Compound Claims
Df. A compound claim is composed of other claims, but has to
be viewed as just one claim
Types of compound claims

Alternatives or Disjunctions: A or B

Conditional: If A, then B

Claim after A is termed Antecedent

Claim after B is termed Consequent
Df. Contradictory of a claim is a statement that always
has opposite truth value

Contradictory of an Alternative or Disjunction: not A and not B

Contradictory of a Conjunction: Not A or Not B

Contradictory of a Conditional: A and not B
Excluding Possibilities (Disjunctive Syllogism) and False Dilemma

Form

A or B

Not A

Therefore, B

Assessment

Valid (disjunctive syllogism) when ONLY two alternatives are available

Weak (false dilemma) when Other alternatives are available: A or
B or C
Valid Reasoning with Conditionals

The Direct Way (Modus Ponens)

If A, then B

A

Therefore, B

The Indirect Way (Modus Tollens)

If A, then B

Not B

Therefore, not A
Invalid (Usually Weak) Reasoning with Conditionals

Affirming the Consequent

If A, then B

B

Therefore, A

Denying the Antecedent

If A, then B

Not A

Therefore, not B
Difference between If and Only If

If expresses a Sufficient Condition (Enough) and is in the Antecedent
Position

Only If expresses a Necessary Condition (Essential) and is in the
Consequent Position

Memory Device on Location in Conditional Statement: SUN

For More Information on How to Understand the Concepts of Causality and
Necessary and Sufficient Conditions, see The
Logic of Causal Analysis
Reasoning in a Chain

Form

If A, then B

If B, then C

Therefore, if A, then C

Types

Valid Way (Hypothetical Syllogism)

Weak Way (Slippery Slope)
Counterarguments
Direct Way of Refuting Arguments

Show at least one Premise is False

Show the Argument is not Valid or is not Strong

Show the Conclusion is False
Indirect Way of Refuting Arguments

Reduce the Argument to the Absurd

Show One or More Claims is False or Collectively Unacceptable if Show
a False or Unwanted Conclusion Follows
Bad Attempts at Refuting Arguments

Phony Refutations

Appeal to Authority

Attack on Person

Appeal to People

Slippery Slope

Ridicule

Straw Person

Put Words in Opponentís mouth

Knock Down Weak Substitute
General Claims
Issue: We need to know how to reason with claims that are asserted
about
all, or some, or a few, or no things
Use of Quantifiers and Inclusion versus Exclusion

Universal Affirmative (inclusive): All S are P

Universal Negative (exclusive): No S are P

Particular (existential) Affirmative (inclusive): Some S is P

Particular (existential) Negative (exclusive): Some S is not P
Some Valid Types of Universal Reasoning

Direct Way of Reasoning with All

All S are P

S

Therefore, P

Reasoning in a Chain with All

All S are P

All P are Q

Therefore, All S are Q

Direct Way of Reasoning with No

All S are P

No Q are P

Therefore, No Q are S
Some Invalid (Weak) Types of Reasoning from Universals and Particulars

Arguing Backward with All

All S are P

P

Therefore, S

Reasoning in a Chain with Some

Some S are P

Some P are Q

Therefore, Some S are Q

Arguing Backward with No

All S are P

No Q are S

Therefore, No Q are P
Arguments Using Almost All and Very Few

Direct Way of Reasoning with Almost All: Strong

Almost all S are P

X is an S

Therefore, (probably) S is a P

Direct Way of Reasoning with Very Few: Strong

Very Few S are P

X is an S

Therefore, (probably) X is not a P

Arguing Backwards with Almost All: Weak

Almost all S are P

X is a P

Therefore, X is an S