Phil 120 week 1 class 1 July 5th 2004

1
Symbolization techniques
some more complex cases
1. I'll go home and watch TV, or I'll think about
the election. 2. I'll go home, and I'll watch TV
or think about the election.
2
Symbolization techniques
some more complex cases
1. I'll go home and watch TV, or I'll think about
the election. 2. I'll go home, and I'll watch TV
or think about the election.
1. Either I'll go home and watch TV, or I'll
think about the election. 2. I'll go home, and
I'll either watch TV or think about the election.
3
Symbolization techniques
some more complex cases
1. I'll go home and watch TV, or I'll think about
the election. 2. I'll go home, and I'll watch TV
or think about the election.
1. Either I'll go home and watch TV, or I'll
think about the election. 2. I'll go home, and
I'll either watch TV or think about the election.
1. (HT) ? E 2. H (T?E)
4
If I believe in God, then if He exists, I gain,
and if He doesn't, then I don't lose. If, on the
other hand, I don't believe in God, then if he
exists, I lose, and if He doesn't, I don't gain.
From this it follows that if I believe, I'll
either gain or not lose, while if I don't
believe, I'll either lose or fail to gain.
5
If I believe in God, then if He exists, I gain,
and if He doesn't, then I don't lose. If, on the
other hand, I don't believe in God, then if he
exists, I lose, and if He doesn't, I don't gain.
From this it follows that if I believe, I'll
either gain or not lose, while if I don't
believe, I'll either lose or fail to gain.B I
believe in GodE God existsG I gainL I
lose(Note 'lose' is not synonymous with 'not
gain'.)
6
If I believe in God, then if He exists, I gain,
and if He doesn't, then I don't lose. If, on the
other hand, I don't believe in God, then if he
exists, I lose, and if He doesn't, I don't gain.
From this it follows that if I believe, I'll
either gain or not lose, while if I don't
believe, I'll either lose or fail to gain.B I
believe in GodE God existsG I gainL I lose
B ? ( (E ? G) (E ? L) )
7
If I believe in God, then if He exists, I gain,
and if He doesn't, then I don't lose. If, on the
other hand, I don't believe in God, then if he
exists, I lose, and if He doesn't, I don't gain.
From this it follows that if I believe, I'll
either gain or not lose, while if I don't
believe, I'll either lose or fail to gain.B I
believe in GodE God existsG I gainL I lose
B ? ( (E ? G) (E ? L) ) B ? ( (E ? L) (E
? G) )
8
If I believe in God, then if He exists, I gain,
and if He doesn't, then I don't lose. If, on the
other hand, I don't believe in God, then if he
exists, I lose, and if He doesn't, I don't gain.
From this it follows that if I believe, I'll
either gain or not lose, while if I don't
believe, I'll either lose or fail to gain.B I
believe in GodE God existsG I gainL I lose
B ? ( (E ? G) (E ? L) ) B ? ( (E ? L) (E
? G) ) ( B ? ( G ? L) ) ( B ? (L ? G) )
9
George will leave unless Mary doesn't leave. But
unless Phil stays, she will leave, and George
won't leave provided that it rains. As a result,
if it rains, Mary won't leave.
