, does not itself show that the answer is correct. It just means that the hypothesis is doing what hypotheses are supposed to do. We also want an hypothesis to fit the facts in question as precisely as possible. If the rusty water pipe hypothesis merely accounted for “a number” people becoming ill, while the less encompassing bad air hypothesis explained why exactly 25 people in a given community would become ill, then in that regard the bad air hypothesis is the better of the two. As it stands now in our scenario, there is reason under the criterion of being explanatory to favor both hypotheses. That’s no surprise as thinking people rarely consider woefully bad hypotheses for very long; on the flip side, viable hypotheses tend to have something going for them to keep them under consideration. Moreover, the hypothesis will ideally explain other analogous questions equally well. For instance, if beekeepers find that their hives of bees in one Washington county are sick and come up with an hypothesis that accounts for it well, then that hypothesis should —in principle —work for other similar cases
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of bee hive illnesses. Hypotheses should thus not be ad hoc and arbitrary; if they answer one puzzling question well, they should be of use with other relevantly similar puzzling questions. # External Consistency A good hypothesis will also be externally consistent . By that we mean that the hypothesis does not conflict with what we know (or think we know) about the world, and that it conforms to the 162 facts as we understand them. That is, all else being equal, we don’t want to embrace an hypothesis that forces us to give up well-established beliefs. For instance, if you follow the motion of Mars in the sky over the course of many nights, you might observe it moving in one direction, then switching back for a time, then moving back in its original direction. This observed oddity of planetary movement is called retrograde motion. What causes it? One less-than-sure-footed astronomer might hypothesize that five-year-old boys are floating in space pushing Mars around. Obviously, this is an embarrassingly ridiculous hypothesis, but it’s ridiculous because it patently goes against what we know to be true about little boys: their lack of existence in space and their lack of power to move planets. We reject the hypothesis out of hand because it lacks external consistency, and —all else being equal —this is enough to make us smile upon a more externally consistent alternative hypothesis. Two competing hypotheses might both be externally consistent; that is, they match up equally with what we are confident is true about the world. For instance, if a mysterious light appears in the sky at night, and we want to theorize about its cause, two people might come up with differing hypotheses: the light is caused by either a military plane or a distress flare shot up
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by someone on the ground. Both hypotheses are consistent with what we know to be true of the world. In this case, we either need to find additional evidence or argumentation for embracing one hypothesis over the other, or, short of that, one hypothesis needs to meet the other criteria better. A potential problem lies in that what we are psychologically confident in may actually be false. Belief and perspective do not by themselves determine truth or reality. We can be mistaken. This perfectly reasonable and humble position is called falliblism (i.e., the acknowledgement that we are fallible, or able to make errors in judgment about the world). So, just because an hypothesis is inconsistent with something we take to be true about the world, it does not follow with certainty that the hypothesis is false. It may be that we are mistaken about the world and the hypothesis is true. To the degree we can be justifiably confident in our belief about the world, to that degree we can be confident that an hypothesis inconsistent with this belief has something seriously wrong with it. One important lesson to learn here is that when making hypotheses, we need to be aware of the assumptions we make in the process. Our assumptions might be mistaken. None of this warrants becoming overly skeptical about every little belief about the world, but we need to be careful nonetheless. # Internal Consistency An hypothesis must also be internally consistent . All the parts of an hypothesis must be consistent with and not contradict each other. A self-contradictory hypothesis has something seriously wrong with it. All else being equal, if one hypothesis is more internally consistent than another, the more consistent one is to be preferred. An hypothesis to a complex problem will usually have
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multiple parts. For instance, if we are interested in why the dinosaurs died, one might come up with a “meteorite hypothesis” having numerous parts. For instance, (a) a meteorite hit the earth causing (b) a huge dust cloud that (c) blocked sunlight and (d) killed plants which caused (e) dinosaurs to starve to death. There are at 163 least five major elements to this hypothesis. Here, so it seems, each part is consistent with the others. The highly influential French philosopher Rene Descartes (1596-1650) is said by many scholars to have offered an hypothesis regarding the nature of reality that was internally inconsistent .Descartes hypothesized that reality is made up of two radically distinct substances: mind and body. What is true of one, is not true of the other. Mind is immaterial, takes up no space, is indivisible, and thinks. Body is material, spatial, divisible, and does not think. We call this two-substance view Dualism . Descartes also hypothesized that with humans the mind and body have a causal relation with each other. The view is called Interactionism . For instance, one can cause one’s arm to move by using one’s mind to think, “Raise my arm!” Also, the body can cause mental events in the mind. If someone kicks your physical knee, that causes the mental event of a pain. A problem facing Descartes is that the combination of Dualism and Interactionism really seems to be internally inconsistent. For it is inexplicable how a non-material entity like Descartes’s mind can have any physical effect on his material body, and vice -versa. The mind has no substance or energy (note that energy and matter are related, and are part of the bodily world); it would be l ike an immaterial ghost trying to punch a living person. The ghost’s “fist”
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would go right through the living man’s face. (If you’ve seen the movie Ghost (1990) starring Patrick Swayze and Demi Moore, you will be aware of this problem.) # Fruitfulness An h ypothesis that will make most inquirers jump with joy will be what we’ll call fruitful . One way an hypothesis can be “fruitful” is to provide opportunities to test it. Some hypotheses are simply impossible to verify or falsify; there’s no way even in principle to tell if they’re true or false. To wax theological once again, if a family member gets sick and we want to know why, if we hypothesize that it’s God’s will, the hypothesis is completely untestable. There is nothing we can do to show if the hypothesis is correct or not. We can pray and ask God to give us a verifying sign of event X, Y, or Z, but if the event does not occur, then we still won’t know that God’s will was not causally involved with the sickness, because God could have decided —for whatever good reason —not to provide the requested sign. If the sign does appear, we’ll not be sure that it actually came from God, or came from Him for that purpose. Maybe He’s “testing” us. There’s no way to know. Scientists sometimes seem to be at odds with believers on various issues. The origin of life, changes within a species, the death of the dinosaurs, the plausibility of a global flood, the existence of God, and similar puzzles often find each party with different (sometimes conflicting) hypotheses. There are many intelligent, informed scientists who believe in God, and as a matter of their faith believe various things that may not be empirically verifiable or falsifiable. Still as scientists, they will also likely seek —when possible —hypotheses
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that can be tested. That’s what in large part makes them scientifically minded. They understand that a true, accurate hypothesis may be untestable, but as long as the possibility remains, they will want —as scientists —to examine other hypotheses that can be tested. All else being equal, an hypothesis that can be tested is preferable to one that cannot. At least, that’s the sort of hypothesis we’ll 164 want to tentatively embrace until a preponderance of evidence or argumentation comes in favoring one hypothesis over another. We also want hypotheses to be fruitful in another way. We want them to lead us to further inquiry, to be springboards, as it were, for continued discussion. If an hypothesis gives no hint as to what we might do or develop for further research or testing, or if the hypothesis in principle suggests no further avenue of discussion, then again it’s not doing much for us. It may be true and accurately answer the question at hand, but as an hypothesis, it’s largely useless to us. For example, someone might attribute a bout of stomach flu to the karmic effects of bad actions performed in a previous life. The law of karma can have explanatory power, be internally consistent, and externally consistent, and but it is not a very fruitful hypothesis, as (a) it’s not at all testable in any practical way, and (b) it gives little or no new insight as to how to test a purported karmic law or how to think or inquire about it further. # Simplicity The Principle of Simplicity urges us to adopt —all else being equal —the simpler of two hypotheses. Called “Ockham’s Razor” in Europe’s Medieval Period, and referred to in India since its Classical Period as “The Principle of Lightness,” this criterion does not
