Phil 120 week 1 class 1 July 5th 2004

1
All dogs are mortal Fido is a dog So Fido is
mortal
2
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal
3
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal
All As are B All Bs are C So all As are C
4
All As are B a is A (a has the property A) So a
is B All As are B All Bs are C So all As are C
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal
5
All As are B a is A (a has the property A) So a
is B All As are B All Bs are C So all As are C
A B C D M K
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal
6
All As are B a is A (a has the property A) So a
is B All As are B All Bs are C So all As are C
All As are B a is A (a has the property A) So a
is B All As are B All Bs are C So all As are C
A B C D M K
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal No zebra is a
donkey
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal
7
All As are B a is A (a has the property A) So a
is B All As are B All Bs are C So all As are C
All As are B a is A (a has the property A) So a
is B All As are B All Bs are C So all As are C
A B C D M K
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal No zebra is a
donkey All zebras are not donkeys Every zebra is
not a donkey
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal
8
All As are B a is A (a has the property A) So a
is B All As are B All Bs are C So all As are C
All As are B a is A (a has the property A) So a
is B All As are B All Bs are C So all As are C
A B C D M K
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal No zebra is a
donkey All zebras are not donkeys Every zebra is
not a donkey Every zebra is a zebra
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal
9
All As are B a is A (a has the property A) So a
is B All As are B All Bs are C So all As are C
All As are B a is A (a has the property A) So a
is B All As are B All Bs are C So all As are C
A B C D M K
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal No zebra is a
donkey A All zebras are not
donkies A Every zebra is not a donkey
A Every zebra is a zebra B
All dogs are mortal Fido is a dog So Fido is
mortal All dogs are mammals All mammals are
mortal So all dogs are mortal
10
Singular terms Aristotle is the father of logic U
of A is large Franks father is in town The men
drinking martini in the corner is dangerous That
is bad I dont like bananas
11
Singular terms Aristotle is the father of logic U
of A is large Franks father is in town The men
drinking martini in the corner is dangerous That
is bad I dont like bananas General terms Ivy
universities are very large Franks parents are
in town People drinking martini in the corner are
drunk
12
Singular terms Aristotle is the father of logic U
of A is large Franks father is in town The men
drinking martini in the corner is dangerous That
is bad I dont like bananas General terms Ivy
universities are very large Franks parents are
in town People drinking martini in the corner are
drunk Mass terms Snow is white Might is right
13
Grammatical predicates Aristotle is the father
of logic U of A is large Franks father is in
town The men drinking martini in the corner is
dangerous That is bad I dont like bananas
14
Grammatical predicates Aristotle is the father
of logic U of A is large Franks father is in
town The men drinking martini in the corner is
dangerous That is bad I dont like
bananas Predicates in PL Aristotle is the
father of logic (Aristotle has the property of
being the father of logic) U of A is large (U of
A has the property of being large) Franks father
is in town The men drinking martini in the corner
is dangerous That is bad I dont like bananas (I
have the property of not liking bananas)
15
Aristotle is the father of logic Fa U of A is
large Lu Franks father is in town Tf The men
drinking martini in the corner is
dangerous Dm That is bad Bt I dont like
bananas Lv Predicates in PL Aristotle is the
father of logic (Aristotle has the property of
