| Phi 270 Fall 2013 |
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Phi 270 F08 test 5
F08 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 (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 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. (You will not find many questions of this sort in the old exams, but exercise 2 for 6.2 and your homework on 6.2 provide examples as do test 3 for F06 and F08 and test 5 for F06.)
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 provide simple examples, and 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).
F08 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. |
Dave found a coin. [Give an analysis using a restricted quantifier, and restate it using an unrestricted quantifier.] answer |
| 2. |
There is an elf who neglects no one. [Do not use ∀ in your analysis of this; that is, use ∃ in your analysis of any quantifier phrases.] answer |
| 3. |
Everyone watched a movie. [On one way of understanding this sentence, it would not be true unless everyone watched the same movie. Analyze it according to that interpretation.] answer |
| 4. |
Someone sang to someone else. 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. |
Rudolph guided the sleigh that flew. 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 Gx
answer
∀x Fx ∃x (Fx ∧ 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 ∀y Rxy
answer
∀x ∃y Rxy |
| Complete the following to give a definition of equivalence in terms of truth values and possible worlds: |
| 8. |
A pair of sentences φ and ψ entails a sentence χ (in symbols, φ, ψ ⊨ χ) if and only if ... answer |
| 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. | |
| 9. |
Bill called Carol and mentioned his father to her. answer |
F08 test 5 answers
| 1. |
Dave found a coin A coin is such that (Dave found it) (∃x: x is a coin) Dave found x
(∃x: Cx) Fdx
C: [ _ is a coin]; F: [ _ found _ ]; d: Dave |
| 7. |
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| 8. |
A pair of sentences φ and ψ entails a sentence χ if and only if there is no possible world in which both φ and ψ are true and χ is false or A pair of sentences φ and ψ entails a sentence χ if and only if χ is true in every possible world in which both φ and ψ are true |
| 9. |
Bill called Carol and mentioned his father to her Bill and Carol are such that (he called her and mentioned his father to her) [x called y and mentioned x’s father to y]xy Bill Carol [x called y ∧ x mentioned x’s father to y]xybc [Cxy ∧ Mx(x’s father)y]xybc [Cxy ∧ Mx(fx)y]xybc C: [ _ called _ ]; M: [ _ mentioned _ to _ ]; b: Bill; c: Carol; f: [ _’s father] |