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suggest we tentatively adopt the hypothesis that is easiest for us to un derstand. We don’t mean “simple” in this sense. Rather, the hypothesis that appeals to the fewest number of entities, or the least complex set of entities is less likely to be mistaken. Imagine two automobiles of equal quality, but one has twice as many moving parts as the other. Which is more likely to break down most often? The more complex car, as it has more ways to break. So too with hypotheses. One making ten claims has more ways to be inconsistent with the world or internally inconsistent with itself, than an hypothesis making only three claims. Years ago, the Honda automobile company ran ads singing, “Honda…we make it simple.” They were saying that Hondas were so simple that they would last a long time without breaking down. Many people liked that idea, bought the cars, and made Honda a major car producer internationally. Another way to look at simplicity is to think of an hypothesis’s “modesty.” A modest hypothesis claims only what is needed to answer the puzzling questions powerfully. That is, the ideal hypothesis is trimmed down to the bare essentials, so that it can do the job of explaining in detail what needs explaining, but makes no extra claim that could end up being false. Simplicity in this sense can initially appear to be in conflict with the robust demands of explanatory power , but it’s not. The best hypothesis will be as streamlined as possible, yet still do their designated job. By way of illustration, let’s go back in time to when the Italian scientist and philosopher Galileo Galilei (1564-1642) was challenging the dominant geocentric view of the universe devised by Ptolemy centuries beforehand. Galileo believed that the Sun was the center
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of the universe (i.e., Copernicus’s heliocentrism), while the Church defended the Earth -centered system long and hard. Technology had not advanced yet to the degree that could provide detailed evidence for one view or to show that one hypothesis was clearly the best. For a time, both sides had little to 165 appeal to other than these five criteria. We might imagine the following conversation between Galileo and his geocentric opponent. (See Galileo ’s Dialogue Concerning the Two Chief World Systems: Ptolemaic and Copernican for his actual arguments along these lines.) Galileo: Well, my development of teles copes still leaves something to be desired, so I can’t yet use precise, detailed measurements of the starry heavens to show that the heliocentric system offered by Copernicus is measurably best, but my hypothesis is better than your Ptolemaic geocentric one, at least as far as hypotheses go. Opponent: Bah! My theory explains things well. It explains why planets and stars appear to move across the night sky in the directions they do, and how they are arranged. G: So does my heliocentric theory. I’ll admit that your picture explains as much as mine, but that’s not where my hypothesis shows its strength. O: Strength? Strength? You can’t handle strength! You want strength? Take a look at the external consistency of geocentricism. If your doofus hypothesis was true, the Earth would be moving through space. But does it feel like the Earth is moving? No! Also, if the Earth is moving rapidly through space, wouldn’t we notice a strong wind constantly coming from one direction? But we don’t! And , if I hold this small rock over this X marked on the table, and drop the rock, if the Earth is moving, the X should slide over to one direction, and the rock
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shouldn’t hit it. But it does hit it…dead on every time! So your hypothesis is not nearly as consistent with what we know about the world. Plus, the Bible says the Earth sits still and the Sun moves around it. It’s in the book of Joshua or somewhere. G: Well, I’m not going to argue today with the Bible, and I’ve got to admit that much of what we normally take to be obviously true about the world is pretty consistent with geocentricism, but my hypothesis is better nonetheless. O: Humph! G: My hypothesis is internally consistent. There are no parts to it that contradict one another. O: So too with mine. G: Yah, I suppos e so. I don’t believe your hypothesis, but it at least seems to hold together internally. O: Now look at the fruitfulness of my geocentric picture. Sailors can assume that it’s true and use it to navigate across vast seas and get exactly where they wish to go. Also, we can test my hypothesis. For instance, if my hypothesis is true, then —given careful calculations —we can predict accurately where Mars will be in the night sky weeks from now, and do so with a high degree of accuracy. G: Yah, but my heliocent ric hypothesis can do the same thing. So it’s a tie as far as fruitfulness goes. O: So what’s your big strength? Why on our geocentric Earth should anyone think that your hypothesis —as an hypothesis —is better than mine? G: Because mine is more simple. To make yours work, that is, to make yours help sailors get across the sea or to draw implications as to where Mars will be later this week, you have to 166 appeal to gobs and gobs of epicycles, deferents, and equants. My Copernican
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system of heliocentricism appeals to far fewer such entities. Thus my hypothesis is simpler. Thus my hypothesis is —all else being equal —to be preferred, at least tentatively, until I improve my scientific instruments and show that I can predict planetary motion far more accurately and with more detail than you can with your soon-to-be outmoded geocentricism. O: I doubt it. You’re always talking about new technology. Our hypotheses appear close to a tie at this point, and given that the Church says the Earth sits still, I think it’s be st to go with that view. G: Shall we then talk about these craters I recently found on the Moon? O: Ack! Heresy! # **Thinking Problems: Criteria for Hypotheses Consider each of two competing hypotheses, and write a mini-dialogue in which characters appeal to the five criteria for hypotheses to support tentatively embracing one hypothesis over the other. 1. The doctrines of karma and reincarnation are true vs. Life ’s a beach, then you die…period 2. Jesus was resurrected from the dead vs. No way José! 3. Evolution vs. Creationism 4. Free will vs. Determinism Answers: Obviously, there are hundreds of ways to write dialogues for each debate. This is a rare time when “answers” will not be provided in this text. But ask yourself: As hypotheses, which criteria does each side meet well? As an hypothesis, does one side meet more of the criteria, or meet some of them better? If evidence for one outweighs the evidence of the other, then we don’t need to worry too much about these criteria; so for the sake of discussion, assume the empirical evidence or strength of argument is either equal or equally non-existent for each. # **Practice Problems: Criteria for Hypotheses Which one of the five criteria for hypotheses is
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the speaker below most clearly considering? 1. “My hypothesis is better because mine appeals to A and B, while yours appeals to A, B, and C.” 2. “Your hypothesis is worse than mine, because yours appeals to A and B, but A and B can’t both be true.” 3. “How on Earth could we ever determine if your hypothes is is true or not?” 4. “Your hypothesis is so vague that it fails to answer any of the question with any precision.” 5. “Your explanation for the origin of life on Earth appeals to a giant silicon -based being deep in space sending a rocket with sperm cells on the nose cone. But we have no reason to believe that there is any such intelligent life out there.” [Note: This was an hypothesis of a Nobel Prize-winning astrophysicist.] 6. “Your hypothesis says that the dinosaurs died d ue to starvation, but it also claims they died due to a virus. Which was it?” 167 7. “You hypothesize that Bob died from suicide. But we who knew him best knew him to be happy and quite content with life.” 8. “You theorize that Sunny Shine’s proclivity to garden and cycle naked is due to a complex set of early maladjusted family relationships that produced neuroses resulting in mannerisms conjoined with environmental factors producing her deviant social behavior. Isn’t it more likely that she enjoys being clothes-free just because it feels good?” 9. “The resurrection hypothesis accounts for the apostles’ later purportedly first -hand testimony of it and willingness to die for it better than any other hypothesis regarding the days following Jesus’ death. There’s no way the apostles would die brutally for what they knew to be a lie.” 10. “I can’t test my theory that after we die life is
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over any more than you can test your theory that the law of karma forces us to be reincarnated. For once we die, either way, we’re not going to be able to let o thers know what happened.” 11. “Your hypotheses consists of claims A, B, C, and D. But we know from experience that C is false. Thus we should reject your hypothesis.” 12. “Your hypothesis regarding the murder implies both that Albert hated his wife and th at he cared for her. No way!” 13. “Evolution makes no appeal to a divine intelligence, yet accounts for life as we know it. Thus it’s a better hypothesis than Creationism.” 14. “Free will matches up with the fact of moral responsibility and moral deliberat ion better than your determinist hypothesis saying that all acts are fully caused by antecedent conditions. Thus the free will hypothesis is better than the determinist hypothesis.” 15. “My hypothesis explains ten aspects of the puzzling question at hand; yours explains only five of them. Thus my hypothesis is a better hypothesis, all else being equal.” Answers: 1. Simplicity 6. Internal consistency 11. External consistency 2. Internal consistency 7. External consistency 12. Internal consistency 3. Fruitfulness 8. Simplicity 13. Simplicity 4. Explanatory power 9. External consistency 14. External consistency 5. External consistency 10. Fruitfulness 15. Explanatory power # Inference to the Best Explanation A growing number of philosophers and other thinkers are appealing to these five criteria for good hypotheses to engage in an inductive line of reasoning: Inference to the Best Explanation. It’s worth seeing how this form of critical thinking can be used. Once again, consider the situation in which there are two or more opposing answers to a question, yet there is insufficient evidence or argumentation to clearly point to one hypothesis being
