CT Test 2

Two Criterias

-Formal -Truth

Syllogism

A deductive argument made up of three statements -two premises and a conclusion.

Invalid

A deductive argument that fails to provide such support

Valid

A deductive argument that succeeds in providing such decisive logical support

Sound

A deductively valid argument that has true premises

Hypothetical syllogism

All three statements are conditional and the argument is valid. If p, then q. If q, then r. Therefore, if p, then r.

Denying the consequent (modus tollens)

Always valid if the premises are true, the conclusion must be true. If p, then q. Not q. Therefore, not p.

Weak

An inductive argument that fails to provide such support

Strong

An inductive argument that succeeds in providing probable -but not conclusive- logical support for its conclusion

Truth-preserving

Because of the guarantee of truth in the conclusion deductively valid arguments are

The terms valid and invalid apply to what types of arguments?

Deductive

Symbolized version example

Either we light the fire or we will freeze. We will not light the fire. Therefore, we will freeze.

Hypothetical Syllogism example

If Ajax steals the money, he will go to jail. If Ajax goes to jail, his family will suffer. Therefore, if Ajax steals the money, his family will suffer.

Affirming the antecedent (modus ponens) example

If Spot barks, a burglar is in the house. Spot is barking. Therefore, a burglar is in the house.

Denying the consequent (modus tollens) example

If it's raining, the park is closed. The park is not closed. Therefore, it's not raining.

Affirming the consequent example

If the cat is on the mat, she is asleep. She is asleep. Therefore, she is on the mat.

Denying the antecedent example

If the cat is on the mat, she is asleep. She is not on the mat. Therefore, she is not asleep.

Deductive argument

Intended to provide logically conclusive support for its conclusion

Inductive argument

Intended to provide probable -not conclusive- support for its conclusion

Bachelors are unmarried. George is a bachelor. He has never taken a wife.

Invalid

Affirming the consequent

Invalid If p, then q. Q. Therefore, p.

Denying the antecedent

Invalid If p, then q. Not p. Therefore, not q.

Is it possible for a valid argument to have true premises and a false conclusion?

No

Independent premise

Offers support to a conclusion without the help of any other premises.

Any senator who is caught misusing campaign funds should resign his seat. Senator Greed should resign.

Senator Greed was caught misusing campaign funds. (implicit premises that makes the argument valid)

Ethel graduated from Yale. If she graduated from Yale, she probably has a superior intellect. She has a superior intellect.

Step 1: Conclusion: She has a superior intellect. -Premises: Ethel graduated from Yale. If she graduated from Yale, she probably has a superior intellect. Step 2: Not deductively valid. Step 3: Inductively strong. Step 4: Does not apply.

Antecedent

The first statement in a conditional premise (the if part)

Consequent

The second statement (the then part)

Dependent premise

They do depend on each other to jointly provide support to a conclusion.

If CNN reports that war has started in Iraq, then war has started in Iraq. CNN has reported exactly that. War must have started.

Valid

Disjunctive syllogism

Valid and extremely simple. Either p or q. Not p. Therefore, q.

Affirming the antecedent (modus ponens)

Valid if the premises are true, the conclusion absolutely must be true. If p, then q. P. Therefore, q.

Cogent

When inductively strong arguments have true premises (good inductive arguments are cogent, bad inductive arguments are not)