Philosophy 12A Homework Assignment #5
November 7, 2008
1
LPML
Symbolizations
Answer the following four (4) questions from pages 158 and 165 of the text.
1. p
.
158 #6
2. p
.
158 #16
3. p
.
165 #5
4. p
.
165 #15
2
Working with a
Given
LPML Interpretation
Answer the following three (3) questions from page 179 of the text.
5. #5
6. #9
7. #12
3
Constructing
LPML Interpretations
Answer the following three (3) questions from page 184 of the text.
8. #6
9. #8
10. #21
I have attached pages 158, 165, 179, and 184 from the 4th printing of
Modern
Logic
to the end of this homework assignment.
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158
Chapter 5: Predication and Quantification in English
!
Exercises
Symbolize each of the following sentences using names, predicates and the
existential quantifier, as appropriate. State your dictionary and say what
domain your quantifiers are relativized to. Show at least one intermediate step
in Loglish for each example.
(1)
Some mathematicians are famous.
(2)
Some mathematicians are not famous.
*(3)
There is no mathematician who is famous.
(4)
Some Germans are famous mathematicians.
(5)
Gödel was a famous German mathematician.
(6)
If Fermat was a French mathematician, then he was famous.
(7)
Ada Lovelace was a brilliant English mathematician but she was not famous.
(8)
Some famous mathematicians are neither German nor French.
(9)
New Orleans is polluted but not smoggy.
(10)
Some cities are smoggy and polluted.
(11)
Some polluted cities are smoggy.
*(12)
Some polluted cities are smoggy and some aren’t.
(13)
No smoggy city is unpolluted.
(14)
No city is smoggy if it is unpolluted.
*(15)
If a wealthy economist exists so does a famous mathematician.
(16)
If no wealthy economist exists then no famous mathematician exists.
(17)
Vampires don’t exist.
(18)
Nothing is both a ghost and a vampire.
(19)
There aren’t any ghosts, nor vampires either.
(20)
If ghosts and vampires don’t exist then nothing can be a ghost without being a
vampire.
3
More symbolizations: the universal quantifier
The other arguments of §1,
B
and
D
, contain the quantifier ‘everyone’. In
Loglish, ‘every’ becomes ‘for every _’ and so the premise of
B
, ‘everyone is hap
py’, is rendered
(1.a)
For every x, x is happy
relativizing ‘for every _’ to the domain of people. In place of ‘every’ we may have
‘each’, or ‘any’, or ‘all’. To turn (1.a) into a sentence of LMPL, we need a symbol
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 Spring '08
 FITELSON
 Philosophy, Logic, Predicate logic, Quantification, Universal quantification, Firstorder logic

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