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better supported than another. Once the equally-supported (or equally-unsupported) hypotheses are on the table, so to speak, we might try arguing by claiming that our hypothesis is better than any of the others, and on that basis should be accepted as most likely the true one. The way we establish that our hypothesis is better than the others is by showing that it best conforms to the criteria above. Perhaps —all else being equal —it answers more of the puzzling question, or perhaps it’s simpler, or perhaps it matches up with established beliefs better. None 168 of this goes to prove that our hypothesis is true, but it does argue that in comparison to the other offered hypotheses, ours is a better-formed answer to the question. Users of Inference to the Best Explanation must be careful to avoid certain pitfalls, though. One obvious potential problem for us is to view our hypothesis as the best because we merely think it the best. That would clearly be begging the question. We can’t say our hypothesis is better than the others without some sort of good reason. If there is objective reason to say our hypothesis is true , then we don’t need Inference to the Best Explanation; that objective reason itself gives adequate justification for believing our hypothesis. What we are limited in doing with Inference to the Best Explanation is arguing that our hypothesis is better formed as an hypothesis than the others, and somehow that makes it more likely for it to be true. This is a tenuous bit of reasoning, but it should at least justify everyone giving a serious look at our hypothesis. Another potential problem to avoid when using Inference to the Best Explanation is a common (perhaps all-too-human) tendency to believe one’s proposed hypothesis, and
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to see more readily how it conforms to the criteria above, while ignoring how the other hypotheses do so. Comparing competing hypotheses by appealing to the five criteria is not an exact science, and often cannot be quantified precisely. It’s usually a matter of considering informally the merits of each hypothesis, weighing the results, and making a thoughtful judgment when possible. Rarely will assessment of opposing hypotheses presented by intelligent and informed people result in a case of one being clearly the “best explanation,” unless, of course, there is some underlying begging of the question. A third potential problem is to inadvertently embrace the informal fallacy of False Dichotomy. Inference to the Best Explanation argues this way: 1. There are two (or three, or four, etc.) opposing hypotheses. 2. My hypothesis fits the criteria for hypotheses best of the two, making it the best explanation. 3. Thus, it is likely that my hypothesis is true. False Dichotomy occurs when someone offers a disjunctive syllogism (i.e., A or B; Not-A; Thus, B) when there is an additional option not being considered. Recall the teenager argument from our section on Informal Fallacies. “Mom, either you let me go to the dance with the biker gang, or my life will be ruined. Surely you don’t want my life to be ruined. Thus, you should let me go to the dance with this gang .” Mothers somehow intuitively know bad arguments, at least when presented by teenagers. They recognize that there is at least a third option not being considered in the daughter ’s first premise: She will not go to the dance with the biker gang, and her life will not be ruined. So, no, permission to boogie with the leather-clad ruffians is denied. So too with Inference to the Best Explanation. We
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must be sure —and have some reason to offer for believing so —that the hypotheses we are comparing are the only ones meriting consideration (and not beg the question i n our hypothesis’s favor in doing so). The burden of proof is on our shoulders to show that there are no additional hypotheses worth considering; and if we cannot offer such justification, then we should limit ourselves to concluding that our hypothesis matches the criteria for hypotheses better than do the others we are considering, and on that basis we are 169 justified in taking it seriously as a viable hypothesis. But this falls somewhat short of being able to claim that we have via this inference pattern given reason to believe our hypothesis is true. The long and the short of it may be that when well-established evidence or cogent/sound reasoning does not clearly establish that one thoughtful hypothesis is more likely to be true over a competitor, Inference to the Best Explanation may be the best line of reasoning we have. Be careful not to overstate its powers, though. # Testing Hypotheses One of the criteria for an ideal hypothesis was its fruitfulness, which included its ability to be tested. We now need to explore how we might reasonably test an hypothesis. The procedure is not obvious, and it was only “discovered” a few hundred years ago. With that process, scientists in Europe were able to make startlingly fast advances in knowledge about the natural world and in technological development. Those advances gave Europe the opportunity to do much good and bad in the world, and to make “the West” a powerful forced internationally. Hypothetical reasoning or the Scientific Method was not the only way of pursuing knowledge, but it has proven to be an effective and productive
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way of sorting out viable from non-viable hypotheses, and thus paves the way for even more advances in theory and practical development. Hypothetical reasoning is useful particularly when we cannot find an answer directly to a puzzling problem. Let’s say we find blue polluting goo floating down a stream, and we want to find the cause of this goo. All we need to do is walk up the stream. If we find a large pipe with this goo pouring out of it, and we see no blue goo flowing down from upstream, we’ve pretty well established where the goo came from. End of inquiry. But if the puzzling question pertains to events that happened in the past (e.g., How did those dinosaurs die?), or far away (e.g., Are mountains forming on Mars the same way they form on Earth?”), then we may not be able to look or test directly to determine the answer. Here we’d need to form an hypothesis, and devise a clever way of testing it indirectly . Ther ein lies the brilliancy of hypothetical reasoning, aka “the Scientific Method.” Hypothetical Reasoning involves a series of steps: 1. Articulate a puzzling problem 2. Collect information 3. Form an hypothesis 4. Draw an implication to the hypothesis 5. Test the implication 6. Draw a conclusion 1. Articulate a puzzling problem We begin the process with a puzzling problem that cannot be answered or explained with direct observation or testing. For instance, if Bill wants to know why Mary is angry (a puzzling problem, at least for Bill), he might ask her. If she’s willing, she’ll tell him: “You bumped into 170 my car when you backed out of our driveway, you idiot!” Bill has no need of hypothetical reasoning here, as he can get his answer directly. Sometimes,
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however, there is no one to ask and no opportunity to observe to get an answer. The cause of events in the distant past can be like this (e.g., a puzzling migration of an ancient civilization from one site to another), or events can occur in unobservable locations (e.g., on other planets, or at the center of the Earth, or at the atomic level). Here we can make use of hypothetical reasoning. 2. Collect information Before we are in a position to make a good hypothesis, we’re going to need some information . If we want to know what caused the dinosaurs to die, we’ll need to know what dinosaurs are, how they lived, and how they might die. We’ll need to draw from our knowledge about the world to form a reasonable answer to the question. If a police detective had the puzzling problem of determining who killed a man lying on the floor, he’d walk around the room looking at every detail he thinks might be relevant. That Barack Obama was the U.S. president in 2010 is probably not relevant here, so the detective would no t consider it. He’d likely consider a note clutched in the dead man’s hands and a knife in his back as relevant. Note that the detective will need to approach this stage of the inquiry already having a general idea as to what is likely to count as relevant information. This takes some previous background knowledge that not everyone has. A good detective will know enough and be experienced enough to make good judgments as to what might be important information regarding a murder. The detective will be observant enough not to let little details slide by his or her observation. Think of the television detective Adrian Monk walking around a crime
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scene with his hands squared up to help focus his search for details that can help him later form an hypothesis. Two points are worth noting already. First, to form a viable hypothesis, one usually needs to have a good deal of background knowledge about the situation. If we know nothing about how dinosaurs lived and how they might die, we’ll be hard pressed to come up w ith a reasonable answer to our question. Also, assumptions grounded in our world view will impact what information we consider to be relevant to the question. If we mistakenly assume, for instance, that all murders are caused by anger, then we’d miss or ig nore any information that might prod us to hypothesize that a murder took place because of greed. If we assume that animals die only from Earth-caused forces (e.g., disease, animal attacks, drowning, earthquakes), then we might miss or ignore information that might warrant our considering a cause of death from space (e.g., a meteorite carrying a deadly virus). We should thus be aware as best we can of any biases or assumptions we bring to the inquiry, and be aware that they can limit what information we collect in the process of forming an hypothesis. 3. Form an hypothesis Forming an hypothesis takes a certain amount of creativity, and that’s why some people are better at it than others. Two police detectives can enter the same room, collect the same information at the crime scene, but only one may pull it all together, see a pattern, and visualize what might have happened. Two auto mechanics examine the same stalled engine, but only one comes up with a reason to explain the problem. Only one, then, might have the creativity —or 171 genius —to form a viable answer to
