Symbolic Logic Homework 1 – All drugs should be legal

1 Introduction to Symbolic Logic
Homework 1
Reconstruct the following arguments in premise/conclusion form, making sure to reformulate the premises and conclusion as declarative sentences, as necessary. (The order of the premises doesn’t matter; just put them in the order that seems to best capture the thread of the reasoning.)
Example: “Jimbo can’t be at the bowling alley. If he went there, he would’ve taken his bowling shoes, but his bowling shoes are still here.”
Premise 1. If Jimbo is at the bowling alley, his bowling shoes wouldn’t be here.
Premise 2. Jimbo’s bowling shoes are here. Conclusion. Jimbo isn’t at the bowling alley.
1. “All drugs should be legal. This follows from the fact that the use of drugs has no negative impact on the freedom or wellbeing of those who don’t use them, and the government has no business prohibiting forms of behavior that have no such impact on those who choose not to engage in them.”
2. “The government has every right to prohibit forms of behavior that are detrimental to society at large. Since the production, sale, and use of certain drugs does have harmful effects on the communities in which it takes place, the government is justified in banning certain drugs.”
3. “If there is a God, then why is there so much needless suffering in the world? If God exists, wouldn’t he/she/it prevent such senseless pain? Since the world contains so much needless suffering, it must be that there is no God.”
4. “God must exist. If there were no God, there would be nothing to explain how the universe came into being, or why the laws of nature are as they are. But there must be an explanation for these things.”
5. “True friends always share their possessions. Since you won’t let me borrow your nose-hair trimmer, it must be that you’re not truly my friend.” Identify whether the following passages are arguments. If it is an argument, then write out the conclusion.
6. “Seeing as I’m a philosopher, I’ll probably never be extremely wealthy. Philosophers rarely strike it rich.”
7. “The human visual system really consists of two separate systems, one for bright (or “photopic”) conditions, and another for dim (or “scotopic”) conditions. These different illumination conditions trigger responses in different types of photoreceptors in the retina. Photopic vision is mediated by cone receptors (of which there are 3 different types), whereas scotopic vision is mediated by rod receptors.” Identify whether the following inferences are deductive or inductive.
8. “You can’t put ketchup on a sandwich, but you can sure put ketchup on a hot dog, so it follows that a hot dog is not a sandwich.”
9. “The sun has always risen in the morning before, so tomorrow it’ll do the same.”
10. “That’s the third person I’ve seen dressed up like Santa Claus today. There must be some sort of convention going on in town.”
11. “All living things are self-sustaining or autonomous to some degree. Hence, viruses aren’t alive, because they are entirely dependent upon host cells to reproduce.” Identify whether the following deductive arguments are valid or invalid. If the argument is valid, then specify whether it also sound or unsound.
12. “Some humans are professors, and some professors are logicians, so some logicians are human.”
13. “Either this argument is valid, or it’s invalid. It’s not invalid. Therefore, this argument is valid.”
14. “All puppies are dogs, and all poodles are dogs, so some poodles are puppies.”
15. “All puppies are dogs, and some hippos are puppies, so some hippos are dogs.” Identify whether the following inductive arguments are strong or weak. If the argument is strong, then specify whether it is also cogent or uncogent.
16. “Every frog that has ever been examined thus far has turned out to be a robot. So it stands to reason that all frogs are robots.”
17. “I sneezed at high noon yesterday. It’s currently 11:59am, so I’m probably going to sneeze in a minute.”
18. “Water at sea level has always boiled at 100°C. So if this glass of water is heated to 100°C at sea level, it will boil too.”
Use the method of counterexamples to demonstrate that the following arguments are invalid by first reconstructing the form of the argument and then providing a substitution instance whose premises are clearly true and conclusion clearly false.
Example: “Some people like chocolate. Some people like cheese. Some people like chocolate and cheese.”
Some A are B. Some organisms are plants.
Some A are C. Some organisms are animals.
Some A are B and C. Some organisms are plants and animals.
(A = people; B = chocolate-lovers; C = cheese-lovers)
19. “Some jazz musicians were born in Philadelphia and some jazz musicians are left-handed, so some left-handed people were born in Philadelphia.”
20. “No act of violence is intrinsically good, and nothing that’s intrinsically good is ugly. So at least some acts of violence are ugly.”

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