1. Determine whether the following arguments are valid or invalid. If valid determine whether they are sound. Be sure to explain what validity is and how you determine whether an argument is valid or not. Explain your answers in as much detail as you can. There is no length restriction on your answer; make it as long as necessary to answer the question in the required detail.
a.) If I study hard I’m sure to get an A in philosophy, but I haven’t studied at all; So I can’t get an A.
b.) If a number is greater than 7 then it is greater than 4. 8 is greater than 7, therefore it is greater than 4.
c.) If I want an A in philosophy I need to study for the exam, since I haven’t studied for the exam that means that I don’t want an A.
d.) No computers can feel pain. The human brain is a computer so no human brains feel pain.
e.) How do I know that Hillary Clinton is a liar? All politicians lie to get ahead and Hillary Clinton is a politician!
f.) If 4 is prime then it is divisible only by 1 and itself. 4 is not prime therefore it is divisible by numbers other than 1 and itself.
g.) Some doctors watch Lost and some people who like Lost are conspiracy theorist so some doctors are conspiracy theorists.
a) isn't a valid argument because the conclusion doesn't follow from the two premises. There's a possibility that you could get an without studying hard.
b) is valid.
Check this site for a good explanation of validity.
http://www.jimpryor.net/teaching/vocab/validity.html
We'll be glad to check the rest of your answers.
a.) This argument is valid. In order to determine whether an argument is valid or invalid, we need to analyze its logical structure. Here, the argument is in the form of a conditional statement: "If I study hard, then I'm sure to get an A in philosophy." The second statement is the negation of the first statement: "I haven't studied at all." Given these two statements, it follows logically that "I can't get an A." Therefore, the argument is valid.
However, the argument may not be sound. Soundness requires both validity and true premises. In this case, we don't have information about whether the person studied hard or not, so we can't determine whether the premises are true.
b.) This argument is also valid. It follows the form of a conditional statement: "If a number is greater than 7, then it is greater than 4." The second statement states that "8 is greater than 7." Therefore, it logically follows that "8 is greater than 4."
The argument is valid because it follows a valid logical form. To determine validity, we need to check if the conclusion follows logically from the premises, regardless of the truth of the premises. In this case, it does. However, soundness requires true premises, and without knowing whether the premises are true, we can't determine if the argument is sound.
c.) This argument is valid. It follows the form of a conditional statement: "If I want an A in philosophy, then I need to study for the exam." The second statement is the negation of the first: "I haven't studied for the exam." Therefore, it logically follows that "I don't want an A."
Again, soundness requires true premises, and in this case, we don't have information about whether the person studied or not, so we can't determine the truth of the premises or the soundness of the argument. But in terms of validity, it is valid.
d.) This argument is invalid. It attempts to generalize that "No computers can feel pain" and then applies it to the statement "The human brain is a computer." This is a fallacy called the Fallacy of Composition, as it concludes that all parts of a whole have the same property as the whole itself. While it is true that no currently known computers can feel pain, it doesn't necessarily mean that human brains, which are different from computers, cannot feel pain. Therefore, the argument is invalid.
e.) This argument is also invalid. It generalizes the statement that "All politicians lie to get ahead" and applies it to the specific individual, Hillary Clinton. While there may be politicians who lie, it doesn't warrant the conclusion that every politician, including Hillary Clinton, is a liar. The argument commits the fallacy of hasty generalization, making an excessive and unwarranted assumption. Therefore, the argument is invalid.
f.) This argument is valid. It states that "If 4 is prime, then it is divisible only by 1 and itself." The second statement is the negation: "4 is not prime." Therefore, it logically follows that "4 is divisible by numbers other than 1 and itself." The argument is valid because it follows a valid logical form.
g.) This argument is invalid. It attempts to make a conclusion based on the existence of some overlap between doctors who watch Lost and people who like Lost being conspiracy theorists. However, the argument doesn't provide enough information to establish a strong connection between being a doctor and being a conspiracy theorist. It commits the fallacy of affirming the consequent, where it assumes that if the consequent (being a doctor) is true, then the antecedent (being a conspiracy theorist) must also be true. Therefore, the argument is invalid.