PHL245H1F 2016 Exam (Relevant Study Questions Only)
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University of Toronto *
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Course
PHL245
Subject
Philosophy
Date
Jan 9, 2024
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16
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UNIVERSITY OF TORONTO
Faculty of Arts and Science
DECEMBER 2016 EXAMINATIONS
PHL245H1-F
Alex Koo
Duration - 3 hours
No Aids Allowed
Last Name: __________________________________________________
First Name: __________________________________________________
Student Number: _____________________________________________
Answer
ALL
questions on the exam paper.
Use examination booklets for rough work if needed.
If you need further space, use an examination booklet and clearly indicate on the exam
paper where your solution is.
The exam consists of 16 pages. Pages 2-15 have questions on them.
The final page (16)is a blank lined page for use if needed.
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Part I: Semantics (30 marks)
1.
Explain why an argument with a contradiction in the premises is valid. What does
this tell us about the concept of validity? (4)
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16
4.
Provide a finite extensional interpretation/model that demonstrates the following
argument is invalid. (4)
∃x(Fx∧Gx∧~D(xx)).
∀x(Gx→∃y(Fy∧D(xy)).
∃x(Hx∧~(Fx∨Gx)).
∴ ~∀x(Hx→∀y(Fy→D(xy)))
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5.
a)
∀x(Fx→∃yB(yx)).
~∀z(Gz∧B(zz)).
∴ ∃y∀x(B(xy)∧Gx).
b)
Provide a finite extensional interpretation/model that demonstrates the
argument from part (a) is invalid. (1)
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6.
We know that a disjunction can actually be expressed as a conditional of the form “if
not one, then the other.” Given this, it is clear that we could easily remove the
disjunction entirely from our logical system without impacting its completeness.
Briefly give some reasons why we should NOT remove the disjunction from our
logical system. (2)
7.
Below is the truth table for the logical connective called the Sheffer Stroke
symbolized by the vertical bar, ∣. Convert each of the following sentences into a
logically equivalent sentence that contains ONLY the Sheffer Stroke as its logical
connectives.
P
Q
P ∣ Q
T
T
F
T
F
T
F
T
T
F
F
T
a) ~P
(1)
b) P∧Q
(2)
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8.
Circle
the single best answer to the following LSAT logic question: (2)
Several critics have claimed that any contemporary poet who writes formal poetry—poetry
that is rhymed and metered—is performing a politically conservative act. This is plainly
false. Consider Molly Peacock and Marilyn Hacker, two contemporary poets whose poetry
is almost exclusively formal and yet who are themselves politically progressive feminists.
The conclusion drawn above follows logically if which one of the following is assumed?
A.
No one who is a feminist is also politically conservative.
B.
No poet who writes unrhymed or unmetered poetry is politically conservative.
C.
No one who is politically progressive is capable of performing a politically
conservative act.
D.
Anyone who sometimes writes poetry that is not politically conservative never
writes poetry that is politically conservative.
E.
The content of a poet’s work, not the work’s form, is the most decisive factor in
determining what political consequences, if any, the work will have.
9.
Provide a shortened truth-table that demonstrates the following set of sentences is
not inconsistent. (3)
{P→~(R∧S), ~(R→(P↔Q)), ~(Q∨W)}
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Page
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Part II: Symbolization (34 Marks)
Symbolize questions 1-8, and translate question 9 using the provided abbreviation
schemes.
1.
A sufficient condition for people and hamsters to feel good is exercising. (3)
E
1
:
a
exercises. F
1
:
a
is a person. G
1
:
a
feels good. H
1
:
a
is a hamster.
2.
Although neither Demar nor Demar’s wife ever watch hockey games, they both
know how to skate. (4)
d
0
: Demar. d
1
: The wife of
a
. A
1
:
a
is a time. D
1
:
a
knows how to skate.
H
1
:
a
is hockey game. G
3
:
a
watches
b
at time
c
.
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3.
