| Phi 270 Fall 2013 |
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Phi 270 F04 test 5
F04 test 5 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.
This test will have a few more questions than earlier ones (about 9 or 10 instead of about 7) and I will allow you as much of the 3 hour period as you want. The bulk of the questions (6 or 7 of the total) will be on ch. 8 but there will also be a few questions directed specifically towards earlier material (see below).
Analysis. This will represent the majority of the questions on ch. 8. The homework assignments give a good sample of the kinds of issues that might arise but you should, of consider, consider examples and exercises in the text as well. In particular, pay attention to the variety of special issues (e.g., how to handle there is or else) that show up.
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 have the option using the rules REP and REC (as well as RUP and RUC) in derivations for restricted quantifiers. You will not be responsible for the rule for the description operator introduced in §8.6 or for the supplemented rules (i.e., PCh+, etc.) used to find finite counterexamples.
Earlier material. These questions will concern the following topics.
Basic concepts. You may be asked for a definition of a concept or asked questions about the concept that can be answered on the basis of its definition. You are responsible for: entailment or validity, equivalence, tautologousness, relative inconsistency or exclusion, inconsistency of a set, absurdity, and relative exhaustiveness. (These are the concepts whose definitions appear in Appendix A.1.)
Calculations of truth values. That is, you should be able to calculate the truth value of a symbolic sentence on an extensional interpretation of it. This means you must know the truth tables for connectives and also how to carry out the sort of calculation from tables introduced in ch. 6—see exercise 2 of 6.4.x).
Describing structures. Describing a structure that is a counterexample lurking an open gap is the last step in a derivation that fails, but I may ask you simply to describe a structure that makes certain sentences true. The derivation exercises in chapters 7 and 8 have led only to very simple structures, but you can find more complex ones in the examples of 6.4.3 (as well as among the old tests—in old versions of both test 3 and test 5).
F04 test 5 questions
| Analyze the following sentences in as much detail as possible, providing a key to the non-logical vocabulary (upper and lower case letters) appearing in your answer. Notice the special instructions given for 1 and 3. | |
| 1. |
Someone was singing [Present your analysis also using an unrestricted quantifier.]
answer |
| 2. |
There is a package that isn’t addressed to anyone.
answer |
| 3. |
An airline served each airport. [This sentence is ambiguous. On one way of interpreting it, it could be true even if no one airline served all airports. Analyze the sentence according to that interpretation of it.]
answer |
| 4. |
At least two people called.
answer |
| Analyze the sentence below using each of the two ways of analyzing the definite description the sleigh Santa drove. That is, give an analysis that uses Russell’s treatment of definite descriptions as quantifier phrases and another analysis that uses the description operator. | |
| 5. |
The sleigh Santa drove was red.
answer |
| Use derivations to show that the following arguments are valid. You may use any rules. | |
| 6. |
∃x (Fx ∧ Gx)
answer
∃x Gx |
| 7. |
∃x (Fx ∧ ∃y Rxy)
answer
∃x ∃y (Fy ∧ Ryx) |
| Complete the following to give a definition of entailment in terms of truth values and possible worlds: |
| 8. |
A sentence φ is entailed by a set Γ (i.e., Γ ⊨ φ) if and only if …
answer |
| Complete the following truth table for the two rows shown. Indicate the value of each component of the sentence on the right by writing the value under the main connective of that component. | ||||||||||||||||||||||||||||||||||||||||
| 9. |
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| Use either tables or a diagram to describe a structure in which the following sentences are true. (That is, do what would be required to present a counterexample when a dead-end gap of a derivation had these sentences as its active resources.) | |
| 10. |
a = c, fa = fb, ¬ Ga, Gb, G(fc), Ra(fb), Rb(fa)
answer |
F04 test 5 answers
| 1. |
Someone was singing Someone is such that (he or she was singing) (∃x: x is a person) x was singing
(∃x: Px) Sx
P: [ _ is a person]; S: [ _ was singing] |
| 7. |
or
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| 8. |
A sentence φ is entailed by a set Γ if and only if there is no possible world in which φ is false while all members of Γ are true or: A sentence φ is entailed by a set Γ if and only φ is true in every possible world in which all members of Γ are true |
| 9. |
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| 10. |
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