10
George will leave unless Mary doesn't leave. But
unless Phil stays, she will leave, and George
won't leave provided that it rains. As a result,
if it rains, Mary won't leave.G George will
leaveM Mary does leaveP Phil staysR It
rains
11
George will leave unless Mary doesn't leave. But
unless Phil stays, she will leave, and George
won't leave provided that it rains. As a result,
if it rains, Mary won't leave.G George will
leaveM Mary does leaveP Phil staysR It
rains
G ? M
12
George will leave unless Mary doesn't leave. But
unless Phil stays, she will leave, and George
won't leave provided that it rains. As a result,
if it rains, Mary won't leave.G George will
leaveM Mary does leaveP Phil staysR It
rains
G ? M (P ? M)
13
George will leave unless Mary doesn't leave. But
unless Phil stays, she will leave, and George
won't leave provided that it rains. As a result,
if it rains, Mary won't leave.G George will
leaveM Mary does leaveP Phil staysR It
rains
G ? M (P ? M) (R ? G)
14
George will leave unless Mary doesn't leave. But
unless Phil stays, she will leave, and George
won't leave provided that it rains. As a result,
if it rains, Mary won't leave.G George will
leaveM Mary does leaveP Phil staysR It
rains
G ? M (P ? M) (R ? G) R ? M
15
George will leave unless Mary doesn't leave. But
unless Phil stays, she will leave, and George
won't leave provided that it rains. As a result,
if it rains, Mary won't leave.G George will
leaveM Mary does leaveP Phil staysR It
rains
G ? M (P ? M) (R ? G) R ? M
Try alsoIf George will leave unless Mary
doesn't leave, and unless Phil stays, she will
leave, and George won't leave provided that it
rains, then, as a result, if it rains, Mary won't
leave. Is this sentence tf-true?
16
If there is an infinite number of points in a
finite line L, then if those points have size, L
will be infinitely long, and if they do not have
size, L won't have length. Line L is neither
infinitely long nor without length. This proves
that there is not an infinite number of points in
L.
17
If there is an infinite number of points in a
finite line L, then if those points have size, L
will be infinitely long, and if they do not have
size, L won't have length. Line L is neither
infinitely long nor without length. This proves
that there is not an infinite number of points in
L.I There is an infinite number of points in
the line LS Points have sizeL Line L is
infinitely longG Line L has length
18
If there is an infinite number of points in a
finite line L, then if those points have size, L
will be infinitely long, and if they do not have
size, L won't have length. Line L is neither
infinitely long nor without length. This proves
that there is not an infinite number of points in
L.I There is an infinite number of points in
the line LS Points have sizeL Line L is
infinitely longG Line L has length
(S ? L) (S ? G)
19
If there is an infinite number of points in a
finite line L, then if those points have size, L
will be infinitely long, and if they do not have
size, L won't have length. Line L is neither
infinitely long nor without length. This proves
that there is not an infinite number of points in
L.I There is an infinite number of points in
the line LS Points have sizeL Line L is
infinitely longG Line L has length
I ? ( (S ? L) (S ? G) )
20
If there is an infinite number of points in a
finite line L, then if those points have size, L
will be infinitely long, and if they do not have
size, L won't have length. Line L is neither
infinitely long nor without length. This proves
that there is not an infinite number of points in
L.I There is an infinite number of points in
the line LS Points have sizeL Line L is
infinitely longG Line L has length
I ? ( (S ? L) (S ? G) ) L G
21
If there is an infinite number of points in a
finite line L, then if those points have size, L
will be infinitely long, and if they do not have
size, L won't have length. Line L is neither
infinitely long nor without length. This proves
that there is not an infinite number of points in
L.I There is an infinite number of points in
the line LS Points have sizeL Line L is
infinitely longG Line L has length
I ? ( (S ? L) (S ? G) ) L G I
22
The line L is infinitely divisible, which means
that between any two points on the line we can
find another point. But the line L can have
another point between any two points only if it
has an infinite number of points. Therefore L has
an infinite number of points.
