Do diagrams; in the diagrams, put conditionals in standard form; identify
which argument form (or
else write “none”); state valid or invalid (even if none of the 7 forms
is present).
Note. If-words are NOT inference indicators!!!
1. [ 1 ] whenever [ 2 ]. And [ 2 ]. Hence [ 1 ].
if 2 then 1 + 2
ß
AA - valid
1
2. [ 3 ], and [ not 3 ] if [ 4 ]. Therefore, [ not 4 ].
3
+ if 4 then not 3
ß
DC - valid
not 4
3. [ not 2 ] every time [ not 3 ]. Thus [ 2 ], because [ 3 ].
if
not 3 then not 2 + 3
ß
DA - invalid
2
4. We know that [ not 2 ]; because [ not 1 ] if [ not 2 ], and [ not 1 ].
if not 2 then not 1 + not 1
ß
AC - invalid
not 2
5. [ 1 ] if [ not 2 ], and [ not 2 ] if [ 3 ]. Therefore [ 1 ] if [ 3 ].
if 3 then not 2 + if not 2 then 1
ß
CC - valid
if 3 then 1
6. [ 1 The President will be embarrassed again] if [ 2 he can't get his tax cut through the Congress]. Since [ 2 it's clear that Congress will defeat the tax cut], [ 1 the President is going to be embarrassed once more].
Skeleton: [1] if [2]. Since [2], [1].
if 2 then 1 + 2
ß
AA - valid
1
7. [ 1 There is no life on Mars], for [
2 the Viking spacecraft experiments would have found carbon
compounds in the Mars soil samples] if [ not 1 there was life
there]. And [ not 2 no such compounds were found by the
experiments].
Skeleton: [1], for [2] if [not 1]. And [not 2].
if not 1 then 2 + not 2
ß
DC - valid
1
8. On the Isle of Salimur, [ 1 it's clear in the morning] whenever [ 2 it has rained the evening before. So [ 2 it must have rained in Salimur yesterday evening], because [ 1 there's not a cloud in the sky there this morning.
Skeleton: On the Isle of Salimur, [1] whenever [2]. So [2], because [1].
if 2 then 1 + 1
ß
AC - invalid
2
9. [ 1 God would have made rich people more generous] if [ 2 He hadn't wanted there to be poor people]. So [ not 2 He must have wanted there to be poor people], because [ not 1 He certainly didn't make rich people more generous]!
Skeleton: [1] if [2]. So [not 2], because [not 1]!
if 2 then 1 + not 1
ß
DC - valid
not 2
10. If [ 1 there ever was a time at which nothing at all existed], then [ 2 there would be nothing existing now]. But clearly [ not 2 there are things now existing]. This proves that [ not 1 there has always been something or other in existence].
Skeleton: If 1, then 2. But clearly [not 2]. This proves that not 1].
if 1 then 2 + not 2
ß
DC - valid
not 1
For the rest, only partial answers are given: conclusions are in color, and the argument form, if any, is noted.
11. Joe's argument is valid,
because it's conclusion is true. And when an argument is valid its conclusion
is true. AC
12. I can't concentrate on homework when the radio's playing,
but I'm concentrating now. That
shows that the radio isn’t playing now.
DC
13. We've now lost all chances of making
the playoffs because we lost last week's game. The
situation was that we win that game or else we lose any playoff chances.
DD
14. The Republicans have a better chance
of winning when the weather's bad, because the voter
turnout will be low if election day weather is bad. And if the turnout
is low the Republicans'
chances are better. CC
15. The President can twist enough arms to get his import quotas
bill passed if he really wants it
to pass. Well, obviously, he doesn't care much
about it, because he's not pressuring any
Congressmen to vote for it. DC
16. When maintenance doesn't spray on schedule in the dorms, the
bugs take over entire floors at
a time. But they sprayed last week as they as they were supposed to,
so the takeover is under
control for now. DA
17. Moe or Lefty is guilty. Moe, it turns out, is definitely guilty.
So Lefty isn't. AD
18. I'll sleep late if I stay up late, and if I sleep late I'll
be late for class. So I'll be late for class
if I
stay up late. CC
19. She's going to flunk the test.
That’s because although if she studies hard she will pass it, she .
really hasn't studied at all! DA