Deductive Validity - PowerPoint Presentation

Slide1

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.Slide2

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!Slide3

MODUS PONENS

If p, then q.

p.

Therefore, q.

If

the soup is green (p),

then

it is poison (q).

The soup is green (p).

Therefore

, the soup is poison (q).Slide4

MODUS TOLLENS

If p, then q.

not q.

Therefore, not p.

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).Slide5

HYPOTHETICAL SYLLOGISM

If p, then q.

If q, then r.

Therefore, if p then r.

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).Slide6

DISJUNCTIVE SYLLOGISM

Either p or q.

Not p.

Therefore, q.

Either I was there (p)

or

I failed the test (q).

I was not there (~p).

Therefore, I failed the test (q).Slide7

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.Slide8

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.Slide9

Some Invalid Argument Forms

Affirming the Consequent

If p, then q.

q.

Therefore, p.

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)Slide10

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.Slide11

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.

If Bob is a bachelor (p), then male (q).

Bob’s not a bachelor (not p).

Therefore, Bob is not male (not q).Slide12

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).

The battery is dead (p).

Therefore, I’m not out of gas (~q). Invalid

Can’t rule out the possibility that both conditions obtained.Slide13

Informal Fallacies.

Unacceptable Premises

Begging the Question

Merely assumes what it purports to show.

He’s a psychic.

T

herefore 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!Slide14

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

!Slide15

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.Slide16

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.Slide17

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.Slide18

Informal Fallacies.

Appeal to Ignorance

Using a lack of disproof as if it was a positive proof.

There’s no proof you cheated on the test. So, Cheating is ruled out.

Using a missing counter proof as failure of opposing view.

You haven’t proved he’s not dead. So, dead he must be. Slide19

Informal Fallacies.

Appeal to Fear.

A

ffirm argument P or X results, where x is a feared circumstance.Slide20

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.