23
The line L is infinitely divisible, which means
that between any two points on the line we can
find another point. But the line L can have
another point between any two points only if it
has an infinite number of points. Therefore L has
an infinite number of points. D The line L is
infinitely divisibleB Between any two points on
the line we can find another pointI There is an
infinite number of points in the line L
24
The line L is infinitely divisible, which means
that between any two points on the line we can
find another point. But the line L can have
another point between any two points only if it
has an infinite number of points. Therefore L has
an infinite number of points. D The line L is
infinitely divisibleB Between any two points on
the line we can find another pointI There is an
infinite number of points in the line L
D
25
The line L is infinitely divisible, which means
that between any two points on the line we can
find another point. But the line L can have
another point between any two points only if it
has an infinite number of points. Therefore L has
an infinite number of points. D The line L is
infinitely divisibleB Between any two points on
the line we can find another pointI There is an
infinite number of points in the line L
D D ? B
26
The line L is infinitely divisible, which means
that between any two points on the line we can
find another point. But the line L can have
another point between any two points only if it
has an infinite number of points. Therefore L has
an infinite number of points. D The line L is
infinitely divisibleB Between any two points on
the line we can find another pointI There is an
infinite number of points in the line L
D D ? B B ? I
27
The line L is infinitely divisible, which means
that between any two points on the line we can
find another point. But the line L can have
another point between any two points only if it
has an infinite number of points. Therefore L has
an infinite number of points. D The line L is
infinitely divisibleB Between any two points on
the line we can find another pointI There is an
infinite number of points in the line L
D D ? B B ? I I
28
Lung cancer is not caused by smoking, and this is
so for the following reasons. Lung cancer is more
common among male smokers than among female
smokers. If smoking were the cause of lung
cancer, this would not be true. The fact that
lung cancer is more common among male smokers
implies that it is caused by something in the
male makeup. But if it is caused by this, it is
not caused by smoking.
29
Lung cancer is not caused by smoking, and this is
so for the following reasons. Lung cancer is more
common among male smokers than among female
smokers. If smoking were the cause of lung
cancer, this would not be true. The fact that
lung cancer is more common among male smokers
implies that it is caused by something in the
male makeup. But if it is caused by this, it is
not caused by smoking.L Lung cancer is caused
by smokingM Lung cancer is more common among
male smokers than among female smokersC Lung
cancer is caused by something in the male makeup
30
Lung cancer is not caused by smoking, and this is
so for the following reasons. Lung cancer is more
common among male smokers than among female
smokers. If smoking were the cause of lung
cancer, this would not be true. The fact that
lung cancer is more common among male smokers
implies that it is caused by something in the
male makeup. But if it is caused by this, it is
not caused by smoking.L Lung cancer is caused
by smokingM Lung cancer is more common among
male smokers than among female smokersC Lung
cancer is caused by something in the male makeup
M
31
Lung cancer is not caused by smoking, and this is
so for the following reasons. Lung cancer is more
common among male smokers than among female
smokers. If smoking were the cause of lung
cancer, this would not be true. The fact that
lung cancer is more common among male smokers
implies that it is caused by something in the
male makeup. But if it is caused by this, it is
not caused by smoking.L Lung cancer is caused
by smokingM Lung cancer is more common among
male smokers than among female smokersC Lung
cancer is caused by something in the male makeup
M L ? M
32
Lung cancer is not caused by smoking, and this is
so for the following reasons. Lung cancer is more
common among male smokers than among female
smokers. If smoking were the cause of lung
cancer, this would not be true. The fact that
lung cancer is more common among male smokers
implies that it is caused by something in the
male makeup. But if it is caused by this, it is
not caused by smoking.L Lung cancer is caused
by smokingM Lung cancer is more common among
male smokers than among female smokersC Lung
cancer is caused by something in the male makeup
M L ? M M ? C
33
Lung cancer is not caused by smoking, and this is
so for the following reasons. Lung cancer is more
common among male smokers than among female
smokers. If smoking were the cause of lung
cancer, this would not be true. The fact that
lung cancer is more common among male smokers
implies that it is caused by something in the
male makeup. But if it is caused by this, it is
not caused by smoking.L Lung cancer is caused
by smokingM Lung cancer is more common among
male smokers than among female smokersC Lung
cancer is caused by something in the male makeup
M L ? M M ? C C ? L
34
Lung cancer is not caused by smoking, and this is
so for the following reasons. Lung cancer is more
common among male smokers than among female
smokers. If smoking were the cause of lung
cancer, this would not be true. The fact that
lung cancer is more common among male smokers
implies that it is caused by something in the
male makeup. But if it is caused by this, it is
not caused by smoking.L Lung cancer is caused
by smokingM Lung cancer is more common among
male smokers than among female smokersC Lung
cancer is caused by something in the male makeup
M L ? M M ? C C ? L L