Critical Thinking

I. Symbolize each of the following passages using statement letters and the symbols –, v, ·, and ?. Be sure to state which letters represent which English sentences. Example “Joe Skates and Susan swims” is symbolized as “J · S,” where J represents “Joe skates” and S represents “Susan swims.” Class 14 (5 points) a. Either Susan is lying or Susan is deceiving herself. b. Interest rates are low, properties are for sale, and it is a good time to get a mortgage. c. Pedro is going to take English as his foreign language or he is going to take German as his foreign language. His native language is Spanish, and he doesn’t want to learn French. d. Golf consumes a lot of resources. If golf consumes a lot of resources, it is an environmentally costly game. Therefore, golf is an environmentally costly game. e. If the presidency is discredited and the rate of voter participation is low, there is evidence of apathy toward national politics. The presidency is discredited, and the rate of voter participation is low. So there is evidence of apathy in national politics. II. A. Represent the following arguments in capital letters and propositional symbols and test them for deductive validity using the longer truth-table technique. Be sure to stipulate what your statement letters represent. Class 15 (9 points) a. Either the Liberals are right or the Conservatives are right, and not both. It’s been shown that Conservatives are wrong. So the Liberals must be right. b. Religious believers are inspired by faith or by reason. Religious believers are inspired by faith. Therefore, religious believers are not inspired by reason. c. Either life has meaning or life has no meaning. If God does not exist, it is not the case that life has meaning. God does not exist. Therefore, life has no meaning. B. Represent the following arguments with capital letters and propositional symbols; indicate which symbols represent which statements; test them for validity using the shorter truth table technique. Class 15 (6 points) a. Either war will continue or peace will be negotiated. Peace will not be negotiated, so war will continue. b. If the prison is well administered, then guards will behave properly, the incidence of assault and drug use will be low, and at least some prisoners will reform as a result of their stay in prison. At least some prisoners have reformed as a result of their stay in prison. Therefore, it must be true that the prison is well administered. C. Symbolize the following passage in propositional form, using capital letters and propositional symbol. Test the argument for validity using the longer truth table technique or the shorter truth table technique as you prefer. Class 15 (8 points) a. We cannot know that the world exists outside of our minds if we do not know that we are awake. If we do not know that we are not dreaming, we do not know that we are awake. So if we do not know that we are dreaming, we do not know that the world exists outside of our minds. We do not know that we are not dreaming. Therefore, we do not know that the world exists outside of our minds. III. Prove the conclusions based on the premises using valid argument forms. (Hint: Keep your “valid moves” sheet in front of you. Class 16 (12 points) a. A ? (B v C); B ? D; D ? G; A · –C; therefore G. b. –(C v D); –D ? –(H · G); (Q ? G) ·H; therefore –Q. c. A v B; –B; –C ? –A; therefore C. IV. Represent the following argument using capital letters and symbols propositional symbols. Test the argument for validity using valid inference patterns and a simple proof procedure. Class 16 (10 points) a. If the media are biased, then news coverage is biased, and if news coverage is biased, people will not have an accurate picture of the world. Unless people have an accurate picture of the world, democracy will not function properly. The media are biased. Therefore democracy will not function properly.