A person who doesn’t like cats is wise, and only in that case does he/she lead a
successful life. (4)
A
1
:
a
leads a successful life. C
1
:
a
is a cat. D
1
:
a
is wise. F
1
:
a
is a person. L
2
:
a
likes
b
.
4.
Unless they aren’t funded by the Government of Canada, parks that people visit are
clean. (4)
c
0
: Canada. a
1
: The Government of
a
. C
1
:
a
is clean. F
1
:
a
is a person. G
1
:
a
is a park.
A
2
:
a
visits
b
.
F
2
:
a
funds
b
.
5.
Despite the fact that Avery’s best friend is the silliest student at UofT, he doesn’t
have any other friends (who are people) besides Avery. (4)
a
0
: Avery. b
0
: UofT. b
1
: The best friend of
a
. F
1
:
a
is a person. A
2
:
a
is a student at
b
.
C
2
:
a
is sillier than
b
. F
2
:
a
is the friend of
b
.
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6.
No board games except for Dominion, which you need at least two people playing
for it to be good, are fun. (4)
d
0
: Dominion. A
1
:
a
is fun. B
1
:
a
is a board game. F
1
:
a
is a person. G
1
:
a
is good.
C
2
:
a
plays
b
.
7.
Exactly one student who takes PHL245 will go on and ace third year logic. (4)
a
0
: PHL245. b
0
: Third year logic. A
1
:
a
is a student. A
2
:
a
takes
b
. B
2
:
a
will ace
b
.
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Page
10
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8.
Symbolize the following ambiguous sentence in TWO logically distinct ways. Provide
an English sentence that clarifies the meaning of each symbolization. (4)
Some person doesn’t ever ride a bike.
B
1
:
a
is a bike. D
1
:
a
is a time. F
1
:
a
is a person. N
3
:
a
rides
b
at
c
.
9.
Translate the following symbolic sentence into an IDIOMATIC English sentence
using the provided abbreviation scheme. (3)
b(a)=a(b)∧∀x(Fx∧H(xc(a))→∀y(Fy∧H(yc(a))→x=y))
a
0
: Lois Lane. b
0
: Superman. a
1
: The alter ego of
a
.
b
1
: The partner of
a
. c
1
: The secret of
a
. F
1
:
a
is a person. H
2
:
a
knows
b
.
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Part III: Derivations (36 marks)
1.
Show the following statement is a theorem of logic using a derivation. Use only the
basic
rules: MP, MT, ADD, MTP, ADJ, S, R, DN, CB, BC, EI, EG, and UI. (6)
∴ ∀x∃y(F(xy)∧Gx)→∃x∃z(F(a(x)z)∧Gz).
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2.
Show the following argument is valid using a derivation. Use only the
basic
rules:
MP, MT, ADD, MTP, ADJ, S, R, DN, CB, BC, EI, EG, and UI. (9)
∀x(Fx∧∀yH(yx)). ~∃yGy∨∃xBx. ∀z∃xH(a(z)x)→~∃z(Bz∨Az). ∴ ~∃x(Fx↔Gx).
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3.
Show the following argument is valid using a derivation. Use only the
basic
rules:
MP, MT, ADD, MTP, ADJ, S, R, DN, CB, BC, EI, EG, and UI. In addition, add the
following rule to your derivation system: (6)
Leibniz’s Law (LL)
φ
α
α=β
------- ∴ φ
β
∀x(Fx→x=a∨x=b). ∼Gb. ∃x(Fx∧Gx) ∴ Fa.
Where φ
β
is a substitution of
any
occurrences of α in φ
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4.
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. (6)
∀x∀y∀z(L(xy)∧L(zy)→L(zx)). ∴ ~L(ab)→∀x~∀yL(yx).
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5.
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. (9)
∀w~(∃zM(wb(z))↔∃yD(ya(yy))). ∀zFz∨∃x∀yD(a(x)y). ∴ ∀x(Fx∨~∀wM(b(x)w)).
Total = 100 Marks
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Extra Lines. If you use these, clearly indicate how the grader should read your proof.
Total Pages (16)