logic 101

1. Validity
and Soundness

2. Inductive and Deductive
Arguments
• Inductive arguments are arguments which do
not attempt to establish a thesis conclusively.
• Rather, they cite evidence which makes the
conclusion somewhat reasonable to believe.
Ex.It won't snow on June 1st this year, because
it hasn't snowed on June 1st for any of the
last 100 years.

3. • Validity is a property of the
argument's form. It doesn't matter what the
premises and the conclusion actually say. It
just matters whether the argument has the right
form. So, in particular, a valid argument need
not have true premises, nor need it have a true
conclusion.
Validity

4. The following is a valid argument:
Identify the pattern.
All cats are reptiles.
Bugs Bunny is a cat.
So Bugs Bunny is a reptile.
Validity

5. Validity
A valid form of argument can never lead you
from true premises to a false conclusion.
Ex.
If Socrates was a philosopher, then he wasn't a historian.
Socrates wasn't a historian.
So Socrates was a philosopher.

6. Question:The conclusion of the argument is true.
But is it a valid form of argument?
Answer:
It is not. How can you tell? Because the
following argument is of the same form, and it
has true premises but a false conclusion.
Validity

7. If Socrates was a horse,
then Socrates was warm-blooded.
Socrates was warm-blooded .
So Socrates was a horse.
IDENTIFY THE PATTERN.
Validity

8. If there is a hedgehog in my gas tank, then
my car will not start.
My car will not start.
Hence, there must be a hedgehog in my gas
tank.
Identify the pattern.
Validity

9. If I publicly insult my mother-in-law, then my
wife will be angry at me.
I will not insult my mother-in-law.
Hence, my wife will never be angry at me.
Identify the pattern.
Validity

10. Either Athens is in Greece or it is in Turkey.
Athens is in Greece.
Therefore, Athens is in Turkey.
Identify the pattern.
Validity

11. If I move my knight, Christian will take my
knight.
If I move my queen, Christian will take my
knight.
Therefore, if I move my knight, then I move
my queen.
Identify the pattern.
Validity

12. • Invalid arguments give us no reason to believe
their conclusions. But be careful: The fact
that an argument is invalid doesn't mean that
the argument's conclusion is false. The
conclusion might be true. It's just that the
invalid argument doesn't give us any good
reason to believe that the conclusion is true.
Validity

13. VALID or INVALID.
Your high idle is caused either by a problem
with the transmission, or by too little oil, or
both.
You have too little oil in your car.
Therefore, your transmission is fine.
Validity

14. VALID or INVALID.
If the moon is made of green cheese, then
cows jump over it.
The moon is made of green cheese.
Therefore, cows jump over the moon.
Validity

15. VALID or INVALID.
Either Colonel Mustard or Miss Scarlet is the
culprit.
Miss Scarlet is not the culprit.
Hence, Colonel Mustard is the culprit.
Validity

16. VALID or INVALID.
All engineers enjoy ballet.
Therefore, some males enjoy ballet.
Validity

17. • Sometimes an author will not explicitly state
all the premises of his argument. This will
render his argument invalid as it is written. In
such cases we can often "fix up" the argument
by supplying the missing premise, assuming
that the author meant it all along.
Validity

18. Ex.
All engineers enjoy ballet.
Therefore, some males enjoy
ballet.
Validity

19. We just need to supply the hidden premise:
All engineers enjoy ballet.
Some engineers are male.
Therefore, some males enjoy ballet.
Validity

20. Try to supply the missing premises in the following
arguments:
If you keep driving your car with a faulty
carburetor, it will eventually explode.
Therefore, if you keep driving your car with a
faulty carburetor, you will eventually get hurt.
Validity

21. Try to supply the missing premises in the following
arguments:
Abortion is morally wrong.
Abortion is not a constitutional right.
Therefore, abortion ought to be against the
law.
Validity

22. Soundness
• An argument is sound just in case it's
valid and all its premises are true.
• A property of both arguments and the
statements in them, i.e., the argument
is valid and all the statement are
true.

