PHL245H1S 2018 Koo Final Exam (Relevant Study Questions Only)

Page 3 of 14 2. Provide a Finite Extensional Model that demonstrates that the following argument is invalid. (3) ∃y(By∧∀x~H(yx)). ∀w(Aw→∃z(Bz∧H(zw)). ∴ ~Aa∨Ba.

Page 6 of 14 8. When we say statements such as “squirrels are brown”, we have learned that this means: all squirrels are brown. But, this universal generalization is clearly false as there are some albino (white) squirrels. Moreover, logicians think that when we say “squirrels are brown,” we already know there are exceptions, so we don’t even mean the universal claim at all. Thus, they argue that the correct way to symbolize “squirrels are brown” is not of the form ∀x(Fx→Bx) and , but rather by invoking a new quantifier called a generic , represented by λ x. So, “squirrels are brown” means: most squirrels are brown, and this is symbolized as λx(Fx→Bx). This allows for the existence of a non-brown squirrel to not contradict the statement claim as it did not mean a universal in the first place. Using the following abbreviation scheme, construct a finite extensional interpretation/model for “squirrels are brown” that illustrates the difference between the universal interpretation, ∀x(Fx→Bx), and the generic interpretation, λx(Fx→Bx), of the statement by making one of them true and one of them false. Briefly explain how your interpretation/model illustrates the difference. (3) F 1 : a is a squirrel. B 1 : a is brown. Part II: Symbolization (36 Marks) Symbolize questions 1-8, and translate questions 9 and 10 using the provided abbreviation schemes. Read the instructions for question 10 carefully. 1. Betty isn’t in a good mood unless there is neither bad coffee nor bad weather. (3) B 1 : a is bad. C 1 : a is a coffee. D 1 : a is weather. G 1 : a is in a good mood. b 0 : Betty.

Page 9 of 14 8. For someone to be happy, it is sufficient that they think a good thought (generic) every day. (4) A 1 : a is a person. H 1 : a is happy. D 1 : a is a day. G 1 : a is a good thought. M 3 : a thinks b at c . 9. Translate the following symbolic sentence into an IDIOMATIC English sentence using the abbreviation scheme provided. (3) ∃x(Dx∧∃y(Fy∧H(xy)∧∃z(Fz∧H(xz)∧~z=y∧∀w(Fw∧H(xw)→w=y∨w=z)))) D 1 : a is a person. F 1 : a is a finger. H 2 : a has b . 10. Define a new operator in our system ℩ (called ‘cane’). This operator combines with a variable, and together with a predicate we get a formula. For example, ℩xFx is a formula. We can understand ℩x as saying ‘the thing such that’ – ℩x is the definite descriptor. ℩x φ x, where φ x is a formula, thus picks out a term or specific individual , and can be used as a term in our symbolizing. Translate the following symbolic sentence into an IDIOMATIC English sentence using the abbreviation scheme provided. (3) ∃x(Fx∧B(x℩w(Aw∧Bw))∧∃y(Fy∧B(y℩w(Aw∧Bw))∧~x=y)) A 1 : a is a march. B 1 : a is against guns. F 1 : a is a politician. B 2 : a attended b .

Page 12 of 14 3. Show the following argument is valid using a derivation. You may use the basic rules as well as the derived rules: CDJ, DM, NC, NB, SC, QN, and AV. (8) ∀xHa(x). ∀x∃y(Hx→F(a(y)b(x))). ∴ ∃x∃y∃z(F(xb(y))∧F(zb(x)))