Deductive Validity

Truth preserving: The conclusion logically follows
from the premises. It is logically impossible for the
premises to be true and the conclusion false, because
the conclusion expresses what is implied by the
combination of premises. If the premises are true,
the conclusion is true.

Because validity is a matter of form, any argument
that exhibits the appropriate form is valid, regardless
of whether the statements it contains are true.

It is not necessary for the establishment of validity to
ascertain the truth of the premises.
the Valid argument

May consist in
◦ false premises and a false conclusion,
◦ False premises and a true conclusion,
◦ True premises and a true conclusion,

Yet still be valid in virtue of its form.

But, it is impossible for a Valid argument to
have true premises and a false conclusion!
MODUS PONENS
If p, then q.
p.
Therefore, q.
1.
2.
3.
If the soup is green (p), then it is poison (q).
The soup is green (p).
Therefore, the soup is poison (q).
MODUS TOLLENS
If p, then q.
not q.
Therefore, not p.
1.
2.
3.
If mind is immortal (p), then mind is
independent of brain activity (q).
Mind does depend on brain activity (not q).
Therefore, the mind is not immortal (not p).
HYPOTHETICAL SYLLOGISM
If p, then q.
If q, then r.
Therefore, if p then r.
1.
2.
3.
If the Fed raises rates (p) , then fewer
qualify for loans (q).
If fewer qualify for loans (q) , then home
sales plummet (r).
Therefore, if the Fed raises rates (p), then
home sales will plummet (r).
DISJUNCTIVE SYLLOGISM
Either p or q.
Not p.
Therefore, q.
1.
2.
3.
Either I was there (p) or I failed the test (q).
I was not there (~p).
Therefore, I failed the test (q).
Sound Argument
While Validity is a desired condition for a
good argument, by itself it is not sufficient.
 We also require that an argument be
sound:

◦ 1. identify premises and conclusion,
◦ 2. determine whether the argument form is
valid.
◦ 3. determine truth of premises.
A test for Invalidity
The method of counter example

Determine whether there is another
argument with the same form that will
allow the premises to be true and the
conclusion false.
If so, the argument is invalid.
Some Invalid Argument Forms

Affirming the Consequent
◦ If p, then q.
◦ q.
◦ Therefore, p.
1.
2.
3.
If Houston is the capital of Texas (p),
Then Houston is in Texas (q).
Houston is in Texas (q).
Therefore, Houston is the capital of
Texas (p)
What’s wrong with affirming the
consequent

The form inadmissibly allows for the
premises to be true and yet the
conclusion false!

So any argument with this form does not
provide a good reason for accepting its
conclusion.
Some Invalid Argument Forms

Denying the Antecedent
◦ If p, then q.
◦ Not p.
◦ Therefore , not q.
Imagine a situation in which the premises
are true and the conclusion false.
1. If Bob is a bachelor (p), then male (q).
2. Bob’s not a bachelor (not p).
3. Therefore, Bob is not male (not q).

Some Invalid Argument Forms

Affirming a Disjunct
◦ Either p or q.
◦ P.
◦ Therefore, not q.

Logical or is interpreted Inclusively . . . either p,
or q, or both!
Either the battery is dead (p) or I’m out of gas
(q).
2. The battery is dead (p).
3. Therefore, I’m not out of gas (~q).
Invalid
 Can’t rule out the possibility that both
conditions obtained.
1.
Informal Fallacies.

Unacceptable Premises
◦ Begging the Question
 Merely assumes what it purports to show.
 He’s a psychic. Therefore he’s able to read minds.
 But, it’s a vicious circle.
◦ False Dilemma
 Presumes a dichotomy when multiple option are
possible.
 Science has no explanation or it’s a miracle.
 But, Additional option – natural but not yet explained!
Informal Fallacies.

Irrelevant Premises
◦ Equivocation
 Terms used ambiguously, i.e., differently from use to use.
 Man is a rational animal. (man used generically for a species)
 No woman is a man.
( man used to specify a sex)
 Therefore, no woman is rational.
◦ Composition
 Is what’s true of the parts true of the whole ?
 Each chemical element is lifeless
 Therefore no chemical composition accounts for life.
 But the sum of parts may have novel new properties!
Informal Fallacies.

Division
◦ Is what’s true of the whole true of the parts?

Argumentum ad Hominem
◦ Argument P is false because Gov. Perry holds it’s
true and Perry is just a wanker.
◦ But, the name-calling has nothing to do with the
soundness of P.

Genetic Fallacy
◦ I saw argument P written in a toilet stall so P is
false.
◦ But, we need not consider the source provided P
is sound.
Informal Fallacies.

Appeal to Authority
◦ Argument P is true because it’s in the Book.
◦ But, only the soundness of P provides
acceptability of P not who published it.

Appeal to the Masses
◦ Everybody said there name isn’t Sonia. So you
can’t really be Sonia.
◦ But, being unpopular doesn’t make it go away.
Informal Fallacies.

Appeal to Tradition
◦ Traditionally our church grows by killing
competitors. So, kill competitors.
◦ But, sound argument guarantees the truth of
its outcome, whereas tradition does not
guarantee its outcome.
Informal Fallacies.
Appeal to Ignorance
1) Using a lack of disproof as if it was a
positive proof.

1) There’s no proof you cheated on the test.
So, Cheating is ruled out.
2)
Using a missing counter proof as failure
of opposing view.
1) You haven’t proved he’s not dead. So, dead
he must be.
Informal Fallacies.

Appeal to Fear.
◦ Affirm argument P or X results, where x is a
feared circumstance.
Informal Fallacies.

Insufficient Premises
◦ Hasty Generalization
 Jumping to conclusions
 Bad Deduction: Some x is y, therefore All x is y.
 Bad Induction: small sample x is y, therefore All x is y.
◦ Faulty Analogy
 Any two things may have some features in common.
Consequently, an argument from analogy can be successful
only if the dissimilarities are insignificant.
◦ False Cause
 Post hoc, ergo propter hoc
 After this, therefore because of this.
 Night follows day doesn’t mean night causes day.