phi_270_F05_test

F05 test 4 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.

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Analysis. Be ready to handle any of the key issues discussed in class--for example, the proper analysis of every, no, and only (§7.2), how to incorporate bounds and exceptions (§7.2), ways of handling compound quantifier phrases (such as only cats and dogs, §7.3), the distinction between every and any (§§7.3 and 7.4), how to represent multiple quantifier phrases with overlapping scope (§7.4). Be able restate you analysis using unrestricted quantifiers, but you will not need to present it in English notation.

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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.)

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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 (by either tables or a diagram). In derivations involving restricted universals you will have the option using the rules RUG, SB, SC, and MRC or instead using RUP and RUC along with rules for unrestricted universals and conditionals. You will not be responsible for the rules introduced in §7.8.

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Analyze the sentences below in as much detail as possible, providing a key to the non-logical vocabulary you use. Restate 1 using an unrestricted quantifier.
1.	`Everyone knew the tune.` [Remember to restate your answer to this using an unrestricted quantifier.] answer
2.	`Sam heard only tunes that he knew.` [Remember to restate your answer in 2 using an unrestricted quantifier.] answer
3.	`No one liked everything on the menu.` answer

Use derivations to show that the following arguments are valid. You may use any rules.
5.	∀x (Fx ∧ Gx) ∀x (Gx ∧ Fx) answer
6.	∀x ∀y (Gy → Rxy) ∀x (Fx → Gx) ∀x (Fx → ∀y Ryx) answer

Synthesize an English sentence with the following logical form; that is, produce a sentence that would have the following analysis:
4.	(∀x: Px) ¬ Fsx P: [ _ `is a person`]; F: [ _ `fit` _ ]; s: `the shoe` answer

Use a derivation to show that the following argument is not valid and present a counterexample by describing a structure that is a counterexample lurking an open gap. (You may describe the structure either by depicting it in a diagram, as answers in the text usually do, or by giving tables.)
7.	∀x (Fx → Rax) Fa ∀x Rxa answer