Deduction: Validity is a matter of
ARGUMENT FORM
Separate out the “content” words from the
“form” words
Separate out the “content” words from the
“form” words
If Washington was assassinated, then he’s dead.
He wasn’t, so he’s not
If Washington was assassinated, then he’s dead.
He wasn’t, so he’s not
If W, then D
Not W
---------So not D
Invalid argument
If Clinton was assassinated, then he’s dead.
He’s not dead, so he wasn’t assassinated.
If Clinton was assassinated, then he’s dead.
He’s not dead, so he wasn’t assassinated.
If C, then D
Not D
---------So not C
Valid argument
No campaign staffers are veterans, so some veterans
are not pompous snobs, since all campaign staffers
are pompous snobs.
No campaign staffers are veterans
All campaign staffers are pompous snobs
-------------------------------------Some veterans are not pompous snobs
No campaign staffers are veterans
All campaign staffers are pompous snobs
-------------------------------------Some veterans are not pompous snobs
No C are V
All C are P
----------Some V are not P
No C are V
All C are P
----------Some V are not P
Supply new content words
preserving the form exactly,
and trying to meet the definition
of “invalid”
An argument is invalid
when it is possible for it to have
a false conclusion despite
having all true premises
No Cats are Dogs
T
All Cats are Animals
T
------------------------Some Dogs are not Animals F
All arguments with that
form are invalid.
No Secretaries of State have been women since
all women are Republicans and no Republicans
have been Secretaries of State.
All women are Republicans
No Republicans have been Secretaries of State
-----------------------------------------------No Secretaries of State have been women
All women are Republicans
No Republicans have been Secretaries of State
-----------------------------------------------No Secretaries of State have been women
All W are R
No R are S
--------No S are W
All W are R
No R are S
--------No S are W
All cats are mammals
No mammals are fish
--------------------No fish are cats
All Cats are mammals
No mammals are animals
-------------------------No animals are cats
T
T
-T
T
F
-F
Sorry, this is a valid argument!
The FORM is valid; the argument is unsound.
Strictly speaking:
Arguments are cases or Substitution Instances of
argument forms. When we say an argument is
invalid, that’s shorthand for saying the argument is
a substitution instance of an invalid argument form.
When we say an argument is valid, that’s
shorthand for saying it is a Substitution Instance
of a valid argument form.
Some people who are desperate are criminals who will
rob you. Some criminals are alcoholics, so some people who
will rob you are alcoholics.
Some people who are desperate are criminals who will
rob you. Some criminals are alcoholics, so some people who
will rob you are alcoholics.
Some P who are D are C who will R. Some C are A,
so some P who will R are A.
Some Cats who are Furry are Animals who will Purr.
Some Animals are Elephants.
---------------------------Some Cats who will purr are Elephants
T
T
-F
A counter-example preserves the FORM of an
argument, and substitutes new content to show
the possibility of that Form generating a False
conclusion from True premises.
It is impossible for a substitution instance of a
valid argument form to begin with true premises
and yield a false conclusion.
Validity and Invalidity are matters of the FORM or
structure of the argument, not matters dependent
on the subject or content of the argument.
All galaxies are structures that contain black holes.
All quasars are structures that contain black holes.
All galaxies are quasars.
All G are S
All Q are S
All G are Q
All dogs are animals
All cats are animals
All cats are dogs
T
T
F
If gene splicing is successful, disease-resistant livestock will be
produced.
If genetics defects can be eliminated, disease-resistant livestock
will be produced.
-------------------------------------If gene splicing is successful, genetic defects can be eliminated.
If G, then D
If E, then D
If G, then E
If Socrates is a man, then he’s mortal.
If Socrates is a goat, then he’s mortal.
If Socrates is a man, then he’s a goat.
T
T
F
No creationists are evolutionists
Some people who believe in the Bible are not creationists
so
Some evolutionists are not persons who believe in the Bible
No C are E
Some P are not C
So
Some E are not P
No cats are dogs
Some animals are not cats
So
Some dogs are not animals
T
T
F
Some politicians are people who will stop at nothing
to win an election.
No people who will stop at nothing to win an election
are true statesmen
So
No politicians are true statesmen
Some P are S
No S are T
So
No P are T
Some animals are mammals
No mammals are fish
So
No animals are fish
T
T
F