Elementary Logic
PHIL 105-302
Intersession 2013
MTWHF 10:00 – 12:00
ASA0118C
Steven A. Miller
Day 2
Implication
“There’s beer in the fridge.”
When said to a visiting friend?
When said to a customer?
When speaking to an alcoholic partner?
Implication
Jon: We’re going out for drinks tonight.
Frank: If we’re doing that, let’s go to
Sidetracks or The Cellar.
Jon: I’m banned from Sidetracks!
What’s the conclusion?
What’s implied?
Implication
The principle of charity: “in formulating
implicit statements, give the arguer the
benefit of the doubt; try to make the
argument as strong as possible while
remaining faithful to the arguer’s
thought” (S, 12).
In general, try to be a friendly and
helpful reader.
Implication
“If you were a real American, you
wouldn’t oppose (the military / paying
taxes / gun control / other issue of the
day).”
Is it an argument?
What’s the implied conclusion?
Implication
The Cubs are the best C-named MLB
team. We know this because the
Cardinals are the worst MLB team,
and the worst cannot be the best.
Implication
1) The Cubs are the best C-named MLB
team.
2) The Cardinals are the worst MLB team.
3) The worst cannot be the best.
What’s the argument’s conclusion?
Implication
1) The Cubs are the best C-named
MLB team.
2) The Cardinals are the worst MLB team.
3) The worst cannot be the best.
What’s missing / implied to complete it?
Implication
1) The Cubs are the best C-named MLB
team.
2) The Cardinals are the worst MLB team.
3) The worst cannot be the best.
4) There are only two C-named MLB
teams: the Cubs and the Cardinals.
Implication
In standard form:
1) There are only two C-named MLB
teams: the Cubs and the Cardinals.
2) The Cardinals are the worst MLB team.
3) The worst cannot be the best.
4) [Therefore,] The Cubs are the best Cnamed MLB team.
Use / mention
Michelle Obama is the First Lady.
Michelle Obama has two daughters.
Michelle Obama has thirteen letters.
Use / mention
Michelle Obama has thirteen letters.
“Michelle Obama” has thirteen letters.
Use / mention
The first letter of Jingle Bells is “D.”
The first letter of “Jingle Bells” is “D.”
The first letter of the words to “Jingle
Bells” is “D.”
Formal / informal
These cookies cost twenty-five cents each.
I have a dollar. I can buy four of them.
1.00 / x = y
x = .25
1.00 / .25 = y
4=y
Formal / informal
Informal logic:
If it’s dark, then it’s night.
It’s dark.
Therefore, it’s night.
Formal logic:
D⊃N
D
∴N
Formal / informal
D⊃N
D
∴N
If I’m disappointed, then I’m nervous.
I’m disappointed.
And so I’m nervous.
Seventh Inning Stretch
(“Take Me Out to the Ballgame, …”)
Argument evaluation
What makes an argument good?
1) true premises
2) conclusion at least probable, given 1
3) premises are related to the conclusion
4) the conclusion can’t be undermined
Argument evaluation
1) true premises
In many cases, this is obvious:
“Carbondale is south of Chicago.”
“Carbondale is north of Chicago.”
But in others, it’s more problematic:
“There is a treasure chest buried
500 feet below where I stand.”
This truth of this latter kind is indeterminate.
Argument evaluation
1) true premises
For our purposes, we’ll treat the latter
kind of sentence, the indeterminate
ones, as true. Or, more properly, we’ll
see what happens if they were to be
true.
Argument evaluation
2) conclusion at least possible, given 1.
The concern here is that the argument is
valid, which means that there is a
particular kind of relationship between
the premise(s) and conclusion.
Argument evaluation
Two kinds of argument:
deductive and inductive
1) deductive argument –
an argument in which the
conclusion follows necessarily
from the premises
Argument evaluation
deductive validity –
1) The conclusion necessarily
follows from the premises.
2) If the premises are true, the
conclusion must also be true.
3) It is impossible for the premises to
be true and the conclusion to be
false.
Argument evaluation
If it’s dark, then it’s night.
It’s dark.
Therefore, it’s night.
This argument is deductively valid:
If its premises are true, its conclusion
cannot be false.
Argument evaluation
Bill drove to work.
Therefore, Bill must be over the age of 16.
Not necessarily valid: impossibility is not
legal or practical but rather logical.
It is conceivable that Bill could be under 16
and driving to work, and so it is possible.
Argument evaluation
Bill drove to work.
Anyone who drives to work must be over
the age of 16.
Therefore, Bill must be over the age of 16.
Valid.
Argument evaluation
A deductive argument is valid when
it is impossible (in the strongest sense)
for the premises to all be true
and the conclusion to be false.
Argument evaluation
2) inductive argument –
an argument in which the
conclusion is likely to follow from
the premises
Argument evaluation
91% of Polish people are Catholic.
Pitor is a Polish person.
We can conclude that Pitor is Catholic.
This argument is inductive:
If its premises are true, its conclusion
may still be false.
Deductive or Inductive?
1) Historians know of no civilizations
that worshiped lizards.
2) So, humans never worshiped
lizards.
Inductive.
Deductive or Inductive?
1) No cats are purple.
2) Sashabear is a cat.
3) So, Sashabear is not purple.
Deductive.
Deductive or Inductive?
1) The sidewalk is wet.
2) Usually, the sidewalk gets wet
from rain.
3) It must have rained.
Inductive.
Argument evaluation
What makes an argument good?
1) true premises
2) conclusion at least probable, given 1
3) premises are related to the conclusion
4) the conclusion can’t be undermined