| Phi 270 Fall 2013 |
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Phi 270 F11 test 5
F11 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. (That is, you should be able to carry out the sort of calculation used to complete the confirmation of a counterexample in chs. 2-5.)
Using abstracts to analyze sentences involving pronouns. You might be asked to represent pronouns using abstracts and variables (i.e., in the way that was introduced in 6.2).
F11 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. |
A road was closed. [Give an analysis using a restricted quantifier, and restate it using an unrestricted quantifier.] answer |
| 2. |
Al hadn’t read any book by Kant. [Do not use ∀ in your analysis of this; that is, use ∃ in your analysis of any quantifier phrases.] answer |
| 3. |
Every philosopher has read a certain book by Kant. [On one way of understanding this sentence, it would be false if there is no one book by Kant that all philosophers have read. Analyze it according to that interpretation.] answer |
| 4. |
Bob spoke to Al and also to at least two other people. 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 analysis 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 read the book that Bob read. 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 ∀y Rxy
answer
∃x Rxx |
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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 Rxx
answer
∀x ∃y Rxy |
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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 are logically equivalent (i.e., φ ≃ ψ) 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. |
Ann called Bill, who called Carol, who called Dave. answer |
F11 test 5 answers
| 1. |
A road was closed Some road is such that (it was closed) (∃x: x is a road) x was closed
C: [ _ was closed]; S: [ _ is a road] |
| 7. |
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| 8. |
A pair of sentences φ and ψ are logically equivalent if and only if there is no possible world in which φ and ψ have different truth values or A pair of sentences φ and ψ are logically equivalent if and only if, in each possible world, φ has the same truth value as ψ |
| 9. |
Ann called Bill, who called Carol, who called Dave. Bill and Carol are such that (Ann called the former, who called the latter, who called Dave) [Ann called x, who called y, who called Dave]xy Bill Carol [Ann called x ∧ x called y ∧ y called Dave]xy Bill Carol [Cax ∧ Cxy ∧ Cyd]xybc C: [ _ called _ ]; a: Ann; b: Bill; c: Carol; d: Dave Also correct: [Cxy ∧ Cyz ∧ Czw]xyzwabcd |