Homework 2

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School

Westmoreland County Community College *

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155

Subject

Philosophy

Date

Feb 20, 2024

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docx

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Uploaded by SargentArmadillo2211

Logic - Homework 2 Please download and complete the assignment as a “.docx” (Word) document and submit to D2L. PART 1 [0.25 Points each] The following exercises are intended to apply your understanding of the difference between deductive and inductive arguments. Determine whether the following arguments are best classified as being deductive or inductive . Explain your answers. Example: “Every insect has six legs. What’s crawling on me is an insect. So what’s crawling on me has six legs.” Answer: Deductive . The first premise says something definite about every insect. The second premise says that an insect is crawling on me. If both premises are assumed to be true, then the conclusion is necessarily true. 1. Most insects have six legs. What’s crawling on me is an insect. Therefore, what’s crawling on me probably has six legs. INDUCTIVE : uses SPECIFIC observations to make a GENERAL conclusion .  The premise is that most insects have six legs, which is a general statement based on common knowledge. The observation that something crawling on you is an insect serves as evidence. The conclusion is that what's crawling on you probably has six legs which is based on the general premise that most insects have six legs, but it allows for the possibility that there may be exceptions. 2. The test’s range of A scores is 90-100. I got an A on the test, thus I got a 98 on the test. DEDUCTIVE : uses GENERAL information to draw a SPECIFIC conclusion.  The premise is that the test's range of A scores is 90-100, which is a specific range provided. The fact that they got an A on the test serves as evidence. The conclusion is that they got a 98 on the test & is drawn by applying the information that an A falls within the range of 90-100 to the specific situation of getting an A on the test. 3. All fires need oxygen. There is no oxygen in that room. So there is no fire in that room. DEDUCTIVE : uses GENERAL information to draw a SPECIFIC conclusion.  The premise is that all fires need oxygen, which is a general statement based on scientific knowledge. The observation that there is no oxygen in that room serves as evidence. The conclusion is that there is no fire in that room & is drawn by applying that fires require oxygen to the specific situation of there being no oxygen in the room. 4. Miley tossed a coin ten times, and in each case it came up heads. I have a feeling that it is a trick coin. I predict the next toss will be heads. INDUCTIVE : uses SPECIFIC observations to make a GENERAL conclusion.  The premise is that Miley tossed a coin ten times, and in each case, it came up heads. This is a specific observation & the feeling or suspicion led to the conclusion that it is a trick coin. This conclusion is based on the specific observations of the

coin consistently landing on heads, leading to the belief that there MAY be something unusual or manipulated about the coin. BUT this conclusion is not certain & is based on a hunch rather than definitive evidence. 5. All elements in periods 1-12 are metals. X is an element in period 5 .Therefore, X is a metal. DEDUCTIVE : uses GENERAL information to draw a SPECIFIC conclusion.  The premise is that all elements in periods 1-12 are metals, which is a general statement based on the periodic table of elements. The fact that X is an element in period 5 serves as the evidence in the conclusion that X is a metal. This conclusion is drawn by applying the general information that all elements in periods 1-12 are metals to the specific situation of X being an element in period 5. 6. Antibiotics have no effect on viruses. You have a disease that is caused by a virus. You are taking the antibiotic Z. Thus the antibiotic you are taking will have no effect on your disease. DEDUCTIVE : uses GENERAL information to draw a SPECIFIC conclusion.  The premise is that antibiotics have no effect on viruses, which is a general statement based on scientific knowledge. The fact that I have a disease caused by a virus am taking the antibiotic serves as evidence. The conclusion is that the antibiotic I’m taking will have no effect on the disease which is drawn by applying the general information that antibiotics do not work on viruses to the specific situation of having a viral disease & taking an antibiotic. 7. Most fruit have seeds. I am eating an orange. All oranges are fruit, so I am eating something with seeds. INDUCTIVE : uses SPECIFIC observations to make a GENERAL conclusion .  The premise is that most fruits have seeds, which is a general statement based on knowledge of fruits. The specific observation is that you’re eating an orange. The conclusion is that you are eating something with seeds. Which is drawn by applying the information that most fruits have seeds to the specific situation of eating an orange. 8. The vast majority of a survey of 600 people who identified themselves as being very religious reported that they were against capital punishment. It is safe to say that the vast majority of all Americans think the same way. INDUCTIVE : uses SPECIFIC observations to make a GENERAL conclusion .  The premise is that the survey of 600 people showed that the vast majority of them were against capital punishment. This is a specific observation based on the survey’s results. The conclusion is that the vast majority of ALL Americans think the same way. This conclusion is drawn by deducing the findings of the survey to the larger population of Americans. 9. Last week, when my car would not start, Mom took me to get a new battery. As soon as I installed it, my car started right up. So my old battery was probably defective. INDUCTIVE : uses SPECIFIC observations to make a GENERAL conclusion .  The premise is that their car would not start, so they got they got a new battery. The specific observation is that as soon as they installed the new battery, their car started right up. The conclusion is that their old battery was probably defective & is

