Philosophy210- Logical Thought

Review Exercises

Possible Answers

 

Translations:

(1) E: j is earlier than k                             P: j is part of k
H: j has k on it at time [1]                   T: at time j, k tastes better than l
B: j is a hamburger                               c: the universal glob of catsup

"x"y"t [(Bx Ù By Ù – $z [Pzc Ù (Hxzt Ú Hyzt)] Ù –Ttxy Ù –Ttyx) ®

     "t1 [($w(Pwc Ù Hxwt1)  Ù–$u(Puc Ù Hyut1))] ® Tt1xy]]

     That was quite hard. It would be nearly as good to treat the taste as a thing, and then to say that the taste of x at t1 is better than the taste of x at t. That way you only need one burger. But what you must not say is that any burger with catsup tastes better than any without. (Supply your own counterexample.)

(2) S: j is a shirt                                       C: j is a collar
P: j is part of k                                   O: j is on k
R: j is shaped into a ring                       H: j has k
j: John                                                  d: the universal glob of dirt

     $x(Sx Ù Hjx Ù $y(Cy ÙHxy Ù $z[Pzd Ù RzÙ Ozy]))

(3) S: j has seen k                                   T: j is troublesome
K: j knows k                                       j: Jesus
i: the speaker of the sentence

     "x[(Tx Ù Six) ® (Kjx Ù "y( y≠j ® –Kyx))]

Here we cannot use an operator for 'know'. The knowledge is not knowledge that something is the case, but acquaintance of a thing. It is the difference between 'I know Henry' (knowledge by acquaintance) and 'I know that Henry is a creep'(knowledge that).

(4) P: j is the president of k       B2,1: at time j, k believes that [1]
G: j is guilty                                        S: j is shot at time k
E: j is earlier than k                             c: Chile

     $y(Pyc Ù "x"t ( B2,1 t y Gx ® $t1( Ett1 Ù Sxt1)))

(5) N: j needs k                                       N1,1: j needs it to be the case that [1]
H: j has k                                           i: the speaker of the sentence
o: the person addressed

     (a) Nio

     (b) N1,1i Noi                          Note that both (a) and (c) require a propositional

     (c) N1,1 $x Hix                        sense of needing, not just a relational sense.

(6) E: j is an egg                                       B: j is boiled
B2: j belongs to k                                P2: j is part of k
P3: j puts k on l                                P: j is a sweet potato
j: Jessica                                              a: the universal glob of applesauce

     $x[ Sx Ù B2xj Ù $y(By Ù EyÙ B2yj Ù $< $z (P2za Ù P3jzx) Ù "<–$w (P2wa Ù P3jwy)]

(7) W1,1: j wants it to be the case that [1]            B: j buys k
D1,1: j decides whether [1]                             W: j works in k
S0,1: it should be the case that [1]                    A: j assigns k
H1,1: j hopes it to be the case that [1]             B: j is a book
l: the library indicated                                      h: the teacher indicated

     $x[ Bx Ù $< H1,1h Ahx Ù –$y $< W1,1y D1,1 y S0,1 $z( Wzl ÙBzx)]

     The last clause is done that way because the library itself can't literally buy anything. Only a person can. But that is not quite right either, because a person who works for the library (or especially in the library) can buy a book that the library doesn't buy. This is a problem with no easy solution. If you saw the problem, then you did well.