Hypothetical syllogisms

syllogism

s a short deductive argument pattern, consisting of twopremises and a conclusion

Modus Ponens

1.If p, then q

2.p

3.Therefore, q

ex;

1.If she jumped off that building, she is hurt.

2.She jumped off that building.

3.Therefore, She is hurt

yes

is modus ponens always valid?

Affirming the Consequent

1.If p, then q

2.q

3.Therefore, p

ex;

1.If she jumped off that building,she is hurt.

2. She is hurt.

3. Therefore, she jumped off that building.

Is affirming the consequent ever valid?

No

Modus Tollens

1.If p, then q

2.Not-q

3.Therefore, not-p

ex;

1.If she jumped off that building, she is hurt

2.She is not hurt

3.Therefore, she did not jump off that building

is modus tollens always valid?

yes

denying the antecedent

1.If p, then q

2.not-p

3.Therefore, not-q

ex;

1.If she jumped off that building, she is hurt

2.She did not jump off that building

3.Therefore, she is not hurt

is denying the antecedent ever valid?

no

chain argument

1.If p, then q

2.If q, then r

3.Therefore, if p, then r

ex;

1.If she jumped off that building, then she is hurt

2.If she is hurt, she needs medical attention

3.Therefore, if she jumped off that building, she needs medical attention

are chain arguments always valid?

yes

broken chain

Here, there is no single bad form, butjust remember that the “middle term”has to line up properly.

If it does, the antecedent of the conditional that has the middle term as its consequent should drop down to the conclusion, and the same with theconsequent in the conditional which has the middle term as its antecedent.

are broken chains ever valid?

no

3 necessary characteristics for a chain argument

A.It must have a middle term (the “letter” that is repeated in the premises but is not in the conclusion.)

B.The middle term must be on the corners (either corner will do).

C.The other two terms will “drop down” from their slots to make a conditional in the conclusion.

If any of these rules are violated, then it is a “broken chain” and invalid.

So, the following argument:

1.If a, then b

2.If b, then c

3.Therefore if a, then c

Is a valid chain argument

b is the middle termit is on the corners and a and c drop down in their slots to make a conditional in the conclusion