being the father of logic) U of A is large (U of
A has the property of being large) Franks father
is in town The men drinking martini in the corner
is dangerous That is bad I dont like bananas (I
have the property of not liking bananas)
16
Predicates in PL One-place (unary)
predicates being odd being even being in
town not liking bananas
17
Predicates in PL One-place (unary)
predicates being odd being even being in
town not liking bananas Two-place (binary)
predicates (relations) being grater than being
equal
18
Predicates in PL One-place (unary)
predicates being odd being even being in
town not liking bananas Two-place (binary)
predicates (relations) being grater than being
equal Three-place (ternary) predicates
(relations) being between
19
Predicates in PL One-place (unary)
predicates being odd being even being in
town not liking bananas Two-place (binary)
predicates (relations) being grater than being
equal Three-place (ternary) predicates
(relations) being between
Predicates in PL One-place (unary) predicates
(properties) being odd being even being in
town not liking bananas Two-place (binary)
predicates (relations) being grater than being
equal Three-place (ternary) predicates
(relations) being between n place (n-ary)
predicates (relations)
20
7.3E3
a. (Ia Ba) Ra
21
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic
22
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id
23
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib
24
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id Ia)
25
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb)
26
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac
27
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac h. (Laa Lac) (Dab Dad)
28
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac h. (Laa Lac) (Dab Dad) i. (Lca
? Dca) (Lcd Dcd)
29
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac h. (Laa Lac) (Dab Dad) i. (Lca
? Dca) (Lcd Dcd) j. (Adc ? Abc) (Acd
Acb)
30
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac h. (Laa Lac) (Dab Dad) i. (Lca
? Dca) (Lcd Dcd) j. (Adc ? Abc) (Acd
Acb) k. Acb ? (Sbc Rb)
31
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac h. (Laa Lac) (Dab Dad) i. (Lca
? Dca) (Lcd Dcd) j. (Adc ? Abc) (Acd
Acb) k. Acb ? (Sbc Rb) l. (Aab Aad) (Lab
? Lad)
32
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac h. (Laa Lac) (Dab Dad) i. (Lca
? Dca) (Lcd Dcd) j. (Adc ? Abc) (Acd
Acb) k. Acb ? (Sbc Rb) l. (Aab Aad) (Lab
? Lad) m. (Sdc Sca) ? Sda
33
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac h. (Laa Lac) (Dab Dad) i. (Lca
? Dca) (Lcd Dcd) j. (Adc ? Abc) (Acd
Acb) k. Acb ? (Sbc Rb) l. (Aab Aad) (Lab
? Lad) m. (Sdc Sca) ? Sda n. (Abd Adb) ? (Lbd
Ldb)
34
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac h. (Laa Lac) (Dab Dad) i. (Lca
? Dca) (Lcd Dcd) j. (Adc ? Abc) (Acd
Acb) k. Acb ? (Sbc Rb) l. (Aab Aad) (Lab
? Lad) m. (Sdc Sca) ? Sda n. (Abd Adb) ? (Lbd
Ldb) o. (Lcb Lba) ? (Dca Sca)
35
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac h. (Laa Lac) (Dab Dad) i. (Lca
? Dca) (Lcd Dcd) j. (Adc ? Abc) (Acd
Acb) k. Acb ? (Sbc Rb) l. (Aab Aad) (Lab
? Lad) m. (Sdc Sca) ? Sda n. (Abd Adb) ? (Lbd
Ldb) o. (Lcb Lba) ? (Dca Sca) p. (Rc ?
Bc) ? Ic ? (Lac ? Lbc) ? (Lcc ? Ldc)
36
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac h. (Laa Lac) (Dab Dad) i. (Lca
? Dca) (Lcd Dcd) j. (Adc ? Abc) (Acd
Acb) k. Acb ? (Sbc Rb) l. (Aab Aad) (Lab
? Lad) m. (Sdc Sca) ? Sda n. (Abd Adb) ? (Lbd
Ldb) o. (Lcb Lba) ? (Dca Sca) p. (Rc ?
Bc) ? Ic ? (Lac ? Lbc) ? (Lcc ? Ldc) q. Rd
Ra ? (Rb ? Rc)
37
7.3E3
a. (Ia Ba) Ra b. (Rc Bc) Ic c. (Bd
Rd) Id d. (Rb ? Bb) ? Ib e. Ib ? (Id
Ia) f. (Ba Ia) (Ib Bb) (Ra ? Rb) g.
Lab Dac h. (Laa Lac) (Dab Dad) i. (Lca
? Dca) (Lcd Dcd) j. (Adc ? Abc) (Acd
Acb) k. Acb ? (Sbc Rb) l. (Aab Aad) (Lab
? Lad) m. (Sdc Sca) ? Sda n. (Abd Adb) ? (Lbd
Ldb) o. (Lcb Lba) ? (Dca Sca) p. (Rc ?
Bc) ? Ic ? (Lac ? Lbc) ? (Lcc ? Ldc) q. Rd
Ra ? (Rb ? Rc) r. (Rd Id) ((Ra Ia) ?