23. Valid argument can never take you from true
premises to a false conclusion. So, if you have a
sound argument for a given conclusion, then,
since the argument has true premises, and since
the argument is valid, and valid arguments can
never take you from true premises to a false
conclusion, the argument's conclusion must be
true. Sound arguments always have true
conclusions.
Soundness

24. If the moon is made of green cheese, then
cows jump over it.
The moon is made of green cheese.
Therefore, cows jump over the moon.
Valid argument which is not sound
Soundness

25. • If Socrates is a man, then Socrates is
mortal. Socrates is a man. So, Socrates is
mortal.
• If Socrates is a horse, then Socrates is
mortal. Socrates is a horse. So, Socrates
is mortal.
Soundness

26. • If Socrates is a horse, then Socrates has
four legs. Socrates is a horse. So,
Socrates has four legs.
• If Socrates is a horse, then Socrates has
four legs. Socrates doesn't have four legs.
So, Socrates is not a horse.
Soundness

27. • If Socrates is a man, then he's a mammal.
Socrates is not a mammal. So Socrates is
not a man.
• If Socrates is a horse, then he's warm-
blooded. Socrates is warm-blooded. So
Socrates is a horse.
• If Socrates was a philosopher then he
wasn't a historian. Socrates wasn't a
historian. So, Socrates was a philosopher.
Soundness

28. Argument Analysis
• An argument is valid if its premises necessarily lead
to its conclusion. That is, if you accept that the
premises are all true, you must accept that the
conclusion is true.
• An argument is sound if it is valid and you accept that
all its premises are true.
• A good, convincing argument is a sound argument.
That is, since you accept all the premises are true, you
must accept the conclusion is true (because the
argument is valid).
• A bad argument is any other kind of argument.

29. Argument Analysis
“Every animal needs to breathe in
order to live.
Fish are animals.
Fish cannot breathe in the air.
Therefore, fish cannot live in the
air.”

30. Here, the claim is that “fish cannot live in the
air.” The premises are “Every animal needs to
breathe in order to live,” “Fish are animals,” and
“Fish cannot breathe in the air.” The argument
is valid – the premises necessarily lead to the
conclusion. The argument is also sound – the
premises are true. It is a good argument.
Argument Analysis

31. “Oranges are green.
All green things make me sick.
Therefore, oranges make me sick.”
Argument Analysis

32. The claim is “oranges make me sick.” The
premises are “Oranges are green,” and “All
green things make me sick.” The argument is
valid – if we accept the premises, we are forced
to accept the conclusion. However, the
argument is not sound – oranges are not, in fact,
green, so one of the premises is false. This is a
bad argument.
Argument Analysis

33. “Broccoli is green.
Some green things make me sick.
Therefore, broccoli makes me sick.”
Argument Analysis

34. The claim is “broccoli makes me sick.” The premises
are “Broccoli is green,” and “Some green things make
me sick.” Here, all the premises are true. However,
the argument is not valid – even if we accept the
premises, we are not forced to accept the conclusion.
Just because some green things are sickening does not
mean that broccoli is. This is a bad or unsound
argument. (Notice, it doesn’t make any difference
whether or not broccoli makes me sick – whether or not
the conclusion is true. Even if the conclusion is true,
the premises have not given us reason to believe that it
is true.)
Argument Analysis

35. “Whales know how to play hockey.
Therefore, Canadians like winter.”
Argument Analysis

36. The claim is “Canadians like winter.” The
premise is “Whales know how to play hockey.”
The argument is neither valid nor sound. It’s a
bad argument. (Again, it doesn’t make any
difference whether the conclusion is true.)
Argument Analysis

37. Usually arguments come in complicated prose.
It is therefore difficult to figure out what the
argument is, let alone whether it is good. Our
first step is to reconstruct the argument. That is,
we must convert the argument into a series of
statements, identifying the premises and the
conclusion and laying them out so that the
premises lead to the conclusion.
•
Reconstructing the
Argument

