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Introduction to Logic
Class 1: What is Logic?
What is Logic?
Definition of Logic:
“Logic is the study of virtue in argument, where an
argument is considered virtuous if it helps us get to
the truth”
A Contrast:
Rhetoric: The study of effective persuasion
Logic: The study of legitimate persuasion
An argument in logic is
not just two people
contradicting and
insulting each other.
For more of what an argument is not: http://www.youtube.com/watch?v=kQFKtI6gn9Y
Definitions
Statement: A unit of language that can be
true or false.
Argument: A connected series of statements
designed to convince an audience of
another sentence.
Conclusion: the statements that an
argument tries to convince an audience
of.
Premises: the statement that an argument
uses to support the conclusion.
For the purposes of this course, these
words will be used interchangeably:
•
•
•
•
Sentence
Statement
Assertion
Proposition
They don’t really meant the same thing, but
we won’t worry about the difference.
Example
1. OJ Simpson
intentionally killed
Nicole Brown.
Premise
2. It is wrong to
intentionally kill
people.
Premise
3. Therefore what OJ did
was wrong.
Conclusion
Canonical Argument Form
1.Premise 1
2.Premise 2
3.Premise 3
4.Conclusion
The Study of Argument
Formal Logic
Informal Logic
The study of arguments
in artificial conditions,
including especially
invented languages. It is
like a laboratory science.
At LCCC this is studied
in Introduction to Logic.
The study of arguments
in the real world. It is
like a field science. At
LCCC, this is covered
in Critical Thinking.
An ob/ob mouse and a normal mouse
Via wikipedia, http://en.wikipedia.org/wiki/File:Fatmouse.jpg#file/ . Licensed under
Creative Commons.
A normal argument and a formal argument.
“Mortality rates for women
undergoing early abortions, where the
procedure is legal, appear to be as
low as or lower than the rates for
normal childbirth. Consequently, any
interest of the State in protecting the
woman from an inherently hazardous
procedure, except when it would be
equally dangerous for her to forgo it,
has largely disappeared.”
Harry Blackmun, Roe v. Wade
Formal Language
• Formal logic replaces the ordinary language of
argument with a symbolic language.
• This language is meant to be free of all
ambiguity and vagueness.
• The language is meant to wear its logical
structure on its face.
• Our formal languages: SL and QL.
How to tell an argument
1. Look to see if some statements support
others.
2. Look for premises and conclusions
Premise indicator words: because, as, for, since, given
that, for the reason that.
Conclusion indicator words: Therefore, thus, hence, so
consequently, it follows that, in conclusion, as a result,
then, must, accordingly, this implies that, this entails
that, we may infer that,
Example 1
Is this an argument?
Cal Ripken has provided years of valuable
service to the Orioles. He has appeared in 19
All-Star games. He was a World Series
champion in 1983. His number has been
retired by the Orioles. Therefore, he deserves
a spot in the Hall of Fame
Example taken from Cathal Woods, Introduction to Reasoning.
Example 1
Is this an argument?
Cal Ripken has provided years of valuable
service to the Orioles. He has appeared in 19
All-Star games. He was a World Series
champion in 1983. His number has been
retired by the Orioles. Therefore, he
deserves a spot in the Hall of Fame
Example taken from Cathal Woods, Introduction to Reasoning.
Example 1
1. Cal Ripken has provided years of valuable
service to the Orioles.
2. He has appeared in 19 All-Star games.
3. He was a World Series champion in 1983.
4. His number has been retired by the Orioles.
5. He deserves a spot in the Hall of Fame
Example taken from Cathal Woods, Introduction to Reasoning.
Example 2
Is this an argument?
“We can suspect that the inventor [of eyeglasses]
was not an academic, for professors delight in
boasting of their inventions, and before the
thirteenth century we have no record by any
such self-styled inventor.” —D.J. Boostin, The
Discoverers
Example from Salmon, Marilee (1995) Introduction to Logic and Critical
Thinking 3rd edition Fort Worth, TX: Harcourt Brace
Example 2
Is this an argument?
“We can suspect that the inventor [of eyeglasses]
was not an academic, for professors delight in
boasting of their inventions, and before the
thirteenth century we have no record by any
such self-styled inventor.” —D.J. Boostin, The
Discoverers
Example 2
1. Professors delight in boasting of their
inventions,
2. Before the thirteenth century we have no
record by any such self-styled inventor.”
3. The inventor [of eyeglasses] was not an
academic.
Example 3
Is this an argument?
“President Clinton today made a parting appeal to
Indians for eased tensions in their region and stronger
ties with America as he looked toward a brief and
diplomatically dicey stop in Pakistan. ‘Friends don't
have to agree on every issue,’ he told business leaders
in a domed room of the Bombay stock market. ‘They
just have to have an honest relationship about it.’”
New York Times March 24, 2000.
Example 3
Not an argument, just reporting
events.
Example 4
Is this an argument?
“In England under the blasphemy laws it is illegal to
express disbelief in the Christian religion. It is also
illegal to teach what Christ taught on the subject of
non-resistance. Therefore, whoever wishes to avoid
being a criminal must profess to agree with Christ’s
teaching but must avoid saying what that teaching
was.”
—Bertrand Russell, Skeptical Essays (1928)
Example 4
Is this an argument?
“In England under the blasphemy laws it is illegal to
express disbelief in the Christian religion. It is also
illegal to teach what Christ taught on the subject of
non-resistance. Therefore, whoever wishes to
avoid being a criminal must profess to agree with
Christ’s teaching but must avoid saying what that
teaching was.”
—Bertrand Russell, Skeptical Essays (1928)
Example 4
1. In England under the blasphemy laws it is
illegal to express disbelief in the Christian
religion
2. It is also illegal to teach what Christ taught
on the subject of non-resistance.
3. Whoever wishes to avoid being a criminal
must profess to agree with Christ’s
teaching but must avoid saying what that
teaching was.
Another Definition
Inference: The connection between statements in
an argument. Argument glue.
• Premise
• Premise
• Conclusion
This motion is
inference
Valid
An argument is valid if it is impossible for
the premises to be true and the conclusion
false.
Sound
An argument is sound if it valid and has
true premises.
A Valid Argument
All people are mortal
Socrates is a person.
Socrates is mortal
Another Valid Argument
All people are carrots
Socrates is a person.
Socrates is carrot
An invalid argument
All people are mortal
Socrates is a mortal
All people are Socrates
A Valid Argument
If George Washington were beheaded, he would
be dead.
George Washington was beheaded.
Therefore George Washington is dead.
An Invalid Argument
If George Washington were beheaded, he would
be dead.
George Washington is dead.
Therefore George Washington was beheaded.
Strong
An argument is strong if the premises would
make the conclusion more likely if they were
true.
Cogent
An argument is cogent if it is strong and the
premises are true.
Deductive
An argument is deductive if it aims at validity
Inductive
An argument is inductive if it aims at strength