Logical Toolkit

Premises

The points of an argument

“Alvin lives in California”

Conclusion

The ending assertion

Usually will end with “Therefore:

Validity

The argument directly supports the premises. If premise 1 and 2 of an argument are true, the conclusion must be true.

Ex. Every resident of LA lives in California.

1. Alvin lives in LA.

2. Therefore, Alvin lives in California.

Soundness

All premises are true and the argument is valid

Antecedent

A

Consequent

B

Modus Ponens

1. If A, then B

2. A

3. Therefore, B

Modus Tollens

1. If A, then B

2. Not B

3. Therefore, not A

What is the invalid inverse of Modus Ponens?

Affirming the Consequent (AC)

1. If A, then B

2. B

3. Therefore, A.

this is invalid because it doesn’t rule out other conditions for B to occur

What is the invalid inverse of Modus Tollens?

1. If A, then B

2. Not A

3. Therefore, not B

Doesn’t rule out specific conditions for B

Conjunctive Syllogism

1. Either A or B.

2. Not A.

3. Therefore, B.

Constructive dilemma

1. Either A or B.

2. If A, then C

3. If B, then D.

4. Therefore, either C or D

Conditional Proof

1. Assume A.

2. Derive: B.

3. Therefore, if A, then B.

Reductio Ad Absurdum

1. Assume A.

2. Derive B and not B.

3. Therefore, not A.

Affirming a disjunct

• Assuming that the inclusive ‘or’ cannot exist without clarification

• Assuming two things cannot be true

Begging the question/circulairity

• he conclusion supports itself

  • based on implicit presumption

• the conclusion supports the second premise (which is false)

• It is technically valid, but unpersuasive