EXERCISE 14.2
1. There exists a unique x satisfying Tove(x). 3. There exists an x such that for all y, y satisfies Tove(y) if and only if y is x. 5. For all x and for all y, both Tove(x) and Tove(y) hold if and only if y is x.
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EXERCISE 14.2 (odd) 1. x y [Dodec(x) Dodec(y) x y] 3. x y [Cube(x) Cube(y) x y z (Cube(z) (z = x z = y)] 5. x [Large(x) Cube(x) z (Large(z) Cube(z) z = x) y (BackOf(y, x) Dodec(y)]
EXERCISE 14.10 1. Ex (Cube(x) AND Ay (Cube(y) I MPL IES y = x) 2. Cube(a
R I K SENGUPTA Homework # 8 P rofessor Delia Fara
12.14 The purported proof is clearly wrong. To see why this is so, note that even though our choice of c was arbitrary, our choice of d depended directly on c. This is because d had to be an object whose s
Homework # 6 RIK SENGUPTA Professor Delia Graff Fara
EXERCISE 9.11 2. I t would not be possible. If 3 were t rue, then every object in the world would be a tetrahedron and small, i.e. the world would consist entirely of small tetrahedra. But then sentence
RIK SENGUPTA Professor Delia Fara PHI 201 Homework 5 LPL 6.17 Fitch won't let me perform the last step (8). This is because in this step we are using step 5, a step that occurs within an earlier subproof. But the statement of step 5, namely Dodec(b), had
RIK SENGUPTA Professor Delia Graff Fara Philosophy 201 Homework 4
EXERCISE 5.12 The justification behind int roducing this claim in our proof is that a number can either be expressed in the form p/q, where p and q are integers (q is non-zero), or it canno
EXERCISE 3.25 RIK SENGUPTA PRECEPTOR: Professor Delia Fara
1. LessContagious(x, y) "x is less contagious than y", where x and y are names of diseases. MoreDeadly(x, y) "x is more deadly than y", where x and y are names of diseases. Here x = AIDS, y = infl
LPL 3.4 EXTRA CREDIT RIK SENGUPTA NOTE: Throughout this proof we define "A is equivalent to B" as "the truth value of A is the truth value of B". Let P be a true sentence and let Q be formed by putting some number of negation symbols in front of P. Case 1
LPL 2.23 RIK SENGUPTA The argument is valid. But it is not sound. The following is an informal proof. We know philosophers have the intelligence needed to be computer scientists. Also, we are given that anyone with the intelligence needed to be a computer
LP L 2.22 R I K SENGUPTA The argument is not valid. So obviously it is not sound. The following is an informal counterexample to it. Let's consider this situation: There are 10,000 people in the world who know how to program a computer. Since anyone who k
EXTRA CRED I T R I K SENGUPTA There is no way that the addition of an extra premise will validate an argument if one of the original premises actually contradicts the conclusion, i.e. if a premise negates the t ruth of the conclusion, then the addition of
P roblem 1.18 L PL EXTRA CRED I T R I K SENGUPTA
1. La rger(capital( Indiana), capital(California) Here the objects (x) that the names refer to are the names of states (which may be capitalized). We introduce the function "capital(x)" to denote the capita
P roblem 1.17 LP L R I K SENGUPTA
The function symbol that I am using is height(x), which takes one argument x the name of a person whose height is being compared. The relation symbols "<" and "=" are used in their usual context, i.e. < refers to less tha
P roblem 1.8 LP L EXTRA CRED I T R I K SENGUPTA
1. We would have the following atomic sentences: i. GaveScruffy(claire, claire) ii. GaveScruffy(max, claire) iii. GaveScruffy(claire, max) iv. GaveScruffy(max, max) v. GaveCarl(claire, claire) vi. GaveCarl(m