| Phi 270 Fall 2013 |
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Phi 270 F09 test 4
F09 test 4 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.
Analysis. Be ready to handle any of the key issues discussed in class—for example, the proper analysis of every, no, and only (see §7.2.2), how to incorporate bounds on complementary generalizations (see §7.2.3), ways of handling compound quantifier phrases (such as only cats and dogs, see §7.3.2), the distinction between every and any (see §§7.3.3 and 7.4.2), how to represent multiple quantifier phrases with overlapping scope (see §7.4.1). You should be able restate your analysis using unrestricted quantifiers (see §7.2.1), but you will not need to present it in English notation.
Synthesis. You may be given a symbolic form and an interpretation of its non-logical vocabulary and asked to express the sentence in English. Remember that the distinction between every and any can be important here, too.
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. If a derivation fails, you may be asked to present a counterexample, which will involve describing a structure. You will not be responsible for the rules introduced in §7.8.1.
F09 test 4 questions
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Analyze the sentences below in as much detail as possible, providing a key to the non-logical vocabulary you use. Also restate your analyses using unrestricted quantifiers. |
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| 1. |
Everyone saw the eclipse. answer |
| 2. |
Al didn’t find any book that he was looking for. answer |
| 3. |
No one ate only potato chips. answer |
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Synthesize an English sentence that has the following logical form; that is, devise a sentence that would have the following analysis: |
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| 4. |
(∀x: ¬ Sbx) Sax S: [ _ saw _ ]; a: Al; b: Bill answer |
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Use derivations to show that the following arguments are valid. You may use any rules. |
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| 5. |
∀x (Gx → Hx)
answer
∀x (Fx ∧ Gx) ∀x Hx |
| 6. |
∀y ∀x (Px → ¬ Fxy)
answer
∀x ∀y (Fyx → ¬ Py) |
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Use a derivation to show that the following argument is not valid and present a counterexample that lurks in an open gap. |
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| 7. |
∀x Rxa
answer
∀x Rxx |
F09 test 4 answers
| 1. |
everyone saw the eclipse everyone is such that (he or she saw the eclipse) (∀x: x is a person) x saw the eclipse
(∀x: Px) Sxe
P: [ _ is a person]; S: [ _ saw _ ]; e: the eclipse |
| 4. |
(∀x: ¬ Bill saw x) Al saw x (∀x: Bill didn’t see x) Al saw x everything that Bill didn’t see is such that (Al saw it) Al saw everything that Bill didn’t see |
| 5. |
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| 7. |
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Counterexample presented by a diagram |