• You are given 15 arguments. You need to identify their premises, conclusions, find their structure, and evaluate them for validity or invalidity.
• The first 6 arguments are examples of categorical syllogisms. This concept is the focus of chapters 5 and 6. You need to identify the structure of the premises and conclusion, and place them in a standard form using the standard categorical propositions, i.e, A, E, I and O. Then, you must use Venn Diagrams to examine their validity or invalidity. You need to provide your translation schema. Please show your work!
• The remaining arguments, #7 to #15, are examples of arguments in propositional logic. This is the focus of chapters 7 and 8 and movie lectures 7 and onwards. You must identify the premises and the conclusion. You must find their structure and then use truth tables to evaluate their validity or invalidity. You need to provide your translation schema. Please show your work!
1. Only valid arguments are sound. No argument with false premises is sound. Therefore, no valid argument has false premises.
2. To be a successful office manager you must be a good liar. Bill Rash was a superb liar. So, Bill was certain to be a great office manager.
3. All insects have articulated bodies, and all animals with articulated bodies have six legs. Therefore, all animals with six legs are insects.
4. Only material bodies have extension Having extension is a property only of things that exist in space. Therefore, only material bodies are in space.
5. Some starvation diets are effective ways to lose weight. However, starving yourself is bad for your heart. Thus, some effective ways to lose weight are bad for your heart.
6. Some politicians are public representatives without ethical values. No public representatives without ethical values are corrupt. Therefore, some corrupt people are politicians.
7. There are only three possibilities: either your sister is mad, or she is telling lies, or she is telling the truth. You know she does not tell lies, and she is obviously not mad, so we must conclude she is telling the truth. (C. S. Lewis, “The Lion, the Witch, and the Wardrobe”)
8. If it were possible to live without fleshhoods, there would be some justification for killing and eating animals. Today we can live happy and well without fleshhoods. Thus, there is no justification for killing animals. (Editorial, “Vegeterianism Today”.)
9. The bank is not open and the laundry is not closed. If the bakery is open, the laundry is closed. Either the bakery or the garage is open, but not both. If the bank is closed, the tailor is closed. Therefore, either the tailor is open or the garage is closed.
10. If the maid is guilty, both the butler was in mansion and driver is an accomplice. Only if the gardener is guilty is the maid not guilty. Either the maid is not guilty or, if the gardener is guilty, the driver is not an accomplice. Therefore, either the butler was in the mansion or if the maid is guilty, the driver is an accomplice.
11. For closed-circuit surveillance cameras to be an effective deterrent to crime, everyone must know they are there. However, for them to be effective in spotting criminals, they must be convert. Therefore, they cannot be effective both in deterring crime and in spotting criminals.
12. If Church’s thesis is true, the function h is computable if and only if it is Turing computable. The function h is computable if and only if the halting problem is solvable. But h is not Turing computable. Therefore, if Church’s thesis is correct, the halting problem is unsolvable.
13. If you predicate what is different, you ascribe to the subject what it is not; and if you predicate what is not different, you say nothing at all. So, when we predicate we either say what is false or we say nothing all. (Bradley, “Appearance and Reality.”)
14. If God exists, then he is all loving and all powerful. If God is all loving, he cares about mortals. If God is all powerful, there can be no evil in the world if God cares about mortals. Therefore, if God exists, there is no evil in the world.
15. If animals feel pain or learn from experience, then animals are conscious. Animals do not feel pain. Animals do not learn from experience. Therefore, animals are conscious.