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the question at hand. Some scientists, doctors, police detectives, and auto mechanics are better than others at this task. The hypothesis will ideally meet the five criteria discussed above. It will explain why the dinosaurs died in some detail, or who killed the man on the floor, how, and why. In both cases, we cannot simply look to see if the hypothesis is true. We can’t go back in time to see what happened to the oversized lizards or to the hapless sap lying on the carpet. The next step really is the key to hypothetical reasoning. 4. Draw an implication of the hypothesis We next draw one or more implications of the hypothesis. This is where many students get confused, so we’re going to take this p art of hypothetical reasoning slowly and proceed thoroughly. We can say that H implies I (or I is implied by H) if and only if the occurrence of H guarantees that I takes place. As there are different levels of guarantees, there will be different levels of strictness in implication. A logical implication will be the strictest. If “H implies I” is meant as a logical implication, then it is absolutely impossible for H to be true and I to be false. It would somehow result in a logical contradiction to say that H is true and at the same time from the same perspective say that I is false. For instance, Ann’s having exactly three coins (H) implies that Ann has an odd number of coins (I). It is impossible for Ann to have exactly three coins and not to have an odd number of coins. Other examples of logical implications include: If Bob is taller than Sam, then Sam is shorter than Bob. If Maria is the sister of Juan,
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then Juan is the sibling of Maria. If Aarav is the father of Krishna, then Krishna is the child of Aarav. If Daria is older than Eva, and Eva is older than Sofia, then Daria is older than Sofia. If the rag is moist, then the rag is damp. If A and B are true, then B is true. If A is true, and B is true, then A and B are true. If all dogs are animals, then it is false that some dogs are not animals. In each case above, if the first claim is true, it is logically impossible for the second claim to be false. There is a logical contradiction in saying otherwise. Claiming that Bob can be taller than Sam and that Sam can fail to be shorter than Bob contradicts itself. Hypothetical reasoning, however, does not require quite this strict a level of implication. Consider the following implications (again presented as “If…, then…” statements): * If a small boy eats five large hamburgers in one sitting, then he will afterwards feel full. * If a radio is tossed out of a high-flying airplane and falls to the ground, then it will break. * If a large meteorite lands on an animal, then that animal will be harmed. * If a man has his head cut off, then he will die. * If a dinosaur fails to eat for 1000 days straight, then it will starve to death. 172 In each case, it is logically possible for the first part of the conditional statement to be true and the second part of the statement to be false, but it is so incredibly unlikely that for all intents and purposes we can say that the second is pretty well guaranteed. Now we can come to the
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key point pertaining to hypothetical reasoning. An implication we draw from an hypothesis must meet two criteria: (i) the implication must be testable directly, and (ii) it must be pretty well guaranteed by the hypothesis. That is, we’ll not demand a logical implication , but for the process of hypothetical reasoning to continue effectively, the hypothesis must give us extreme confidence that the implication will be true. We’ll discuss the first criterion shortly, but here are some hypotheses with suggested “implications” that are not truly implications. That is, the purported “implication” does not f ollow from the hypothesis; the hypothesis does not guarantee in any practical manner that the purported implication will obtain. * If brontosauruses used to live in what is today Bellevue, Washington, then we’d today find brontosaurus bones in every backyard there. * If Bob killed the man lying on the floor, then Bob’s fingerprints will be on the knife in the man’s back. * If this afternoon is warm and sunny, then Sunny Shine will be tending her garden today. * If a bear messed up the campsite, then there will be bear fur all over the place. * If God exists, then my request offered in prayer will be granted. * If my request offered in prayer is not granted, then God does not exist. For an implication to do anything in hypothetical reasoning, we must be able to say confidently that if the hypothesis is true, then that lets us know that the implication is surely true. The implication can’t just be consistent with the hypothesis; and we can’t be satisfied with saying that the implication might be true if the hypothesis is true. # **Practice Problems: Hypotheses and Implications For each hypothesis and implication suggested below, determine whether the purported implication is truly
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implied by that hypothesis (it need not be a logical implication as defined above). 1. H: A lion killed the dead wildebeest lying here before us. I: The wildebeest carcass will show signs of claw or teeth marks. 2. H: The wind blew a tree over a power line causing the blackout in our house. I: Other houses nearby using the same power line will exhibit blackouts, too. 3. H: The maid killed the butler in the kitchen with a gun. I: The maid will admit to the killing. 4. H: Your car won’t run because you are out of gasoline. I: The car will run after you fill the gas tank with gasoline. 5. H: Your radio isn’t working because it’s not plugged in. I: By plugging the radio in, it will start working. 6. H: This society is generally opposed to murder. I: People will never murder one another in this society. 7. H: Jan studied for her logic test. I: Jan did well on her logic test. 173 8. H: Mehdi moments ago swallowed the packet containing the secret formula. I: If we looked inside Mehdi’s body, we’d find the packet. 9. H: Fatima is a college student who wants to be an anthropologist. I: Fatima will major in Anthropology. 10. H: Malaya is a woman. I: Malaya wears what she believes to be traditional women’s clothing. Answer: 1. Implication 6. Not an implication 2. Implication 7. Not an implication 3. Not an implication 8. Implication 4. Implication 9. Not an implication 5. Implication 10. Not an implication 5. Test the implication As we said, there are two character traits any good implication must have in hypothetical reasoning. For all practical purposes, the implication must be guaranteed by the hypothesis, and it must be testable directly. It’s
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because the hypothesis itself cannot be tested directly that we even go through the hypothetical method process. If an implication we draw is not itself testable, then we are back in the woeful state where we started. Of course, we might draw implications that are guaranteed by the hypotheses, but which are not themselves testable. Imagine the following line of reasoning that does so: “You want to know why the dinosaurs died? I’ll tell you! My hypot hesis is that ancient aliens landed on Earth and sucked all the cosmic vital energy from the behemoths, leaving them dead on the ground where they lay. An implication to my hypothesis, is —of course —that these aliens understood a lot about cosmic vital ener gy.” Aside from the many problems with the hypothesis itself (as an hypothesis), the implication that is drawn is not testable (although it is likely guaranteed by the hypothesis). There is nothing we can do to verify or falsify that ancient aliens knew a lot about this so-called “cosmic vital energy.” Imagine a slightly revised pronouncement: “You want to know why the dinosaurs died? I’ll tell you! My hypothesis is that ancient aliens landed on Earth and injected the dinosaurs with a virus that gave the behemoths arthritis, and then not being able to move easily, the dinosaurs died. An implication to my hypothesis, is —of course —that the bones of these dinosaurs will show traces of arthritis.” Here at least we have an implication that is testable. We can dig up dinosaur bones, and see if they show signs of arthritis (a process that is quite do-able in many cases). Whether the bones do or do not show such signs will tell us something important about the hypothesis. So, we may not be able to test directly
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the hypothesis itself, but for hypothetical reasoning to work, we must be able to test to see if the implication (which is different from the hypothesis) will come out to be true of false. 174 6. Draw a conclusion If the test of the implication comes out negative (i.e., false), that tells us one thing about the hypothesis. If the test of the implication comes out positive (i.e., true), that tells us something else about the hypothesis. Let’s think abstractly for a moment. Let H stand for the hypothesis, and I stand for the implication we draw from it. Then after testing the implication, let’s imagine we get a negative result; the implication turns out to be false. If H, then I [that’s the implication we draw from the hypothesis] Not-I [the test of the implication comes out negative] What should we conclude? The deductive propositional logic pattern of Modus Tollens tells us: If H, then I Not-I Thus, not-H If I is truly an implication of H, and if I tests out as false, then Modus Tollens tells us that the hypothesis must be false. We thus have used hypothetical reasoning to disprove an hypothesis. For instance: If a meteorite hit the Earth causing dust that blocked enough sunlight to kill plants and starve dinosaurs, then there should be uniform a layer of dust (allowing for changes in geographical topography) underground around the world. [For the sake of this example, let’s pretend that this is a good implication.] The chief scientist in the process gets underpaid graduate students to go around the world and dig holes looking for that layer of dust. And now let’s imagine that no such layer of dust is found. What’s the result? Well, if the hypothesis is true, there should be a layer of
