Formal Logical Fallacies

by Gregg Allen Trickett, written 03/17/23

the Propositional Form
if P, then Q.
P {antecedent},
therefore Q {consequent}.

Affirming the Consequent or converse error
if P, then Q.
Q,
therefore P.
- the conclusion P is not necessarily a consequence of Q.

Illicit Commutativity
if P, then Q.
therefore if Q,
then P.
- Q remains unproven.

Denying the Antecedent
if P, then Q.
not P,
therefore not Q.
- the conclusion does not follow the premise, Q may betrue or false.

Affirming a Disjunct
P or Q is true.
P is true,
therefore Q is not true
- P and Q could both be true.

Denying a Conjunct
not both P and Q are true.
P is not true,
therefore Q is true.
- P and Q could both be false.

Undistributed Middle
all Ps are Qs.
T is a Q,
therefore T is P.
- Q is common while not distributed.

all Ps are Qs.
some Ts are Ps,
therefore all Ts are Qs.
- P is distributed in the premises while T is not.

Who has measured the waters in the hollow of His hand, and marked off the heavens by the span, and calculated the dust of the earth by the measure, and weighed the mountains in a balance and the hills in a pair of scales? Isa 40:12