Transcript Slide 1

For Friday, read chapter 2, sections 1-2 (pp.
12-19). As nongraded homework, do the
problems on p. 19.
Graded homework #1 is due at the beginning
of class on Friday.
What is Logic? Logic is the study of methods
for evaluating arguments.
An argument is a set of statements, one of
which is the conclusion and the rest of which
(the premises) are meant to provide rational
support for the conclusion.
What is a statement? It’s the sort of
sentence that could be true or false.
How do we evaluate arguments?
All humans are reptiles.
All reptiles live in trees.
Therefore, all humans live in trees.
What’s good about this argument? What’s
bad?
We separate questions of form from
questions about the truth and falsity of
premises (or conclusions).
About form: Does the conclusion follow from
the premises?
About the status of the premises: Are the
data accurate? Are the assumptions correct?
Are the premises true?
All humans are reptiles.
All reptiles live in trees.
Therefore, all humans live in trees.
The form of this reasoning is:
All As are Bs.
All Bs are Cs (where C = things that live in
trees)
Therefore, all As are Cs.
In logic we address questions about form
only (see Forbes’s comments about topic
neutrality and independence of actual truth or
falsity).
So, my description of Logic should really say,
“Logic is the study of methods of evaluating
reasoning, i.e., the step(s) taken from the
premises to the conclusion of an argument.”
We will be studying deductive logic, which
applies to arguments the premises of which
are supposed to guarantee the truth of their
conclusions.
In everyday life, much of our reasoning is
inductive. It involves probabilities: we ask
what is likely to be true based on some
premises (evidence, data).
Validity is the central concept in the study of
deductive logic
An argument is valid if and only if it is necessary
that if the premises are all true, then the conclusion
is true.
Put differently, an argument is valid if and only if it is
impossible for all of the premises to be true and the
conclusion false at the same time (that is, in a
single situation).
Any argument that is not valid is invalid.
Soundness
If possible, we would like our arguments to
be valid and to have all true premises. An
argument with both characteristics (valid, with
all true premises) is sound.
Any argument that is not sound is unsound.
An unsound argument is either invalid or has
at least one false premise (or both).
All whales are fish.
No fish live in trees.
Therefore, no whales live in trees.
Valid? Sound?
Answer: Valid, but unsound; one false
premise is enough to make the argument
unsound.
Some fruits are green.
Some fruits are apples.
Therefore, some fruits are green apples.
Answer: Invalid, and unsound—even though
all three statements in the argument are true.
A note about ‘some’: For our purposes,
‘some’ means ‘at least one’.
These arguments involve category relations:
all humans are said to be in the category of
reptiles.
But for the next few weeks, we’ll be studying
sentential logic; we will treat entire simple
sentences as single units:
If I win the lottery, then I’ll be rich.
I just won the lottery.
Therefore, I’m rich
Sentential Logic
The system contains three kinds of symbol, each
playing a different role:
1. The five sentential connectives: ~ (tilde), &
(ampersand), v (vee), → (arrow), and ↔ (doublearrow).
These connect together (or preface) symbols of the
second type
2. Capital letters A-Z abbreviate simple (or atomic)
statement. These are grammatically simple
sentences that have no words corresponding to
sentential connectives in them.
‘~’ abbreviates ‘not’ and equivalent
phrases, such as ‘it is not the case that’
Joanne is not tall. (J: Joanne is tall)
~J
It is not the case that Tom is a lawyer. (T:
Tom is a lawyer)
~T
‘&’ abbreviates ‘and’ and equivalent terms
José is a doctor and Martin is a lawyer. (J:
José is a doctor; M: Martin is a lawyer)
J&M
Theresa is poor, even though she is a doctor.
(P: Theresa is poor; D: Theresa is a doctor)
P&D