drawn by connecting the observation of the car not starting with it then starting after the installation of a new battery. Based on the observed outcome, there could be other factors that resulted in the car not starting. 10.Anyone over 21 years of age can legally play the slot machines in Las Vegas. Riggs is 33 years old. Riggs can legally play the slot machines in Las Vegas. DEDUCTIVE : uses GENERAL information to draw a SPECIFIC conclusion.  The premise is that anyone over 21 years of age can legally play the slot machines in Las Vegas. This is a general rule based on the legal age requirement for gambling. The conclusion is that Riggs can legally play the slot machines & is drawn by applying the general rule that anyone over 21 can play the slot machines to the specific situation of Riggs being 33 years old. Since Riggs is older than 21, it follows that Riggs meets the age requirement and can legally play the slot machines. PART 2 [0.25 Points each] Determine whether the following inductive arguments are strong or weak . Most insects have 6 legs. What’s crawling on me is an insect. So what’s crawling on me has 6 legs. Answer: Strong . If we assume the premises are true, then the conclusion is probably true. 11.The test’s grade range of A scores is 90-100. I got an A on the test, so I got a 98 on the exam. WEAK : While the premise states that the grade range for an A is 90-100, it is not a guarantee that getting an A automatically translates to receiving a score of 98 on the exam. The conclusion goes beyond what the premise can support, making the argument weak. 12.Cleetus tossed a coin ten times, and in each case it came up heads. Therefore, the next toss will be tails. WEAK : The outcome of previous coin tosses does not affect the outcome of future tosses. Each coin toss is an independent event, and the probability of getting heads or tails remains the same for each toss. Therefore, it is not logically guaranteed that the next toss will be tails just because the previous ten tosses were heads. 13.Cleetus tossed a coin ten times, and in each case it came up heads. Therefore, the next toss will be heads. STRONG : The premise states that most elements in periods 1-12 are metals, which implies a general trend or pattern. The conclusion follows logically from this premise, stating that if X is an element located somewhere in period 1-12, it is likely to be a metal based on the general trend. While it is not a guarantee that X is a metal, the argument is strong because it is based on a reasonable generalization. 14.Most elements in periods 1-12 are metals. X is an element located somewhere in period 1-12. Therefore, X is a metal.

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STRONG : The premise states that MOST of the elements in periods 1-12 are metals & the conclusion follows this premise, stating that if X is an element located somewhere in period 1-12, it is likely to be a metal based on the general trend. 15.Most Poodles bark a lot. My cousin just got a Poodle. Therefore, my cousin’s Poodle will probably bark a lot.

STRONG : The premise states that most Poodles bark a lot & the conclusion follows soundly from this premise. the argument is strong because it is based on a reasonable generalization. PART 3 [0.25 Points each] State whether the following sets of propositions are consistent or inconsistent with each other. If they are not, describe the contradiction either explicit in, or logically entailed by, the set. Example: Cats are cuddly. All cuddly things have fur. Snowball is cuddly. Snowball is a hedgehog. Hedgehogs don’t have fur. Answer: Inconsistent . All cuddly things must have fur, but Snowball is both furless and cuddly. That’s a contradiction. 16.Vigilantes are criminals. Bruce Wayne is Batman. Batman is a vigilante who fights crime. There is a crime-fighting criminal. INCONSISTENT : The contradiction arises from the statement "Vigilantes are criminals" and the statement "Batman is a vigilante who fights crime." If vigilantes are considered criminals, it contradicts the claim that Batman, who is a vigilante, fights crime. This implies that Batman is both a criminal and fighting against crime, which is inconsistent. 17.Either I like cheese or I like beer. Both beer and cheese are products of fermentation. I don’t like cheese. If I like beer, then I like beets. I don’t like beets. INCONSISTENT : “ If I like beer, then I like beets. I don’t like beets.” It is impossible for both of those statements to be simultaneously true. 18.Bears eat beets. Stephen hates bears. Packers hate Bears. Adama loves the Galactica . CONSISTENT : Based on the given propositions, each statement conveys an individual notion or reality without any conflicting details. 19.Adama is the commander of the Galactica . The commander is the highest ranked officer and everyone reports to him. Starbuck is an officer on the Galactica and reports to the commander. Starbuck does not report to Adama. INCONSISTENT : “ S tarbuck is an officer on the Galactica and reports to the commander” & “Adama is the commander of the Galactica” BOTH contradict the statement "Starbuck does not report to Adama." 20.If Walt committed the murder, then he was in the victim's apartment and did not leave before 11. He was, in fact, in the victim's apartment. If he left before 11, then the doorman saw him. However, neither the doorman saw him nor did he commit the murder. INCONSISTENT : "If Walt committed the murder, then he was in the victim's apartment and did not leave before 11" and the statement "He was, in fact, in the victim's apartment. If he left before 11, then the doorman saw him." These statements imply that if Walt was in the victim's apartment, he did not leave before 11 and the doorman would have seen him. However, it is stated that neither the doorman saw him, nor did he commit the murder.

Homework 2

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