Phi 270 F03 test 1
F03 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 entailment (or validity), equivalence, tautologousness, absurdity, and inconsistency. 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.
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 symbol ∧ and with the both … and … way of expressing forms).
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 new rule Adj would be convenient to use but, of course, it is never necessary (but you should be ready to use EFQ and ENV as well as Ext, Cnj, and QED).
F03 test 1 questions
| 1. |
Define entailment by completing the following: Γ ⊨ φ if and only if … . (Your answer need not replicate the wording of the text’s definitions, but it should define entailment in terms of truth values and possible worlds. Remember that Γ is a set, not a sentence, though its members are sentences.) answer |
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| 2. |
Define absurdity by completing the following: φ is absurd if and only if … . (Your answer need not replicate the wording of the text’s definitions, but it should define absurdity in terms of truth values and possible worlds.) answer |
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| 3. |
Is it possible for there to be a pair of sentences φ and ψ where (i) φ ≃ ψ (i.e., φ and ψ are equivalent) and (ii) φ and ψ together form an inconsistent set (i.e., the set {φ, ψ} is inconsistent)? If it is possible for both (i) and (ii) to be true of a pair of sentences φ and ψ, describe (in terms of the possibilities for truth values) what φ and ψ must be like. If it is not possible, explain why in terms of possibilities for truth values. (Hint: this is not a trick question but it may trip you up if you try to answer it intuitively; you’ll do better to just think through the consequences of the definitions of equivalence and inconsistency.) answer |
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| 4. |
Give an example of implicature, presenting a sentence and describing situations in which it (i) is true and not misleading, (ii) is true but misleading, and (iii) is false. Explain your answer. answer |
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| 5. |
Analyze the sentence below in as much detail as possible, presenting the result in both symbolic and English notation (i.e., using The road was completed and opened to traffic, but it was closed for repairs and has not been re-opened |
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Use derivations to check whether each of the entailments below holds. If one fails, confirm a counterexample by providing a table in which you calculate the truth values of the premises and conclusion on an extensional interpretation (i.e., an assignment of truth values) which is a counterexample lurking in an open gap. |
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| 6. |
A ∧ B, C ∧ (D ∧ E) ⊨ B ∧ D
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| 7. |
A ∧ B, D ∧ E ⊨ (A ∧ C) ∧ D
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F03 test 1 answers
| 1. |
Γ ⊨ φ if and only if there is no possible world in which φ is false while all members of Γ are true |
| 2. |
φ is absurd if and only if there is no possible world in which φ is true |
| 6. |
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