Chapter 3
Disjunctive Syllogism
*Either p or q. Not p. Therefore, q.* -valid and simple -(p or q can be denied btw)
Hypothetical Syllogism
*If p, then q. If q, then r. Therefore, if p, then r.* -all 3 statements are conditional -Argument ALWAYS valid
Denying the Antecedent
*If p, then q. Not p. Therefore, not q.* -Invalid pattern because it's possible for the premises to be true and the conclusion false
Modus Tollens (denying the consequent)
*If p, then q. Not q. Therefore, not p.* -always valid (if premises are true, conclusion MUST also be)
Affirming the Consequent
*If p, then q. q. Therefore, p.* -Invalid pattern because it's possible for the premises to be true and the conclusion false
Modus Ponens (affirming the antecedent)
*If p, then q. p. Therefore, q.* -always valid (if premises are true, conclusion MUST also be)
*Inductive* argument signal terms
- likely -probably -chances are -it is plausible that
*Deductive* argument signal terms
-it necessarily follows that -it logically follows that -absolutely -necessarily -certainly
Valid Argument Forms
1. Affirming the antecedent 2. Denying the consequent 3. Hypothetical Syllogism 4. Disjunctive Syllogism
Invalid Argument Forms
1. Affirming the consequent 2. Denying the antecedent
Conditional, deductive, *If-Then* common argument patterns contain
1. Antecedent 2. Consequent
What must a good argument have?
1. Proper structure: the conclusion must logically follow the premises 2. TRUE premises
Assessing Long Arguments
1. Study text until you "get it" 2. Find conclusion 3. Identify premises 4. Diagram the argument
Weak Inductive Argument
An inductive argument that fails to provide such support for the conclusion
Strong Inductive Argument
An inductive argument that succeeds in providing probable *but not conclusive* logical support for its conclusion
Why are inductive arguments NOT truth-preserving?
Because the truth of the conclusion cannot be guaranteed by the truth of the premises. An inductively strong argument is such that if its premises are true, its conclusion is *probably* or *likely* to be true (compared to deductively valid)
When GOOD, inductively strong arguments have TRUE premises, they are
Cogent
All dogs are mammals. All cows are mammals. Therefore, all dogs are cows.
Ded. Invalid
If Socrates has horns, he is mortal. Socrates is mortal. Therefore, Socrates has horns.
Ded. Invalid
All dogs have fleas. Bowser is a dog. So Bowser has fleas.
Ded. Valid
All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
Ded. Valid
Investigation of Implicit Premises: Step 3
Evaluate the reconstituted argument. If you're able to identify a credible implicit premise that makes the argument either valid or strong, assess this revised version of the argument, paying particular attention to the plausibility of the other premise or premises.
Bowser is a cat. All cats are mammals. Therefore, Bowser is a mammal.
False Premises (Bowser is a dog...) True Conclusion
All dogs have flippers. All cats are dogs. Therefore, all cats have flippers.
False premises False Conclusion
Judging Arguments: Step 1
Find the argument's conclusion and then its premises
1. Antecedent
First statement in a conditional premise *the "if" part*
98% of humans are mortal. Socrates is human. Therefore, Socrates is likely to be mortal.
Inductively STRONG arguments (compare to deductively valid)
MOST dogs have fleas. Therefore, Bowser, my dog, probably has fleas.
Inductively STRONG arguments (compare to deductively valid)
Ninety-eight percent of humans are mortal. Socrates is human. Therefore, Socrates is likely to be mortal.
Inductively strong
Most dogs have fleas. Therefore, Bowser, my dog, probably has fleas.
Inductively strong argument
Dependent premises
Multiple premises that depend on eachother to jointly provide support to a conclusion -if one is removed the support that the remaining premise supplies is undermined or completely cancels out Ex: 3 + 4
Is the support that an *inductive argument* can give absolute?
No! BUT it can vary from weak to extremely strong
Is this a GOOD inductively strong argument? Scientific studies show that 99% of dogs have 3 eyes. So it's likely that the next dog that I see will have 3 eyes.
No, its premise is false
Are Bad inductive arguments cogent?
Nope!
Is it possible to have a valid argument with true premises and a false conclusion?
Nope!
All pigs can fly. Vaughn is a pig. Therefore, Vaughn can fly.
Proper structure BUT FALSE premises
A deductively valid argument that has TRUE premises is said to be:
SOUND: good argument! gives good reasons to accept its conclusion
2. Consequent
Second statement *"then" part*
Counterexample method (pg. 83)
Test for the validity or invalidity of an argument *can prove invalidity by creating a parallel argument that will have true premises and a FALSE conclusion*...
Bowser is a dog. All dogs are mammals. Therefore, Bowser is a mammal.
True Premises True Conclusion
Invalid deductive argument
fails to provide support for conclusion -The conclusion does NOT logically follow the premises
Independent Premises
offers support to a conclusion WITHOUT help of any other premises Ex: 7 or 6
Deductive Argument
provides logically conclusive support for its conclusion
Inductive Argument
provides probable *not conclusive* support for the conclusion
Valid deductive argument
succeeds in providing decisive and conclusive logical support -are *truth-preserving* -if the premises are true, the conclusion must be ABSOLUTELY true
A GOOD inductive argument must have
true premises
Good arguments have
true premises
Is the support that a *deductive argument* can give absolute?
yes! the conclusion will be true or it will not
Is this an inductively strong argument? Scientific studies show that 99% of dogs have 3 eyes. So it's likely that the next dog that I see will have 3 eyes.
yes, the conclusion logically follows from the premises, BUT....
