Tag Archives: Logic

How recognizing a fallacy helps sniff out a poor argument

10 May

All cows have four legs

My dog Fido has four legs

Therefore, Fido is a cow

Pastor John Piper explained in a rebroadcasted sermon how high school geometry had grounded him in clear thinking.  Mathematical laws, one leading to a next, trained him to use deductive reasoning.  With practice in drawing valid and true conclusions, he developed a ‘nose’ for truth, as he put it.  The practical effect for him has been to alert him to ‘fishy’ conclusions that stink, that is they don’t add up, given the premises provided.

Looking at the syllogism above, we notice something and we ‘smell’ something:

  1. Premises 1 & 2 are in fact TRUE – cows have 4 legs and dogs normally do as well
  2. But we know that the conclusion is FALSE.  Our dog Fido is NOT a cow.

For me, the quickest way to explain why our sense of ‘fishiness’ is spot on, is to draw out each premise.

Take All cows have 4 legs.

Step 1:  draw a circle – label it Creatures with 4 legs.

2 cirlces

Step 2: draw a smaller circle somewhere inside the first circle.  This represents ALL COWS.  Every cow that ever WAS, IS, WILL BE  is in that circle.  (assuming no handicapped cows)

Step 3:  Mark an X in the big circle called, Creatures with 4 legs.

Circles with X

Do you spot the problem?  We don’t know where to place Fido.  Does he belong in the circle of cows? or out of the circle of cows?  From the information given, the 2 premises, that cannot be determined.

Therefore, the conclusion is false.  Why?  Because the new premise that ‘Fido is a cow’ assumes too much.  It might be, but it might not be.

There is of course, a technical way of categorizing the validity of the syllogism.  But for me, just sketching it out is simplest.

When I taught in a classical Christian school in Yorktown, Va, logic was a mandatory class for 7th and 8th graders.  I instructed the younger students in the joy of spotting fallacies (much to the annoyance of their parents who thereafter had to be on their guard!).  The 8th graders were at the perfect age to begin to understand how to analyze and formulate good arguments.

I believe that this tool in clear thinking is invaluable to young teens AND adults.  This kind of knowledge is powerful and builds confidence when they head out into a world such as ours:

Woe to those who call evil good, and good evil: who substitute darkness for light and light for darkness; who substitute bitter for sweet and sweet for bitter!  Woe to those who are wise in their own eyes and clever in their own sight!  Isaiah 5: 20-21 (NASB)