PHIL 1500 – Critical Thinking

Symbolization Exercises - Solutions

Symbolize the following arguments showing all the logical connectives used. Circle the letter in each atomic sentence that you will use in your symbolization.

1. Georgia will play Tennessee again this fall. Georgia will win the SEC (C)hampionship only if they (W)in that game. But a necessary and sufficient condition for Georgia to go to the (S)ugar Bowl is that they win the SEC championship. So if Georgia wins the Tennessee game, they will go to the Sugar Bowl.	C W S C ____________ W S
2. Neither (R)ussia nor (C)hina will support a U.S. attack on Iraq. There will not be a (U).N. ultimatum on arms inspection in Iraq unless either Russia or China supports a U.S. attack on Iraq. If there is no U.N. ultimatum on arms inspection in Iraq and the U.S. (A)ttacks Iraq anyway, then (S)audi Arabia will not allow the U.S. to use bases within its borders. So either the U.S. will not attack Iraq or Saudi Arabia will not allow the U.S. to use bases within its borders.	~(R C) ~U (R C) (~U A) ~S ________________ ~A ~S
3. Only if (G)ravity deflected light would (S)tars appearing on opposite sides of the sun during a total eclipse appear closer together than at other times. But if light is deflected by gravity, light must have (M)ass. So unless light has mass, stars appearing on opposite sides of the sun during a total eclipse will not appear closer together than at other time.	S G G M ____________ M ~S
4. The (R)ecession will end soon if and only if more (J)obs are created and (I)nflation remains low. If interest rates remain (L)ow, inflation will remain low. (C)onsumer confidence will improve only if more jobs are created. So since interest rates will remain low, either consumer confidence will not improve or the recession will end soon.	R (J I) L I C M L _______________ ~C R
5. Mary took (G)eometry and (C)alculus in high school, but Linda didn't take g(E)ometry or c(A)lculus. If they ((M)ary and(L)inda) had both gone to Lincoln High, they would both have taken calculus. So they didn't both go to Lincoln High.	"they had both gone to Lincoln High" means Mary had gone and Linda had gone. In this particular example, we lose no essential information if we represent this by a single letter. But If either "Mary went to Lincoln" or "Linda went to Lincoln" occurred alone anywhere in the argument, we could make a mistake when we test the argument for deductive validity. (G C) ~(E A) (M L) (C A) _______________ ~(M L)
6. Henry didn't (F)ire the gun. Otherwise, he would have had gun powder (R)esidue on his hands. If he had gun powder residue on his hands, the (P)araffin test would have revealed it. But the paraffin test was negative.	"Otherwise" means "If the preceeding sentence is false, then..." ~~F R R R ~P ____________ ~F
7. A necessary condition for the car to (S)tart is a good (B)attery. If the (L)ights work and the (H)orn works, then the battery is good. The lights and horn work. So the car will start.	S B (L H) B L H ________________ S
8. If (D)eterminism is true, we (C)an not do other than we do, hence we are not (R)esponsible for what we do. If (I)ndeterminism is true, then human actions are (R)andom, hence not (F)ree, hence we are not responsible for what we do. Either determinism or indeterminism is true. Therefore, we are not responsible for what we do.	Each occurrence of the word "hence" represents an "if-then" statement. D ~C ~C ~R I R R ~F ~F ~R D I _____________ ~R
9. People are different from animals either in (K)ind or in (D)egree. If we are different in kind, then there should be at least one (C)haracteristic we obviously have that animals don't. There is no obvious difference; therefore we must be different in degree. But if we are only different from animals in degree then we're essentially just (A)nimals.	The explicit intermediate conclusion, that we are only different from animals in degree should not be represented as a premise, and we don't need to represent it as a conclusion. It should follow from the premises before it. But the MAIN conclusion of the argument is unstated: that we are essentially just animals. K D K C ~C D A ____________ A
10. I'm buying my mother a new (W)atch for Christmas; but if I buy the watch, I can't afford the (T)able saw my father has been wanting. If I can't get him the table saw, I can still get him (B)ooks or a new (J)acket. If I get him books, I can afford a gift for my favorite (A)unt. If I buy him a jacket, I cannot. I want to give my aunt a Christmas present.	No explicit conclusion is given. We can only supply a conclusion if we assume the speaker is going to do what he wants to do (get a present for his aunt) and then figure out what follows from the premises. In this case, the correct conclusion for the speaker to draw is that he must get books for his father if he is going to do everything else he wants to do. W W ~T ~T (B J) B A J ~A A ____________ B