Socratic Logic - Reasoning

Compound Syllogisms

 

The following are the notes I have taken from Peter Kreeft's wonderful Socratic Logic textbook. I highly recommend you buy it. This is a book which deals with classical logic (as opposed to modern symbolic logic.) It is easily the best overall book on logic I have ever read and one of the few I have that are worth making notes from. I even have a small duotang with these notes in it I can carry around and reference on a regular basis.

 

Three Types of Compound Syllogisms:

A. Hypothetical Syllogisms

B. Disjunctive Syllogisms

C. Conjunctive Syllogisms

 

Hypothetical Syllogisms

 

Pure hypothetical syllogisms are rare, all three propositions are hypothetical. These are actually simple, categorical syllogisms 'in disguise'.

 

 

In mixed hypothetical syllogisms only first proposition is hypothetical, the others are categorical.

 

Four types:

 

A . Affirming the Antecedent

 

p  => q, p, therefore q

 

(valid)

 

B. Denying the Consequent

 

p => q, not q, therefore not p

 

(valid)

 

C. Affirming the Consequent

 

p  => q, q, therefore p

 

(invalid)

 

D. Denying the Antecedent

 

p  => q, not p, therefore not q

 

(invalid)

 

Disjunctive Syllogisms

 

These are either / or syllogisms.

 

p  v q (either p or q)

 

A. p v q, p, therefore not q.

 

B. p v q, q, therefore not p.

 

C. p v q, not p, therefore q.

 

D. p v q, not q, therefore p.

 

Simple.

 

Conjunctive Syllogisms

 

A. Affirmative

 

p & q

 

B. Negative

 

not p & not q

 

(Only the negative can be proven.)

 

 

 

< Prev		Next >