Truth Tables - Logic
Philosophical Methods
What do Logicians do?
› For many philosophical
questions, philosophers tend
to create arguments in which
the premises are deeply-held
intuitions.
› Philosophers use logic to
uncover where people's
intuitions differ.
› Philosophers evaluate both
reasoning and content of
arguments.
ENTHYMEMES
Often one or more
premises in an
argument will be
implied because
some arguments
depend on
background
knowledge that the
author assumes
the reader has.
The President of the United States is powerful
_______________________________
Obama is powerful
What is implied here?
Obama is the President of the United States
TRUTH TABLES
Truth Tables are
used to evaluate
the validity of
arguments more
precisely. It is a
table that allows us
to keep track of all
possibilities in a
concise manner.
Here are the basics before we create some
Truth Tables…
Example:
-Let P stand for:
“The atomic number of
hydrogen is 1.”
-Let Q stand for:
“The atomic number of
helium is 2.”
-Then “P and Q” means:
“The atomic number of
hydrogen is 1 and the atomic
number of helium is 2.”
Example (cont.)
P
Q
__________
P and Q
Here’s a very simple Truth Table...
› Sooo…..if given this
argument:
› The Truth Table would look
like this:
P
Q
P and Q
P
T
T
T
Q
T
F
F
F
T
F
F
F
F
__________
P and Q
How do we fill this in, exactly?
› OK…Let’s look at this:
(Have students help fill this in.)
› 1. The truth values in the first
2 columns are put into the
table by running through all of
the possibilities.
› 2. Next, cover all possible
combinations of truth values.
› 3. Column 3 – Here we fill in
the truth value on each row
by thinking about what “P and
Q” means.
› 4. Intuitively, “and” means
that both sentences joined by
“and” are true. So, P and Q
should be true only when
“both” P and Q are true.
› 5. The argument is VALID!
Here’s another example…
› P: Today is a weekday.
› Q: Tomorrow is a weekend.
P
________
Not Q
In English: Today is a
weekday. Therefore,
tomorrow is not a weekday.
Fill-in the Truth Table Below
Let’s see if we were correct!
P
Q
Not Q
T
T
F
T
F
T
F
T
F
F
F
T
Is the argument valid?
The Premise (P) is true in rows one and
two. The Conclusion is false on one of
those rows. So there is at least one case
in which all of the premises are true but
the conclusion is false.
The argument is INVALID!
› Intuitively, “not” tells us that
“not Q” is true whenever Q
is false and vice versa.
› There is a column in the
truth table for Q even
though it’s not a premise
because we need it to work
out all of the possibilities…
so we know the values for
“not Q”.
WHAT YOU CAN
LOOK FORWARD
TO NEXT!
In the next
PowerPoint, we
will learn how to
translate English
into even more
symbols!
Stay tuned.