| Phi 270 Fall 2013 |
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Phi 270 F06 test 1
F06 test 1 topics
The following are the topics to be covered. The proportion of the test covering each will approximate the proportion of the classes so far that have been devoted to that topic. Your homework and the collection of old tests will provide specific examples of the kinds of questions I might ask.
Basic concepts of deductive logic. You will be responsible for the concepts listed in appendix A.1. You should be able to define each in terms of possible worlds and truth values, and you should be prepared to answer questions about them, justifying your answer by reference to the definitions. Appendix A.1 includes relative exhaustiveness and all the concepts you’ve seen are special cases of it, so in principle, all are fair game. However, if I ask about something like mutual exclusiveness I’ll tell you how it is expressed using relative exhaustiveness. That does mean that you need to be able to understand how relative exhaustiveness is defined in special cases where there are no assumptions on the left of the arrow or no alternatives on the right; that means you need to know what it means to say, for example, that “φ, ψ ⊨.”
Implicature. Be able to define it and distinguish it from implication. Be able to give examples and explain them. Be ready to answer questions about it, justifying your answer by reference to its definition.
Analysis. Be able to analyze the logical form of a sentence as fully as possible using conjunction and present the form in both symbolic and English notation (that is, with the logical-and symbol ∧ and with the both … and … way of expressing forms).
Synthesis. Be able to synthesize an English sentence that has a given logical form.
Derivations. Be able to construct derivations to show that entailments hold and to show that they fail. I may tell you in advance whether an entailment holds or leave it to you to check that using derivations. There may be some derivations where the rule Adj introduced in 2.4 would be convenient to use; but it is never necessary. You should be ready to use EFQ and ENV as well as Ext, Cnj, and QED; but derivations involving the latter three are much more likely.
F06 test 1 questions
| 1. |
Define tautologousness by completing the following with a definition in terms of truth values and possible worlds:
φ is a tautology if and only if …
answer
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| 2. |
Explain what truth values are possible for sentences φ and ψ that are both mutually exclusive (i.e., φ, ψ ⊨) and jointly exhaustive (i.e., ⊨ φ, ψ). answer |
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The nursery rhyme “Jack and Jill” contains the line
Jack fell down and broke his crown
Even when this is taken out of context, it is natural to suppose that Jack broke his crown as a result of falling down rather than that falling down and the injury were simply two things that happened to him. I would claim that this tie between the two events is an implicature rather than an implication of the sentence. |
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| 3. |
Explain what I mean when I make that claim in a way that shows you understand the definition of implicature. (You need not support or reject my claim; I’m asking you only to explain what it means.) answer |
| 4. |
If the line did imply (rather than merely implicate) that Jack’s broken crown was the result of the fall, the sentence would not be a conjunction of Jack fell down and Jack broke his crown. Explain why this is so in a way that shows you understanding the meaning of implication and the conditions under which conjunctions are true. answer |
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Analyze the sentence below in as much detail as possible, presenting the result using symbolic notation and also English notation (i.e., using |
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| 5. |
The building was completed on time and with no cost overruns, but not everyone was satisfied with it.
answer |
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Use derivations to check whether each of the claims of entailment below holds. If an entailment fails, confirm a counterexample by providing a table in which you calculate the truth values of the premises and conclusion on an assignment of truth values that is a counterexample lurking in an open gap. Your table should show the value of any compound component of the premises and conclusion by writing this value under the main connective of the component. Do not use the rule Adj in the first derivation, but you may use it in the second. |
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| 6. |
A ∧ C, B ∧ D ⊨ B ∧ C
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| 7. |
A ∧ (D ∧ E), B ∧ F ⊨ (A ∧ B) ∧ C
answer |
F06 test 1 answers
| 1. |
φ is a tautology if and only if there is no possible world in which φ is false (or: if and only if φ is true in every possible world) |
| 6. |
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