Different people use the same words for colors, though they sometimes disagree; for example whether something is blue or green. But each person’s experience of colors is quite different from each other person’s experience. For one thing, many associations are different: the colors of one person’s mother’s clothes and one person’s toys are likely to be different from those of another.

.)Write out the premises and conclusions for each of the following arguments. Edit the extraneous material and produce a clear and concise version of each argument. Insert any implicit assumptions, and indicate any sub-conclusions. Number the premises and conclusion(s) and produce a diagram for the argument using the method outlined in our course text.

 

1. Different people use the same words for colors, though they sometimes disagree; for example whether something is blue or green. But each person’s experience of colors is quite different from each other person’s experience. For one thing, many associations are different: the colors of one person’s mother’s clothes and one person’s toys are likely to be different from those of another. Also, the colors you see depend on the whole structure of your brain. So, it is very likely that the experience one person has when they see a color is completely different from the experience someone else has when they see the same color.

 

 

2. We value the earth and the life that it supports. But one of the main problems for the earth is the human race. There are so many humans that they exclude other species, and industrial societies cause ecological disasters. Humans are intelligent enough to love the earth and to see the harm they are doing it. So, one duty that humans can understand is the duty to reduce the damage to the planet. This will mean an earth with far fewer humans on it. It seems to be the case then, that the earth would be best with no humans at all.

 

 

3. (10 marks) The following statement represents the conclusion for an argument. The statement is expressed in the form of two alternatives. Select one of the alternatives and, following the Principle of Charity, construct an argument with relevant premises in support of that alternative. Considering the argument you made, construct a counterargument with the other alternative as the conclusion. Construct your argument and counterargument such that the counterargument is the one you consider to be more convincing.

“The possession, ownership, and sale of handguns should/should not be outlawed.”

 

 

Questions  #4 – #8

Translate the following sentences into sentential logic using upper case letters to represent affirmative ordinary language sentences. Clearly identify the simple sentences you are symbolizing and the symbol you are using to represent them. (3 marks each for a total of 15 marks.)

4. Either Jodie Foster or Patrick Walsh wear black to the Grammys but it is not the case that both do.
5. Tanzania becomes a banking center given that Zanzibar attracts foreign capital.
6. Vancouver does not allow smoking in restaurants.
7. If Walsh fails to win, then either Harper wins or Walsh and Harper are tied.
8. If either David Beckham or Patrick Walsh attend the charity concert, then neither Britney Spears nor Christina Aguilera will attend.

 

Questions #9 – #10

Symbolize the following arguments, using symbolized simple sentences and the relevant logical constants. Indicate the upper case letters you use to symbolize ordinary language simple sentences. Provide a truth tables to discern whether the arguments are valid or invalid. Explain what you see in your truth tables that displays your answers. (10 marks each. 20 marks total.)

9. If Janet did not alter the truth table, then Justin intended to expose a genuine flaw in the truth table. It seems to be the case that she did alter the truth table. So, Justin is innocent of the intention of exposing a genuine flaw in the truth table.

 

10. Erik attains Valhalla given that he is valiant. And Erik is depressed assuming that he is not valiant. Furthermore, Erik fails to attain Valhalla only if he is not depressed. Thus, Erik is depressed.

 

11. Symbolize the following argument, using the provided upper case letters to represent affirmative ordinary language simple sentences. Use the Short Method to determine the validity of this argument. Explain how you determined your answer. (10 marks.)

“Wittgensteinians are right if logic is embedded in language. But logic is embedded in language if and only if logic varies as language varies. And logic is language-relative if logic varies as language varies. Moreover, given that logic is language-relative, contradictions may be true in some languages. Therefore, Wittgensteinians are right only if contradictions may be true in some languages.”

[W = Wittgensteinians are right. E = Logic is embedded in language. V = Logic varies as language varies. R = Logic is language relative. C = Contradictions may be true in some languages.]

12. Provide a truth table to obtain an answer to the following questions. Be sure to show your work. Explain how your truth table indicates your answer. (15 marks)

Molly Perry expresses her philosophy as follows: “If the mind is identical to the brain, then personal freedom does not exist and humans are not responsible for their actions. If personal freedom does not exist, then the mind is identical to the brain. Either humans are responsible for their actions or the mind is not identical to the brain. If personal freedom exists, then humans are responsible for their actions.” Is it possible that Molly’s philosophy makes sense? If so, what does it say about the mind, personal freedom and responsibility?

 

Questions #13 – #14. Provide a formal proof of validity for the following valid deductive arguments. You can use only the rules of inference introduced in the text. (5 marks each. 10 marks total)

 

13)       1.  A  -> B

2. ~ A -> (C v D)
3. ~ B
4. ~ C /\ D

 

14)       1.  ~J v K