Tag Archives: Universal Affirmative

When a valid argument feels wrong – Logic to the rescue!!

29 Jul

So what do you do when someone’s argument is in the correct form, but you know that there’s still a problem?  

In a previous post I asked you to ‘draw’ out this syllogism:

All roads lead to Rome

Old Cabin Cove is a road

Therefore, Old Cabin Cove leads to Rome

Here’s what it should look like where BOTH the outer red square and the blue circle represent P1, and P2 is represented by the red X within the blue Roads circle.  We can CLEARLY see with our eyes that Old Cabin Cove is situated within the larger red square, “Things that lead to Rome”

Things that lead to Rome

As you can tell visually, the conclusion does not overreach the scope of the two premises P1 and P2. The syllogism IS, therefore, in the correct form and is considered VALID.  But our work does not end there.  You can FEEL that something else is wrong.

Anecdotally, I live on the gravel road, “Old Cabin Cove” in Western NC and I can attest that it does NOT lead to Rome.  It leads up a forested hill to our house and stops there!

What do we do then, with this valid syllogism?  We examine the truth of each of the 2 premises.

  • Let’s start with P2: Is ‘Old Cabin Cove’ a road?  YES! – no problem there.
  • Now for P1:  Do all roads lead to Rome?  NO!  Here’s the problem.  You already knew that, but what is illustrative in our simple example is this:  to DISPROVE an ALL or ‘A’ statement (also called a Universal Affirmative)  find ONE counter-example.  If there is JUST ONE single solitary road in the universe that does NOT lead to Rome, then the statement, “All roads lead to Rome” is false.
  • Why?  Thanks to the Law of Non-Contradiction which states that “A and non-A cannot both be true in the same way at the same time”.  Therefore we can’t say:  All roads lead to Rome and Some roads do NOT lead to Rome.
  • But we CAN say that Some roads lead to Rome and have that be a true statement.  (By the way, it takes only ONE road leading to Rome to make it true that ‘some roads lead to Rome’)

Back to our syllogism – if we want true premises, then we have to modify them to reflect reality:

P1   Some roads lead to Rome

P2   Old Cabin Cove is a Road

Tf……NOTHING!!!! –  we CAN’T conclude that Old Cabin Cove leads to Rome. It might and it might NOT.

Just like in our previous ‘cat and cuddly pets’ syllogism, our conclusion cannot reach further than P1 and P2, even if both of the premises are TRUE.  Here’s the sketch of what that would look like. We simply do not know where to place our X representing Old Cabin Cove.

Old Cabin Cove and Some roads

In our next post, I will share some real life examples of how knowing the Law of Non-Contradiction can help evaluate an argument you might read or hear.