| Phi 270 Fall 2013 |
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Phi 270 F03 test 4
F03 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 (§7.2), how to incorporate bounds and exceptions (§7.2), ways of handling compound quantifier phrases (such as only cats and dogs, §7.3), the distinction between every and any (§§7.3 and 7.4), how to represent multiple quantifier phrases with overlapping scope (§7.4). Be able restate you analysis using unrestricted quantifiers, 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. (This sort of question is less likely to appear than a question about analysis and there would certainly be substantially fewer such questions.)
Derivations. Be able to construct derivations to show that entailments hold and to show that they fail (derivations that hold are more likely). 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.
F03 test 4 questions
| Analyze the sentences below in as much detail as possible, providing a key to the non-logical vocabulary you use. Restate 2 using an unrestricted quantifier. | |
| 1. |
No one called the new number
answer |
| 2. |
Sam asked everyone he could think of
[Remember to restate this one using an unrestricted quantifier.]
answer |
| 3. |
If any door was opened, the alarm sounded
answer |
| 4. |
Only people who’d read everything the author had written were asked to review the book
answer |
| Use derivations to show that the following arguments are valid. You may use any rules. | |||
| 5. |
∀x (Fx ∧ Gx)
answer
∀x Gx |
6. |
∀x (Fx → Gx)
answer
∀x ∀y (Gy → Rxy) ∀x ∀y (Fy → Rxy) |
| Use a derivation to show that the following argument is not valid and describe a structure (by using either a diagram or tables) that is a counterexample lurking an open gap. | |
| 7. |
∀x (Fx → Rxa)
answer
Fa → ∀x Rxx |
F03 test 4 answers
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| 7. |
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Counterexample presented by tables
(This counterexample lurks in both gaps; the value of F2 is needed only for the 1st and the value of R21 only for the 2nd.) |
Counterexample presented by a diagram |
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