Phi 270 F03 test 3
F03 test 3 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.
Analysis. Two sorts of questions are possible here corresponding to the sorts of analyses you have done in chs. 5 and 6: (i) analysis by truth-functional connnectives only with atomic sentences as the ultimate components (the focus would, of course, be on conditionals--i.e., on the symbolic representation of if, only if, and unless), (ii) analysis using truth-functional connnectives and the ideas of predicates, individual terms, and functors.
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 form might be either a truth-functional compound of unanalyzed component sentences or a form built from predicates, individual terms, and functors.
Derivations. Be able to construct derivations to show that entailments hold and to show that they fail. I may tell you in advance whether an entailment holds or leave it to you to check that using derivations. There will be some derivations where detachment and attachment rules may be used and where they will shorten the proof. But there will be others where you must rely on others rules, either because detachment and attachment rules do not apply or because I tell you not to use them. In particular be ready to use the rule RC (Rejecting a Conditional) from ch. 5.
Remember that, if a derivation, includes forms built using predicates presenting a counterexample will require the description of a structure and not merely an assignment of truth values.
F03 test 3 questions
| Analyze the sentences below in as much detail as possible using only connectives; that is, you should not identify components that are individual terms (or predicates or functors). Present the result in both symbolic and English notation. Be sure that the unanalyzed components of your answer are complete and independent sentences; also try to respect any grouping in the English. | |
| 1. |
If it was cloudy, Bob didn’t see the eclipse
answer |
| 2. |
Unless the lock is broken, you can get in only if you have a key
answer |
| Use derivations to checkwhether each of the entailments below holds. You may use detachment and attachment rules. If an entailment fails, present a counterexamplethat divides an open gap. | |
| 3. |
A → ¬ C, B → C ⊨ A → ¬ B
answer |
| 4. |
(A ∧ B) → C ⊨ B → (¬ C → A)
answer |
| Analyze the sentence below in as much detail as possible. In this case you should identify components that are individual terms, predicates, or functors. Be sure that the unanalyzed components of your answer are independent (in particular, that none contains a pronoun whose antecedent is in another). | |
| 5. |
If Sam asked Tom to drive him to the meeting, then he is the person who called earlier
answer |
| 6. |
Dave’s father called the mother of the child who hit him
answer |
| Use a derivation to show that the entailment below holds. You may use detachment and attachment rules. | |
| 7. |
a = b ∧ Rac ⊨ fa = c → Rb(fb)
answer |
F03 test 3 answers
| 1. |
If it was cloudy, Bob didn’t see the eclipse it was cloudy → Bob didn’t see the eclipse it was cloudy → ¬ Bob saw the eclipse
C → ¬ S
C: it was cloudy; S: Bob saw the eclipse |
| 3. |
|
| 5. |
If Sam asked Tom to drive him to the meeting, then he is the person who called earlier Sam asked Tom to drive him to the meeting → Sam is the person who called earlier [ _ asked _ to drive _ to _ ] Sam Tom Sam the meeting → Sam = the person who called earlier Astsm → s = p A: [ _ asked _ to drive _ to _ ]; m: the meeting; p: the person who called earlier; s: Sam; t: Tom |
| 6. |
Dave’s father called the mother of the child who hit him [ _ called _ ] Dave’s father the mother of the child who hit Dave C([ _’s father] Dave)([the mother of _ ](the child who hit Dave)) C(fd)(m([the child who hit _ ]d)) C(fd)(m(hd)) C: [ _ called _ ]; d: Dave; f: [ _’s father]; h: [the child who hit _ ]; m: [the mother of _ ] |
| 7. |
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