| Phi 270 Fall 2013 |
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Phi 270 F10 test 5
F10 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 course, consider examples and exercises in the text as well. In particular, pay attention to the variety of special issues that show up (e.g., how to handle there is or else).
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 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. You should be able to complete a row of a truth table for a sentence formed using truth-functional connectives.
Using abstracts to analyze sentences involving pronouns. You might be asked to represent pronouns using abstracts and variables (i.e., in the way introduced in 6.2).
F10 test 5 questions
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Analyze the following sentences in as much detail as possible, providing a key to the items of non-logical vocabulary (upper and lower case letters apart from variables) that appear in your answer. Notice the special instructions given for each of 1, 2, and 3. |
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| 1. |
Sam saw a supernova. [Give an analysis using a restricted quantifier, and restate it using an unrestricted quantifier.] answer |
| 2. |
None of the flights Al was on were delayed. [Do not use ∀ in your analysis of this; that is, use ∃ in your analysis of any quantifier phrases.] answer |
| 3. |
Someone ate every cookie. [On one way of understanding this sentence, it would be false if the cookies were eaten by several people. Analyze it according to that interpretation.] answer |
| 4. |
Fred had to make at least two connections. answer |
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Analyze the sentence below using each of the two ways of analyzing the definite description. That is, give an analysis that uses Russell’s treatment of definite descriptions as quantifier phrases as well as one that uses the description operator to analyze the definite description. |
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| 5. |
Al opened the package. answer |
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Use a derivation to show that the following argument is valid. You may use any rules. |
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| 6. |
∀x (Fx ∨ Gx)
answer
∃x ¬ Fx ∃x Gx |
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Use a derivation to show that the following argument is not valid, and use either a diagram or tables to present a counterexample that lurks in an open gap of your derivation. |
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| 7. |
∃x (Fx ∧ Gx)
answer
Ha ∃x (Fx ∧ Hx) |
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Complete the following to give a definition of entailment in terms of truth values and possible worlds: |
| 8. |
A set Γ entails a sentence φ (i.e., Γ ⊨ φ) if and only if ... answer |
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Analyze the sentence below using abstracts and variables to represent pronominal cross reference to individual terms (instead of replacing pronouns by such antecedents). A letter standing for an individual term should appear in your analysis only as often as the individual term appears in the original sentence. |
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| 9. |
Al called both Bill, who called him back, and Carol, who didn't. answer |
F10 test 5 answers
| 1. |
Sam saw a supernova A supernova is such that (Sam saw it) (∃x: x is a supernova) Sam saw x
(∃x: Nx) Ssx
N: [ _ is a supernova]; S: [ _ saw _ ]; s: Sam |
| 7. |
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| 8. |
A set Γ entails a sentence φ if and only if there is no possible world in which φ is false while every member of Γ is true or A set Γ entails a sentence φ if and only if φ is true in every possible world in which every member of Γ is true |
| 9. |
Al called both Bill, who called him back, and Carol, who didn't Al, Bill, and Carol are such that (the first called both the second, who called him back, and the third, who didn't) [x called both y, who called x back, and z, who didn't call x back]xyz Al Bill Carol [x called y, who called x back ∧ x called z, who didn't call x back]xyzabc [(x called y ∧ y called x) ∧ (x called z ∧ ¬ z called x)]xyzabc [(Cxy ∧ Cyx) ∧ (Cxz ∧ ¬ Czx)]xyzabc C: [ _ called _ ]; a: Al; b: Bill; c: Carol |