(Rb Ib)) ? (Rc Ic)
38
Quantifiers many a few few most some at least
one little much at most three all every any each
none a(n) not one whatever whichever
39
Existential quantifier There are dogs At least
one thing is a dog There is at least one thing
which is a dog There is at least one thing which
has the property of being a dog
40
Existential quantifier There are dogs At least
one thing is a dog There is at least one thing
which is a dog There is at least one thing which
has the property of being a dog ?xDx
41
Existential quantifier There are dogs At least
one thing is a dog There is at least one thing
which is a dog There is at least one thing which
has the property of being a dog ?xDx Universal
quantifier Everything is a dog Each thing is a
dog Each and every thing is a dog All things are
dogs Anything is a dog
42
Existential quantifier There are dogs At least
one thing is a dog There is at least one thing
which is a dog There is at least one thing which
has the property of being a dog ?xDx Universal
quantifier Everything is a dog Each thing is a
dog Each and every thing is a dog All things are
dogs Anything is a dog ?xDx
43
Negations of simple quantified sentences It is
not the case that there are dogs There are no
dogs Nothing is a dog There is no thing that is a
dog
44
Negations of simple quantified sentences It is
not the case that there are dogs There are no
dogs Nothing is a dog There is no thing that is a
dog ?xDx
45
Negations of simple quantified sentences It is
not the case that there are dogs There are no
dogs Nothing is a dog There is no thing that is a
dog ?xDx It is not the case that everything is
a dog Not everything is a dog Not all things are
dogs
46
Negations of simple quantified sentences It is
not the case that there are dogs There are no
dogs Nothing is a dog There is no thing that is a
dog ?xDx It is not the case that everything is
a dog Not everything is a dog Not all things are
dogs ?xDx
47
7.4E3
a. Pj ? (?x)Px
48
7.4E3
a. Pj ? (?x)Px b. (?x)Px ? Pj
49
7.4E3
a. Pj ? (?x)Px b. (?x)Px ? Pj c. (?y)Py ? (Pj
Pr)
50
7.4E3
a. Pj ? (?x)Px b. (?x)Px ? Pj c. (?y)Py ? (Pj
Pr) d. (?z)Pz Pr
51
7.4E3
a. Pj ? (?x)Px b. (?x)Px ? Pj c. (?y)Py ? (Pj
Pr) d. (?z)Pz Pr e. Pr ? (?x)Px
52
7.4E3
a. Pj ? (?x)Px b. (?x)Px ? Pj c. (?y)Py ? (Pj
Pr) d. (?z)Pz Pr e. Pr ? (?x)Px f. (?y)Py
(?z)Pz
53
7.4E3
a. Pj ? (?x)Px b. (?x)Px ? Pj c. (?y)Py ? (Pj
Pr) d. (?z)Pz Pr e. Pr ? (?x)Px f. (?y)Py
(?z)Pz g. (Pj ? Pr) (Pr ? (?x)Px)
54
7.4E3
a. Pj ? (?x)Px b. (?x)Px ? Pj c. (?y)Py ? (Pj
Pr) d. (?z)Pz Pr e. Pr ? (?x)Px f. (?y)Py
(?z)Pz g. (Pj ? Pr) (Pr ? (?x)Px) h. ( Pj
? (?x)Px) (Pj ? (?x)Px)
55
7.4E3
a. Pj ? (?x)Px b. (?x)Px ? Pj c. (?y)Py ? (Pj
Pr) d. (?z)Pz Pr e. Pr ? (?x)Px f. (?y)Py
(?z)Pz g. (Pj ? Pr) (Pr ? (?x)Px) h. ( Pj
? (?x)Px) (Pj ? (?x)Px) i. (?y)Sy (?y)Py
56
7.4E3
a. Pj ? (?x)Px b. (?x)Px ? Pj c. (?y)Py ? (Pj
Pr) d. (?z)Pz Pr e. Pr ? (?x)Px f. (?y)Py
(?z)Pz g. (Pj ? Pr) (Pr ? (?x)Px) h. ( Pj
? (?x)Px) (Pj ? (?x)Px) i. (?y)Sy
(?y)Py j. (?x)Sx ? (?x)Px
57
7.4E3
a. Pj ? (?x)Px b. (?x)Px ? Pj c. (?y)Py ? (Pj
Pr) d. (?z)Pz Pr e. Pr ? (?x)Px f. (?y)Py
(?z)Pz g. (Pj ? Pr) (Pr ? (?x)Px) h. ( Pj
? (?x)Px) (Pj ? (?x)Px) i. (?y)Sy
(?y)Py j. (?x)Sx ? (?x)Px k. (?x)Sx ? (?y)Py