| Phi 270 Fall 2013 |
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Phi 270 F06 test 5
F06 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 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).
Using abstracts to analyze sentences involving pronouns. You might be asked to represent pronouns using abstracts and variables. (You will not find questions of this sort in the old exams, but your homework on this topic and exercise 2 for 6.2 provide examples.)
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).
F06 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. |
Someone called Tom. [Give an analysis using a restricted quantifier, and restate it using an unrestricted quantifier.] answer |
| 2. |
Not a crumb was left, but there was a note from Santa. [Do not use ∀ in your analysis of this; that is, use ∃ in your analysis of any quantifier phrases.] answer |
| 3. |
A card was sent to each customer. [On one way of understanding this sentence, it would be true even if no two customers were sent the same card. Analyze it according to that interpretation.] answer |
| 4. |
At most one size was left. 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. |
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| 5. |
Ann found the note that Bill left. 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 (Gx → Hx) ∃x Hx |
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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 (Rxa ∧ Ray)
answer
∃x Rxx |
| 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 (in symbols, φ ≃ ψ) 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). An individual term should appear in your analysis only as often as it appears in the original sentence. | |
| 9. |
Ann wrote to Bill and he called her. answer |
F06 test 5 answers
| 1. |
Someone called Tom Someone is such that (he or she called Tom) (∃x: x is a person) x called Tom
(∃x: Px) Cxt
C: [ _ called _]; P: [ _ is a person]; t: Tom |
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Using the description operator: Ann found the note that Bill left [ _ found _ ] Ann (the note that Bill left) Fa(Ix x is note that Bill left) Fa(Ix (x is a note ∧ Bill left x)) Fa(Ix (Nx ∧ Lbx)) F: [ _ found _ ]; L: [ _ left _ ]; N: [ _ is a note]; a: Ann; b: Bill |
| 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 φ and ψ have the same truth value as each other in every possible world |
| 9. |
Ann wrote to Bill and he called her Ann and Bill are such that (she wrote to him and he called her) [x wrote to y and y called x]xy Ann Bill [x wrote to y ∧ y called x]xyab [Wxy ∧ Cyx]xyab C: [ _ called _ ]; W: [ _ wrote to _ ]; a: Ann; b: Bill |