An introduction to the basic concepts of logic.

1. Logic
basic concepts and methods
George W. Matthews
Pennsylvania College of Technology
Fall 2015

2. What is an argument?
Any series of statements in which one (the
conclusion) is meant to follow from or be
supported by, the others (the premises).
An attempt to show that one statement is true on
the basis of other statements.
A presentation of the evidence for a claim.
Not a verbal fight that has two (or more) sides.

3. Statements
Sentences that say something about something.
Statements are either true or false.
examples
“The cat ate my homework.”
“Xena is the tenth planet.”
“It is never acceptable to kill
another human being.”
Statements are distinguished from other kinds of
sentences like questions, commands, exclamations
which are neither true nor false.

4. Premise Indicators
Premises are given information that we are asked
to accept as a basis for argument.
Premise indicators tell us which claims the
argument starts from.
examples
Since . . .
Because of . . .
Assume for the sake of
argument that . . .
We all know that . . .

5. Conclusion Indicators
Conclusions are the points being established by the
argument.
Conclusion indicators tell us where the argument is
going.
examples
Therefore . . .
Thus . . .
So we can see that . . .
It follows that . . .

6. Identify Premises and Conclusion
We know for a fact that my client was not at
the scene of the crime. Furthermore, the chief
prosecution witness is a known perjurer. Thus
my client is not guilty.

7. Identify Premises and Conclusion
We know for a fact that my client was not at
the scene of the crime. Furthermore, the chief
prosecution witness is a known perjurer. Thus
my client is not guilty.
in standard form
My client was not at the scene of the crime.
The chief prosecution witness is a known
perjurer.
My client is not guilty.

8. Identify Premises and Conclusion
Christopher Columbus was a criminal. This is
because whoever steals land or gold, enslaves
people or kills innocent people is a criminal and
he did all of the these things.

9. Identify Premises and Conclusion
Christopher Columbus was a criminal. This is
because whoever steals land or gold, enslaves
people or kills innocent people is a criminal and
he did all of the these things.
in standard form
Whoever steals land or gold, enslaves people or
kills innocent people is a criminal.
Christopher Columbus did all of the these
things.
Christopher Columbus was a criminal.

10. What makes a good argument?
The best, most persuasive arguments are both
valid and sound.
definition: In a valid argument, if the
premises are true, the conclusion must be true.
definition: A sound argument is a valid
argument with premises that are really true.

11. Valid or invalid?
All human beings are mortal.
Socrates is a human being.
Whoever is going to die worries about dying
occasionally.
Socrates worries about dying occasionally.
This argument is in standard form.
If the premises are true must the conclusion also
be true?

12. Valid or invalid?
All human beings are mortal.
Socrates is a human being.
Whoever is going to die worries about dying
occasionally.
Socrates worries about dying occasionally.
This argument is in standard form.
If the premises are true must the conclusion also
be true?
YES, this argument is VALID.

13. Valid or invalid?
All human beings are animals.
Plato is an animal.
Plato is a human being.
If the premises are true must the conclusion also
be true?

14. Valid or invalid?
All human beings are animals.
Plato is an animal.
Plato is a human being.
If the premises are true must the conclusion also
be true?
NO, this argument is INVALID.

15. Valid or invalid?
If abortion is wrong it should be illegal.
Abortion is wrong.
Abortion should be illegal.
Can the premises both be true and the conclusion
be false?

16. Valid or invalid?
If abortion is wrong it should be illegal.
Abortion is wrong.
Abortion should be illegal.
Can the premises both be true and the conclusion
be false?
No. The only way for the conclusion to be false is
if at least one of the premises were false, so this
argument is VALID.

17. Valid or invalid?
If abortion is wrong it should be illegal.
Abortion is wrong.
Abortion should be illegal.
Can the premises both be true and the conclusion
be false?
No. The only way for the conclusion to be false is
if at least one of the premises were false, so this
argument is VALID.
But is it sound?

18. Sound or unsound?
Poor people do not have much money.
It costs a lot of money to buy first class airline
tickets.
So poor people do not fly first class except in
unusual circumstances.
This argument is VALID.

19. Sound or unsound?
Poor people do not have much money.
It costs a lot of money to buy first class airline
tickets.
So poor people do not fly first class except in
unusual circumstances.
This argument is VALID.
To check if it is sound we need to know if the
premises are really true.
The first premise is true by definition and the
second is true in fact.

20. Sound or unsound?
Poor people do not have much money.
It costs a lot of money to buy first class airline
tickets.
So poor people do not fly first class except in
unusual circumstances.
This argument is VALID.
To check if it is sound we need to know if the
premises are really true.
The first premise is true by definition and the
second is true in fact.
Thus this argument is SOUND, the conclusion is
really true.

21. Sound or unsound?
Poor people do not have much money.
If you do not have something, you must not
want it.
So poor people are poor of their own free will,
because they want to be poor.
Are both premises of this argument true?
The first premise is true by definition.
The second premise is false – so this argument is
UNSOUND, even though it is VALID.

22. Sound or unsound?
If abortion is wrong it should be illegal.
Abortion is wrong.
Abortion should be illegal.
This is a valid argument, but are the premises
really true?
The second premise needs more argument to back
it up since it is not obviously true.
The first premise is false.
This argument is UNSOUND.

23. Summary: analyzing arguments

24. Summary: analyzing arguments
identify
argument

25. Summary: analyzing arguments
identify
argument
invalid
DISCARD – conclusion does not follow

26. Summary: analyzing arguments
identify
argument
invalid
DISCARD – conclusion does not follow
valid

27. Summary: analyzing arguments
identify
argument
invalid
DISCARD – conclusion does not follow
valid
unsound
DISCARD – premises false

28. Summary: analyzing arguments
identify
argument
invalid
DISCARD – conclusion does not follow
valid
unsound
DISCARD – premises false
sound
ACCEPT – conclusion is true