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dust that can be found. But there is no such layer of dust. So the hypothesis must be false. Another example: The detective hypothesizes that Andy killed the man on the floor by picking up a knife and stabbing the man with it. One implication would be that Andy has the strength to use a knife. The detective goes to Andy to ask him some questions, and finds out that Andy has been in a coma for the past month, and could not have used the knife. The detective concludes that his hypothesis about Andy killing the man with a knife must be rejected. Hypothetical reasoning is thus pretty adept at disconfirming, falsifying, or ruling out bad hypotheses. That is, this line of reasoning is a powerful tool in showing that a theory or hypothesis should be rejected. Things are little different when we use it to confirm hypotheses or to show that they are true. Consider the following abstract scenario: If H, then I [we draw an implication from our hypothesis] I [the implication tests positively, that is, the implication comes out to be true] What can we conclude here? That the hypothesis is true? That would look like this: 175 If H, then I IThus, H But this is an example of the formal fallacy known as Affirming the Consequent. Any argument fitting this pattern will be invalid. The first two claims do not guarantee the conclusion; that is, it is possible for the first two claims to be true and the conclusion false. So —and here’s a subtle point about much of the science and police work based on hypothetical reasoning —hypothetical reasoning can disprove an hypothesis, but it can’t really prove an hy pothesis to be true. That said, hypothetical reasoning can give use good reason
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to be happy with an hypothesis. We might say that if the procedure is used well, it can confirm an hypothesis. Going back to the dinosaur/meteorite hypothesis/implication, if those underpaid graduate students dug holes all over the world and did find a uniform layer of dust, that would not prove the meteorite hypothesis to be true, but it would confirm it somewhat. It would give us reason to think that we might be on the right track. So what should we do then? Come up with another implication! If the full meteorite hypothesis is true, then there should be an extra thick layer of dinosaur bones near the layer of dust, because it’s the dust that was the indirect cause of the dinosaurs’ death. So the primary investigating scientist sends her graduate-student minions out to re-dig those holes and to look this time for an extra thick layer of dinosaur bones. Eureka! They find them! The scientist is really happy about her hypothesis at this point, because two things the hypothesis pointed to showed up to be true. Can she further confirm her hypothesis and get even more grant money? Yes! She needs to draw yet another implication. Hm. “If my hypothesis is true,” she might reason, “there should also be an extra thick layer of plant fossils near the extra thick layer of dinosaur bones we just found, since the plants’ death is what caused the dinosaurs to starve. Minions! Dig once again!!” If the now weary graduate students find the expected plant fossils, then that adds further confirmation to the hypothesis. This procedure will never deductively prove the hypothesis to be true (for that would engage the hypothesis’s proponents in the fallacy of Affirming the Consequent), but it can provide so much confirmation that only drooling idiots will
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say, “Well, you haven’t proven your point; and besides, it’s just a theory .” It’s responses like this that can drive otherwise stable scientists to drink. # Oh, if it were only that easy… …life would be pleasant, carefree, and long, instead of nasty, brutish, and short. You didn’t really think science was this straightforward, did you? If it were, someone would have discovered a cure for every form of cancer by now, and we’d understand how your le ast favorite U.S. P resident got elected. We’ve already hinted at many potential problems in using hypothetical reasoning. (i) We may be dumb as dirt and not even understand the question pertaining to the puzzling phenomenon. (ii) We may not know enough about the world or have enough intellectual creativity to come up with a viable hypothesis answering the question. (iii) We may be unable to see what would be implied by our hypothesis. (iv) The “implication” we come up with may not be truly implied (or guaranteed) by our hypothesis. (v) The implication 176 we come up with may be useless because it’ s not testable. (vi) The underpaid graduate students we use to test our good implication may do poor work (due to laziness, inebriation, human error, or having slacked off during their training in lab science classes) and not get accurate test data. (vii) We may overstate our results by saying that we’ve proved our hypothesis to be true when all we really should have said is that we’ve confirmed it. The additional complexity we now need to understand pertains to the last part of the process in which we draw a conclusion from the results of our test of the implication. So far, we’ve been thinking in fairly simple and simplistic terms: If H, then I or
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If H, then I I Not-I Thus, H is confirmed Thus, not-H On the left, we conclude that we’ve confirmed our hypothesis; on the right we conclude that we’ve disproved our hypothesis. Neither assessment is quite correct because the vast majority of philosophically interesting hypotheses are complex critters consisting of more than one claim. Earlier, when we were looking into the enviable character traits of being internally consistent and simple we noted that many hypotheses make more than one claim. More often than not, the hypothesis is actually a conjunction of claims such as A+B+C+D+E. The dinosaur/meteorite hypothesis had about that many parts to it. So, in a sense, H=(A+B+C+D+E). So, what is actually happening in hypothetical reasoning is this: If A+B+C+D+E, then I or If A+B+C+D+E, then I I Not-I Thus, A+B+C+D+E is confirmed Thus, not-(A+B+C+D+E) Consider the line of reasoning above and to the right. What is it that will make you reject as false A+B+C+D+E as a whole? If any one or more parts of it are f alse, then you’d say that the conjunction (an “and” statement) as a whole is false. For instance, figure out when you would agree or disagree with the four statements below as wholes: 1. Elephants fly, Oregon is a state in the USA, and 2+2=4. 2. Mermaids exist, Oregon is south of California, and the Seattle Mariners are a baseball team. 3. Paris Hilton is a space alien, the Earth has three Moons, and 2-1=1. 4. Circles are round, Ronald Reagan was a U.S. president, and 2+3=5. You disagree with numbers 1, 2, and 3 because there is at least one claim in the conjunctions that is false. The only way a conjunction can be true is if each of its parts (i.e., its conjuncts ) is true, as with
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number 4. So, if a conjunction is found to be false, then all we really know at that point is that one or more of its elements is false. So for the use of hypothetical reasoning above and to the right, all we can say is that we’ve disproved A+B+C+D+E . But it might be that only A (or B, or C, or D, or E, or A+B , or A+B+C , etc.) is false. Actually, the key part of the hypothesis might be true, and some relatively unimportant part of the hypothesis is false. The point is that we have 177 only gotten started in narrowing down the core problem of our hypothesis. We might still have hope that the key element is true, regardless of what we found out above to the right. An analogous problem lies in using hypothetical reasoning as we did above to the left where we concluded that we’d confirmed our hypothesis. Since Affirming the Consequent is an invalid inference, we are not justified in saying that the truth of I confirms all of A+B+C+D+E . It may be that part of this complex hypothesis is enough to guarantee I, and that’s why the results of the test on I came out positive. I being true really only confirms something about H (i.e., A, or B, or C, or A+B , or A+B+C , etc.), but further work is needed to confirm that H as a whole is true or that only certain parts of H are true. So it may be overstating things to even say that the hypothetical method disproves or confirms much of anything. Still, it’s a powerful tool for considering hypotheses, and if we pay enough attention to the details, we can warrant enough confidence in an hypothesis to make
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looking elsewhere for others a seemingly pointless task. Sometimes rational inquiry can give you enough to send a rocket to the Moon and have it land safely in exactly the intended spot, without deductively proving any part of the inquiry and discovery process along the way. Such is life with inductive reasoning. # **Thinking Problems: Hypothetical Reasoning 1. Your desktop computer suddenly stops working. Think of an hypothesis to explain this phenomenon, and draw one good, testable implication to this hypothesis. 2. Imagine that you just baked a dozen chocolate chip cookies, placed them atop a counter, and told your precocious five-year-old son to stay away from them until after dinner. You go upstairs to print some more re-election fliers for your Senate race, and hear a crash in the kitchen. You run down to find a half dozen warm cookies and the plate smashed on the floor. Your son sits in the corner of the kitchen by the swinging door, and says, “Mommy, a ghost came in, ate some cookies, and dropped the plate. He just left.” How might you use hypothetical reasoning to determine what really happened? 3. Read about planet Neptune, and briefly explain how the method of hypothetical reasoning played a role in its discovery. ( 4. Read the Sherlock Holmes short story by Sir Arthur Conan Doyle titled, “The Adventure of the Redheaded League.” Briefly explain one way Sherlock Holmes uses hypothetical reasoning in the story. ( Answers: 1. Many good responses are possible. For instance: H1: the building’s power is suddenly shut down. I: the room lights won’t work either. H2: you accid ently unplugged your computer from the wall. I: the plug will not be plugged in. 2. Multiple scenarios are possible. For instance: Puzzling problem: missing cookies [we might tackle one puzzling