38. Take Socrates’s argument in the Apology:
“For Death is to be as it were nothing, and to be deprived
of all sensation... And if no sensation remains, then death is like
a dreamless sleep. In this case, death will be a blessing. For, if
any one compares such a night as this, in which he so profoundly
sleeps as not even to see a dream, with the other nights and days
of his life, and should declare how many he had passed better and
more pleasantly than this night, I think that not only a private
man, but even the great king himself, would find so small a
number that they might be easily counted.”
Reconstructing the
Argument

39. • The first step is to identify the conclusion. Go
through the passage and try to find the point.
What is Socrates trying to establish?
It’s buried in there: “Death will be a blessing.”
Reconstructing the
Argument

40. To proceed, we first have to get rid of anything unnecessary –
mere rhetorical flourishes, repetitions, and irrelevancies. Go
through the passage and get rid of anything that doesn’t support
the conclusion in some way:
•“For Death is to be deprived of all sensation... if no sensation
remains, then death is like a dreamless sleep. ...death will be a
blessing. ...if any one compares such a night [of sleep without
dreams]... with the other nights and days of his life, and should
declare how many he had passed better and more pleasantly than
this night, I think.. [he] would find so small a number...”
Reconstructing the
Argument

41. Once we’ve dispensed with what we don’t need, we can
reformulate the argument as a series of statements:
•Death is to be deprived of all sensation.
•If no sensation remains, death is like a dreamless sleep.
•Anyone will consider a dreamless sleep better than
most days and nights.
•---
•Death is a blessing.
Reconstructing the
Argument

42. • Now we’re ready to add anything that seems to be missing.
Are there any premises that seem to be assumed, but aren’t
stated?
1. Death is to be deprived of all sensation.
2. If no sensation remains, death is like a dreamless sleep.
3. Death is like a dreamless sleep.
4. Anyone will consider a dreamless sleep better than most days
and nights.
5. Anyone will consider death better than most days and nights.
6. Anything that is better than most days and nights is a blessing.
7.---
8.Death is a blessing.
Reconstructing the
Argument

43. • Now, we need to say something about the inference in the argument. We
need to say how the argument is put together. We should identify assumed
premises and sub-arguments – conclusions that are premises for the main
conclusion. This will also help us to identify if anything else is missing.
1. Death is to be deprived of all sensation. (Assumption)
2. If no sensation remains, death is like a dreamless sleep. (Assumption)
3. Death is like a dreamless sleep. (Conclusion from 1 and 2)
4. Anyone will consider a dreamless sleep better than most days and nights.
(Assumption)
5. Anyone will consider death better than most days and nights. (Conclusion
from 3 and 4)
6. Anything that is better than most days and nights is a blessing.
(Assumption)---
7. Death is a blessing. (From 3, 5, and 6)
Reconstructing the
Argument

44. Once we’ve reconstructed an argument –
shown what we think it is and how it is
supposed to work – we can begin to say
whether an argument is good or bad. We
need to evaluate the argument’s validity
and soundness.
Reconstructing the
Argument

45. • Socrates’s argument that death is a blessing in the Apology is interesting, but suffers
from some weaknesses. As it stands it is not convincing. In the first place, Socrates
cannot establish what death really is, but only what people think about it. He never
discusses what death is, only what people think about it. Therefore, he cannot reach
his intended conclusion. Moreover, the whole argument hinges on whether it is correct
to say that lack of sensation is like a dreamless sleep. Sleeping seems to imply the
possibility of waking, so it is quite different in this respect from a complete lack of
sensation. Is it fair to say that a corpse, or even a stone, is doing something “like
sleeping” just because they cannot sense anything? If we do not accept this assumed
analogy, Socrates’s argument does not follow. That said, Socrates does raise the
interesting point that death might be compared to the rest of the days of one’s life. In
this case, it might be that death is better than some days, but worse than the very best
days. If so, then death is perhaps not something to seek, but not something to fear,
either. Even if death is not a blessing, perhaps it is not a curse, either. Socrates’s
argument does lead us to reconsider our common view of death as something
invariably bad and the worst of all possibilities.
Critiquing an Argument