Phi 270 F03 test 5
F03 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 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 assignment 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.
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 have the option using the rules REP and REC (as well as RUP and RUC) in derivations for restricted quantifiers. You will not be responsible for the rule for the description operator introduced in §8.6 or for the supplemented rules used to find finite counterexamples.
Earlier material. These questions will concern two topics.
Basic concepts. You may be asked for a definition or asked questions about them that can be answered by reasoning from their definitions. You are responsible for: entailment or validity, equivalence, tautologousness, inconsistency of a set, relative inconsistency or exclusion, absurdity, and relative exhaustiveness.
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.x).
F03 test 5 questions
| Analyze the following sentences in as much detail as possible, providing a key to the non-logical vocabulary (upper and lower case letters) appearing in your answer. Notice theadditional instructions given for the first. | |
| 1. |
Tom sent something to Sue
answer |
| 2. |
Everyone heard a sound. [This is ambiguous but you need only analyze one interpretation; justchoose the one that seems most natural to you.]
answer |
| 3. |
There is someone who knows just one other person.
answer |
| Analyze the sentence below using each of the two ways of analyzing the definite description the package. That is, analyze it using Russell’s analysis of definite descriptions as quantifier phrases and then analyze it again using the description operator. | |
| 4. |
The package rattled.
answer |
| Use derivations to show that the following argument is valid. You may use any rules. | |
| 5. |
∃x Fx
answer
∀x Gx ∃x (Fx ∧ Gx) |
| Use a derivation to show that the following argument is not valid and use either tables or a diagram to describe a structure dividing an open gap. | |
| 6. |
∃x ∀y Rxy
answer
∃x Rax |
| Complete the following to give a definition of equivalence in terms of truth values and possible worlds: |
| 7. |
A sentence φ is equivalent to a sentence ψ (i.e., φ ≃ ψ) if and only if …
answer |
| Answer the following question and explain your answer in terms of the definitions of the basic concepts it involves. | |
| 8. |
Suppose you are told that (i) φ ⊨ ψ and (ii) ψ is inconsistent with χ (i.e., the set formed of the two is inconsistent). What can you conclude about the relation between of φ and χ? That is, what patterns of truth values for the two are ruled out (if any are); and, if any are ruled out, what logical relation or relations holds as a result.
answer |
| Complete the following truth table by calculating the truth value of the sentence on each of the given assignments. In each row, write under each connective the value of the component of which it is the main connective and circle the truth value of the sentence as a whole. | ||||||||||||||||||||||||||||||||||||||||
| 9. |
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F03 test 5 answers
| 1. |
Tom sent something to Sue ∃x Tom sent x to Sue ∃x Ntxs C: [ _ sent _ to _ ]; s: Sue; t: Tom |
| 2. |
Everyone heard a sound (∃x: x is a sound) everyone heard x (∃x: x is a sound) (∀y: y is a person) y heard x (∃x: Sx) (∀y: Py) Hyx H: [ _ heard _ ]; P: [ _ is a person]; S: [ _ is a sound] |
| 5. |
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| 6. |
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| 7. | φ and ψ are equivalent if and only if there is no possible world in which they have different truth values (or: if and only, in every possible world, each has the same value as the other) |
| 9. |
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