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problem at a time; the breakage of the plate is a separate puzzling problem, although it’s probably related to the loss of the cookies]. Hypothesis: the son got up on the counter and ate some cookies. Implication: the son would have cookie crumbs and melted chocolate in his mouth. Test: the mother looks in the son’s mouth and finds no cookie crumbs or 178 chocolate. Results: Her hypothesis is disproved, as the kid did not have enough time to rinse his mouth clean; the missing cookies must be due to something other than the son eating them. 3. Puzzling problem: Uranus had strange, unexpected perturbations in its orbit. Hypothesis: an unknown planet existed whose gravitational pull was affecting the orbit of Uranus. Implication: this previously unknown planet would be in spot X in the night sky at a particular time. Test: a planet was found in exactly the spot predicted. Results: the “new planet” hypothesis was confirmed. 4. Multiple answers are possible. Look for a specific question Holmes is trying to answer. He will then form an hypothesis, draw an implication form it, and then test that implication. Why, for instance, do you think he was tapping his stick on the ground outside the Redheaded League’s office? # **Practice Problems: Hypothetical Reasoning Are the following claims true or false? 1. An hypothesis can have at most one implication. 2. Only one hypothesis may accurately explain a given puzzling problem. 3. In hypothetical reasoning, the hypothesis must be testable directly. 4. In hypothetical reasoning, the implication must be testable directly. 5. In hypothetical reasoning, the test of an hypothesis will either confirm or disprove it. 6. In hypothetical reasoning, the test of an implication will either confirm or disprove a simple, one-part hypothesis. 7. In hypothetical reasoning, the puzzling problem must
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imply the hypothesis. 8. If an hypothesis says a liquid is an acid, then an implication would be that placing blue litmus paper in the liquid will cause it to turn red. 9. The person forming the hypothesis and implication must be the person performing the test on the implication. 10. One’s worldview can impact what hypotheses one is willing to entertain in answering a puzzling problem. Answers: 1. False 6. True 2. False 7. False 3. False 8. True 4. True 9. False 5. False 10. True 179 # Chapter 13: Definitions and Analyses Far too often when people are debating the answer to some question, they end up talking at cross purposes. Someone listening in might say, “Oh, they’re just wrapped up in semantics” or “They aren’t even talking about the same thing.” The likel y problem in this debate is that each side is using the same word but meaning something different by it. Imagine a dispute about God’s existence in which one woman is referring to the supremely perfect being of traditional theism while the other is talking about a lesser being like Zeus of ancient Greece. The two interlocutors could bound on indefinitely without ever gaining ground, all because neither took the time to define her terms. Definitions thus are an important part of reasoning, and are worth exploring in some detail. Definitions are usually desired for a word . We might, for instance, want to know someone’s definition (or meaning) of the word ‘God’. Once we understand each other, we can then move forward to examine reasons for believing in the existence or non-existence of such a being. If Sue is trying to demonstrate that a supremely perfect being exists, and Mandy is trying to show that a lesser god (like Zeus) does not,
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their conversation will be surreal at best. Definitions assist in avoiding two problems in rational conversations: ambiguity and vagueness. A term can be ambiguous when it has multiple clear meanings. The word ‘bat’, for instance, may refer to a lathed piece of lumber intended to smack baseballs, or it can refer to a cave-dwelling flying mammal. If someone uses the word ‘bat’ in a conversation and I cannot detect the intended meaning, I may need to ask for a definition. Also, some words are vague ; they have a generally understood meaning, but their specific meaning remains unclear. Imagine someone explaining that bonsai are not tall trees. (We refer here to the Japanese art form of pruned trees growing in small pots or trays.) The word “tall” here is vague. We know generally speaking what it means to be tall, but what counts as “tall” in the context of bonsai? If the bonsai enthusiast explains further that by “tall” he refers to trees over six feet in height, the vagueness dissipates, and the conversation or debate may continue with all involved knowing what the other is talking about. The word ‘poor’ can be both ambiguous and vague, as in “Shahd is poor.” Are we saying that Shahd is poor in spirit? Poor in skill or quality? Poor financially? Let’s disambiguate the word, and say that we are referring to financial status. She lacks money in some sense. Still, the word is vague, as the specific meaning remains unclear. Compared to many villagers of poorer countries, Shahd might be quite rich, but compared to Bill Gates, she might be woefully impoverished. If I ask, “What do you mean by ‘poor’?” I’d be asking for clarification. “I mean she has less annual income that 90 percent of the people in the town
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she lives in,” the other might reply. “Okay,” I can continue, “I now know what you mean by ‘poor’ in this context.” Let’s also introd uce some vocabulary. A definition is made up of two things: the definiendum (the word to be defined) and the definiens (the words doing the defining). Definition = Definiendum + Definiens 180 An example of a definition is, “The word ‘ice’ means frozen water.” Here, “Ice” is the definiendum, and “frozen water” works as the definiens. Another technical nicety pertains to proper use of quotation marks. If we are quoting someone or using a word, we’ll use double quotation marks (unless we are in a British or Bri tish-aligned country, in which case we’ll do everything backwards compared to how the USA does it). Note that in the USA, periods and commas are placed before (i.e., inside) double quotation marks. If we are referring to or mentioning a word (not quoting it), then we use single quotation marks. For instance, if we want to say that the word ‘snorkel’ has seven letters in it, we’d punctuate the word exactly as we just did. Also —in the USA —when we use single quotation marks, commas and periods are properly placed after the quotation mark. For the following examples pay attention to the placement of quotation marks, periods, and commas: * Bob said, “I love snorkels!” * Sally said, “Snorkel.” * Sally said, “I love to say the word ‘snorkel’.” * Sally said, “Bob whispered with glee, ‘Snorkel.’” * Hamza said, “I use a snorkel when swimming.” * “I too like snorkels,” Youssef said. * Bob said, “Snorkels are fun to use”; later he said, “They are particularly fun to use in the ocean.” * The word ‘snorkel’ has seven lett ers in it. Quotation marks are
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used so haphazardly, what with newspapers throwing punctuation out the window in grappling with the confinements of the fourth-grade reading level of their intended readership, and of the narrow size of their text columns. British magazine and book editors will do one thing, Americans something else, and far too many don’t seem to care. Philosophers and linguists pay the most careful attention to these things, so it’s little wonder that students have seen a dizzying variance in punctuation styles. In this text, too, there has been an effort to keep things simple, and to use double quotation marks (or italics) to quote, set apart, or emphasize words or phrases. For the most part, this text will continue in this vein, but the rigors of critical thinking as it relates to definitions demand that we be at least aware of the issue. # Purposes of Definitions There are many reasons for wanting clarification on a word or phrase. Let’s consider the following purposes of definitions: Lexical Precising Stipulative Persuasive Theoretical 181 Lexical Purpose A lexical definition provides the general meaning of a word or phrase as understood by the majority of ordinary people. Dictionaries are sometimes called “lexicons,” and attempt to provide exactly this meaning. If I want to know what most people mean by the word ‘snorkel’, I can look in a dictionary and find something akin to the following: 1: any of various devices (as for an underwater swimmer) to assist in breathing air while underwater ; 2: a tube housing air intake and exhaust pipes for a submarine’s diesel engine. If there are multiple definitions, then the first listed in the dictionary will be the most popular or most common (at least at the time of that edition’s publication). Lexi cal definitions thus give a general, sometimes overly
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simple meaning understood by most “people on the street.” If you do not know what a word means, a lexical definition may be enough to give you a basic facility in using the word. Meanings can, of course, change over time, and that is why —at least in the USA where language tends to be rather fluid and ever-changing —it’s important to have access to the latest edition of a good dictionary. The most common meaning of ‘pot’, ‘lid’, and ‘gay’ may have meant on e set of things 100 years ago, but it’s quite possible the most common meanings have shifted today. We thus can be mistaken in our belief about a lexical definition, and reliable dictionaries help us understand the meaning words more accurately. Precising Purpose Sometimes we have a general understanding of what a word means, but need a more precise definition of it in a particular circumstance. Here is where we’d want a precising definition. Such a definition has as its purpose to make a generally understood meaning more specific to a particular situation. Precising definitions often have a clause pointing out their precising nature: “For the purposes of X , Y means Z.” For instance, we all know what it means to be financially poor , but imagine the problem if a bank acquires access to $50,000,000 for loans to “poor” people, and advertised the opportunity by saying, “Loans available to the poor!” One person in the bank’s Bellevue, Washington neighborhood might take himself to be poor, when he’s actually fil thy rich compared to many people around the world, but impoverished compared to some of the upper-level Microsoft administrators living in Medina on Lake Washington. What the bank needs to do is provide a precising definition of “poor,” and say, perhaps in small print,
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that “For the purposes of this bank loan, ‘poor’ means having a net annual family income of no more than $10,000.” Now we know what ‘poor’ means in this specific situation. Sometimes a word has more than one meaning, and we need a precising definition to tell us the context for the particular intended meaning. The word ‘strike’, for instance, has a variety of meanings pertaining to baseball pitches, bowling scores, labor disputes, the lighting of a match, or a blow to the face with a fist. If Theresa simply says, “A strike is a good thing,” we’ll not know if we should agree with her or not. But if she defines her terms as follows, then all is clear: “A strike— in the context of a miner looking for gold —is a good thing, at least for the miner.” 182 Precising definitions sometimes overlap with lexical ones, as a word might have multiple ordinary meanings, but each is used in a distinct circumstance. The lexical definitions may need to provide context for each partial definition. The lexical definitio n of ‘strike’ might say, in part, “1: in the context of labor disputes, an organized halt of labor; 2: in the context of baseball, a pitch that is delivered past the batter over the plate, below the batter’s shoulders, and above the batter’s knees…” It’s n o surprise that people might have more than one purpose for a definition. Stipulative Purpose A stipulative definition is offered when there is a need for a new word to name a new or selected object, or when a word with an established meaning is given a new usage. For instance, if I invent a machine that washes dishes and tells me the time, I get to choose what to call it, and I
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might stipulate that it be called a “washclock.” If zoologist Barry has discovered how to mate a horse with a gorilla (even though none of us can think of a good reason to do so), and the tender moment produces offspring, Barry gets to stipulate what to call the ensuing critters. Perhaps he’ll call them “horsillas.” That would be a stipulation on his part. Or Barbara could decide t hat she wants to call the dan delions in her front lawn “imps.” We can’t say that she’s wrong. The word ‘imp’ may already have an established meaning (an imp is a devilish little creature), but if Barbara wants to stipulate that that’s what she means by ‘imp’, then that’s her business. In a sense, stipulative definitions can’t be wrong. If Stan decides to call the wrinkles in his elbows “glips,” there’s no one who can tell him not to do so. Any use of language may be counter to accepted meaning, but if Stan wants to call those fissures glips, he can. He stipulated it; he decided that that’s what he wished to call them. If, moreover, the word catches on and works its way into day-to-day parlance, then if the editors of dictionaries are doing their job well, the lexical definiens of ‘glip’ may very well become “elbow wrinkles.” That is, what started out as a rather arbitrary stipulation can become so popular as to have a commonly shared meaning ripe for a lexical definition. Persuasive Purpose If what we wish to do with a definition is to persuade emotively someone to a given position, then we want a persuasive definition. Persuasive definitions use emotive, affective language to try to sway people to one side or another. They do not usually tell us what people normally mean by the
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word, so they are not lexical. Nor are they usually new words selected for a new or subjectively selected object, so they are not stipulative. Usually the person offering the definition is trying to avoid using logic or evidence to c onvince another; he’s trying to stir emotions (positively or negatively) so that the other will feel good or bad about the thing being defined. For instance: * ‘Abortion’ refers to the senseless slaughter of innocent babies for self-centered motives. * ‘Abortion ’ refers to the natural right of all women to experience liberty and self-autonomy. 183 Well, who would want to slaughter an innocent baby? And who would not support women’s rights to autonomy? But neither of these “definitions” explains what abortion is. They provide no cognitive information; they simply stir emotions. Note the use of words and phrases that we associate with bad (or good) things. A more informative definition would use language that is emotionally neutral. Here are a couple more examples: * The word ‘c hess ’ refers to a silly and puerile game fit only for the socially inept * The word ‘c hess ’ refers to a noble game fostering the highest intellect, uniting cultures, and giving rise to clear, methodical thinking. Theoretical Purpose Finally, a theoretical definition attempts to provide a developed, full understanding of what a word means. Usually, theoretical definitions are desired when the meaning as embraced by most “people on the street” is insufficient. Philosophically or scientific ally complex words often require such definitions. Philosophers, for instance, will often discuss the nature of “moral goodness.” “What does ‘morally good’ mean?” they might ask. Appealing to a dictionary will hardly help, nor can a philosopher simply say, “I stipulate that ‘moral goodness’ means X! There, the conversation is over.” Theoretical definitions
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are an attempt at giving a true, informative understanding of potentially complex words. From the philosophy of Britain’s John Stuart Mill (1806 -1873), we might define ‘good act’ as an act that maximizes happiness for all involved. The German philosopher Immanuel Kant (1724-1804) might have defined it as that which is consistent with the Categorical Imperative. Both of these definitions need explanation to be fully informative, but that’s what a theoretical definition aims to do. Theoretical definitions of words referring to philosophically interesting concepts are decidedly open to intelligent debate. There have been a number of viable attempts at defini ng ‘good act’ over the millennia. Such debates are more often over the better analysis of a concept than over the meaning of the related word, so perhaps we should defer further discussion along these lines until we look at analyses more closely. If a word refers to a fairly simple item, like a square, then a theoretical definition may be quite similar to a lexical definition: ‘Square’ means an enclosed, planar geometric figure with four equal sides and four right angles. But try getting a definition of an electron from people walking the streets, and it will surely be unserviceable for a physicist studying subatomic particles. Such scientists need a richer, more informative definition than will likely be found in a lexicon. We’ll revisit the deeper needs of theoretical definitions shortly when we discuss analysis. # **Practice Problems: Purposes of Definitions For each definition below, determine whether its single clearest purpose is lexical, precising, stipulative, persuasive, or theoretical. 184 1. ‘Crosshair’ means a fine wire or thread in the focus of the eyepiece of an optical instrument used as a reference line in the field or for marking the instrumental axis. 2. ‘ Golf ’ refers to a ridiculous
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“sport ” in which grown men dress up like idiots and chase a little ball around on overly fertilized fields of unnatural grass. 3. Bernadette just developed a new variety of cannabis. She’s going to call it ‘Bellevue Blitzkrieg’. 4. ‘Magnetic’ refers to a magnet’s moment (also called magnetic dipole moment and usually denoted μ) that is a vector characterizing the magnet’s overall magnetic properties. For a bar magnet, the direction of the magnetic moment points from the magnet’s south pole to its north pole, and the magnitude relates to how strong and how far apart these poles are. In SI units, the magnetic moment is specified in terms of A •m 2.5. ‘Magnetic’ means 1. a. Of or relating to magnetism or magnets. b. Having the properties of a magnet. c. Capable of being magnetized or attracted by a magnet. d. Operating by means of magnetism; 2. Relating to the magnetic poles of the earth; 3. Having an unusual power or ability to attract. 6. Euthanasia is the cold-hearted murder of helpless souls who can’t cry for help. 7. For the purposes of a baseball game, the word ‘pitch’ refers to the throwing of a ball by the pitcher to the batter. 8. The Chinese philosopher Kongzi (551-479 BC) used the word ren to refer to the fullness of developed human nature in which people can and wish to empathize with others, and wish to seek after the well-being of others. 9. “Motion sickness” means sickness induced by motion (as in travel by air, car, or ship) and characterized by nausea. 10. The word ‘pin’, in golf, refers to the flag pole placed in each hole’s cup. 11. “To make my discussion simpler, I’m going to refer to contributory causes as ‘INUS conditions’.” 12. ‘Strife’ means a bitter, sometimes
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violent conflict or dissention. 13. ‘Communism’ refers to a godless ideology festering in intellectually feeble countries and oozing its way to mindless, lazy masses. 14. A ‘valid’ argument is one in which it is impossible for the premises to be true and at the same time and from the same perspective the conclusion be false. 15. ‘Knowledge’ means adequately justified cognitive assent to a proposi tion that corresponds truly with the world. Answers: 1. Lexical 6. Persuasive 11. Stipulative 2. Persuasive 7. Precising 12. Lexical 3. Stipulative 8. Theoretical 13. Persuasive 4. Theoretical 9. Lexical 14. Theoretical 5. Lexical 10. Precising 15.Theoretical # Types of Definitions Definitions that attempt to provide the cognitive meaning of a word fall into two basic camps: extensional and intensional . An extensional (aka denotative) definition provides examples or a 185 list of members of the group referred to by the word being defined. The list might be complete —as with “‘Highest mountain in the world’ means Mt. Everest” or “‘Ocean’ means the Atlantic, Pacific, and Indian”; the list might instead be partial, as with “‘Country’ is something like Per u, Angola, or France” or “‘Baseball team’ means something like the Giants, Mariners, Yankees, or White Sox.” Intensional (aka connotative) definitions provide a description, or character traits of the thing referred to by the word being defined. For instance, * ‘Ice’ means frozen water. * ‘Wife’ means married woman. * ‘Jolly’ means jovial. * ‘Philosophy’ comes from two Greek words together meaning love of wisdom. * ‘Hot’, for spas, refers to the water’s ability to raise the mercury in a thermometer to ov er 95 F. Here the definitions are attempting to provide the meaning of the definiendum. With extensional definitions, all we get are examples, or a list of what counts as being a
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member of the definiendum. Examples may help, but they do not really provide an explanation of what the word means. At best, they may serve as illustrations for the meaning conveyed by a more informative intensional definition. There are at least three kinds of extensional definitions: Demonstrative definitions Enumerative definitions Definitions by sub-class A demonstrative (aka ostensive) definition simply points to an example of the thing referred to by the word being defined. If a woman wishes to provide a demons trative definition of ‘chair’, she might point to or direct ou r attention toward a chair. “What does ‘chair’ mean?” we might ask. She points to one, and ideally we nod in understanding. “Oh, it’s one of those things.” She could also draw a picture of a chair and direct our attention to that. If limber enough, and perhaps majoring in performance art, she might hunch down, make herself look like a chair, and point to herself. A more common extensional approach is the offer of enumerative definitions. These provide specific, named examples of the things the word refers to. For instance: * ‘Baseball player’ is someone like Willie Mays, Babe Ruth, or Hank Aaron. * ‘U.S. State’ means something like Alabama, Oregon, Indiana, or Hawaii. * ‘Mountain’ refers to things like Mt. Si, Mt. Rainier, and Mt. Everest. A more general extensional approach is to use a definition by sub-class . Here, we don’t provide specifically named examples; we instead provide classes or groups that exemplify the thing referred to by the word we’re trying to define. For instance: 186 * ‘Baseball player’ i s something like a second baseman, an outfielder, or a pitcher. * ‘College major’ is a focused study in a reas like psychology, philosophy, or chemistry. * ‘Machine’ means something like a computer, automobile,
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threshing mill, or radio. Extensional definitions, again, offer no explanation of a word. Examples may help illustrate a more informative definition, but if you really do not know what the word ‘mountain’ means, hearing that it is something like Mt. Si, Mt. Rainier, or Mt. Everest could just as easily tell you that ‘mountain’ means something people climb on, or something with rocks and trees on it, or something found on maps, or something tall. In a day-to-day setting, an extensional definition may be all we need to get a basic idea of what a word is likely to mean, and we can usually ask for clarification if we need more information. It’s with intensional definitions, however, that the most cognitive information is conveyed, and that’s the main purpose of most definitions. There are many ways of attempting to convey the meaning of a word. Some are more useful in some contexts; others are more useful in other contexts. Let’s examine the following kinds of intensional definitions: Etymological definitions Operational definitions Synonymous definitions Analytical definitions An etymological definition appeals to the etymological roots of a word or phrase to be defined, explains what it means in the original language, and hopes that will help people understand the present meaning of the word. Many words used in English, for instance, have roots in Latin, Greek, Sanskrit, or Arabic. So if we wish to define ‘ignition’, we might say “‘Ignition’ comes from the Sanskrit word ‘Agni’, which is the name of the Hindu fire god.” Other examples of etymological definitions include the following: * ‘Gymnasium’ comes from two Greek words meaning place of naked training. * ‘Karma’ comes from the Sanskrit verb kr , which has the double meaning of to do and to make. * ‘Pornography’ comes from the Greek word
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pornographos , which means depicting prostitutes. * ‘Algebra’ comes from the Arabic word al-jabr , which means completing or restoring broken parts. Etymological definitions can be interesting, and they can give some insight (historical or otherwise) into a word’s use and meaning, but they often are of limited use when the primary goal is to convey today’s meaning as used in ordinary or technically precise discussion. Every philosophy instructor feels compelled to tell his or her class that the topic under discussion comes from the Greek words phileo and sophia , and that Philosophy is thus the love of wisdom. But does “love of wisdom” really do much to explain what students will be doing in a philosophy class for the next ten weeks? And what about the meaning of ‘gymnasium’ ? It could put a whole new slant on co-ed PE. 187 Operational definitions provide a test by which to determine if something is accurately referred to by the word being defined. For instance, if we wanted to define ‘hot’ in the context of ironing, we could say “‘Hot’— in the context of an iron used for pressing clothes —refers to a temperature high enough that when you lick your finger and quickly touch the iron the iron sizzles.” Other examples include: * Peanut oil is ‘hot’ in a wok when it begins to shimmer a nd just before it starts to smoke. * A liquid is ‘acidic’ if blue litmus paper turns red when it touches the liquid. * ‘Passing’ means—in the context of Smith’s Logic class— receiving a GPA of 0.85 or better on the tests. * ‘Tall enough’ for this roller coa ster means you stand above the hand held out by this wooden figure. A synonymous definition provides a synonym for the definiendum. As long
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as the person asking for clarification of a word understands the synonym, such a definition can be of practical use. For example: * ‘Physician’ means doctor. * ‘Damp’ means moist. * ‘Arid’ means dry. * ‘Jocular’ means jovial. World language students are often quite satisfied with synonymous definitions. Oftentimes, though, a word referring to a complex thing may not have an exact synonym in the language used. We’d be hard pressed to find exact, accurate synonyms for ‘love’, ‘justice’, and ‘time’; and if we did find one, it may not be of much help, since if people do not know what the original word means, they may not know what the synonym means either. The most informative type of intensional definition is what we can call analytical , as it gives an analysis of what the term means. Finally, among all the types of definitions we’ve looked at so far, this one attempts to explain accurately what characterizes the things referred to by the word being defined. A common, effective, and highly informative way of doing this is to provide the genus and difference of the word. The genus refers to the general kind of thing the word refers to. For instance, consider, “‘Skyscraper’ means tall building.” Here “building” is the genus , as that word refers to the general kind of thing a skyscraper is. But what kind of building? An igloo? A mud hut? A doghouse? A two-story apartment? No, skyscrapers are tall buildings. “Tall” here functions as the difference in the definiens. Scientists use the method of genus and difference to name animals and plants. The genus points to the kind of thing they are, and the difference differentiates them from all the others within that genus. Of course the word ‘tall’ can be vague, so further
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elaboration may be necessary, but we now have a basic cognitive understanding of what the word ‘skyscraper’ means, and this is far more than extensional or other int ensional definitions are likely to do for us. Both the genus and the difference may contain multiple traits. “‘Son’ means male offspring” has only one trait (and one word) per genus and difference, but “‘Boy’ means young human male” 188 (intending “human male” for the genus) has two traits for the genus (human + male). Of all beings that are both human and male, boys are the young ones. Also, when presented in English, a genus and difference definition need not state the genus first. English is flexible enough not to require that one comes before the other. Note, moreover, that sometimes it’s not clear which of two traits is the genus and which is the difference. That’s okay! Consider “‘Ice’ means frozen water.” We could intend to get across the idea that of a ll frozen things (the genus), ice is water (as opposed, for example, to frozen hydrogen or yogurt); or we could intend to get across the idea that of all forms of water, ice is the frozen form (as opposed, for example, to water vapor). Either way, we are c onveying what ‘ice’ means, and were doing so accurately and informatively. Here are some more examples of definitions attempting use of the analytical method of genus and difference (with the intended genus underlined and the intended difference in italics): * ‘Husband’ means married man. [The genus and difference could easily be switched here.] * ‘Square’ means enclosed geometric figure with four equal sides and four right angles .* ‘Hammer’ means a tool used for pounding .* ‘Student’ means a person who studies .* ‘Biology’ means the study of
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life .* ‘Coffee mug’ means a handheld container with a handle used for holding and drinking coffee .* ‘Logic teacher’ refers to an instructor who wishes to torment students with useless information .Note that some analytical definitions may be false, as these are not mere stipulations stating how someone arbitrarily wishes to use a word. This is an attempt to explain what the word actually means, given current usage in a given context. To define ‘circle’ as a flyin g elephant would be false, because circles are enclosed geometric figures, not aerial pachyderms. # **Practice Problems: Types of Definitions For each definition below, determine which type it most clearly illustrates. Do not be concerned with whether the definitions are accurate or not. 1. ‘Calculator’ means a machine that can add and subtract numbers. 2. ‘Flower’ is something like a rose, lily, daisy, or tulip. 3. ‘Tool’ means instrument. 4. ‘U.S. President’ refers to people like George Washington, Abraha m Lincoln, and George W. Bush. 5. ‘Civilized’ comes from the Latin word civis ¸ referring to living in community. 6. ‘Sentence’ means the kind of thing you are presently looking at. 7. Cooking oil is said to be ‘hot’ if you toss in a few drops of water and the water splatters. 8. ‘Tiger’ means a cat that is large and striped. 9. ‘Company’ means something like Microsoft, Starbucks, or Boeing. 10. ‘Book’ refers to things like novels, collections of short stories, and atlases. 11. ‘Frigid’ means cold. 12. ‘Building’ means something like this [as the definer points to a building]. 189 13. ‘Igloo’ means house made of ice. 14. ‘Heavyweight’ refers in boxing to people who step on a scale and the scale indicates over 200 pounds. 15. ‘Pen’ means an instrument with ink use d for writing and drawing.
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