Episode 50: Sheeplock and Dachson in “A Champagne Deduction”

Having successfully solved the case of the missing waterer and developed a firm grasp of abductive logic Sheeplock and Dachson we’re headed to their next assignment.  They arrived at the Farnston residence at mid-day and greeted what appeared to be a couple in the midst of a rather intense argument.  Sheeplock casually chewed his cud while waiting for them to settle down – after all he was paid by the hour.  Dachson checked his watch regularly, not wanting to miss afternoon tea. 

When the Farnston’s finally settled down, Sheeplock asked them what their disagreement was all about.  It turns out Bob and Sally Farnston were hosting a dinner party and planned to start with Mimosas to loosen up their friends who were notoriously tight-lipped until they’d had enough drinks.  The problem was their friends would only drink Mimosas made with Humbold’s Extra Bubbly Champagne and the store only had a few bottles left so Bob got another brand as well in case they ran out, thinking it would be OK.  Sally thought it was a huge problem and would ruin the dinner party because no one would talk without enough drinks.  Neither could predict what would happen.

Dachson had a bit of a smile, knowing what was coming next.  Sheeplock thought for a moment and then spoke.  You have given me all the information I need to settle your dilemma.  A successful dinner must have good conversation.  In order to have such conversation, your guests need to loosen their tongues with the proper libations.  If your guests will only drink Mimosas made with Humbold’s and what you have is not enough to inebriate them then having another brand makes no difference.  They will not talk and you will not have a successful party.  To have success, then, you must check other stores for more Humbold’s Champagne.  This I have deduced.  At that point, Sheeplock glanced at Dachson as if looking for approval and was relieved to see a head nod and happy tail wag.

Dachson was happy because Sheeplock had correctly applied deductive reasoning.  This method of reasoning states that if the premises, or facts, are true then the conclusion must also be true.  In the case here: if guests only drink Mimosas made with Humbold’s champagne, the guests need a certain amount of drink in them to loosen up and talk, and the party is ruined if no one talks, then it must follow that if there is not enough Humbold’s champagne the guests will not loosen up, they will not talk, and the party will be ruined.

An age-old syllogism directly shows us a perfect example of deductive logic:

               If Sheeplock is a sheep

               And all sheep chew their cud

               Then Sheeplock must chew his cud

“Sheeplock must chew his cud” is a deduction (conclusion) based on the other two premises.  If those are true, then the conclusion must be true.  If instead we say If Dachson is a sheep and all sheep chew their cud then Dachson chews his cud we know this is false because Dachson is not a sheep, he’s a dog.   You may recall from our earlier examination of syllogisms that If A=B and B=C then A=C.  If you can state your argument like this, then you know you are using deductive reasoning.

Deductive reasoning is important. It is one of the two main types of logic, along with inductive reasoning, which used in the scientific method.  A researcher will gather their premises, test them to insure they are valid, and then deduce a conclusion based on them.  For instance, take an object and weigh it very accurately.  Now, completely burn the object, carefully keeping all of the ash.  Weigh the ash very accurately and see that it is lighter.  You can deduce that mass is lost during the burning process.  If the two weights were the same you could deduce that burning has no effect on the mass of an object.  (Hint, it should be lighter afterwards!)

If you use deductive logic, you must ensure that your premises are correct.  So, if you see an instance of a conclusion drawn from a deduction you should know that verifying the premises is critical.  You may see cases where a premise was just wrong such as If my car gets 200 miles per gallon and it hold 10 gallons then I can drive 2000 miles before filling up would obviously be wrong because no car has that kind of mileage.  You might say that My cars owner’s manual states that it gets 18 mpg and has a 10 gallon tank so I can drive 180 miles between fill ups would be a correct deduction based on the facts at hand.  However, after several trips you may find you are only getting 16 mpg (tire pressure, idling, wind, etc can affect mileage) you will have to amend one of your premises.  It was correct initially, but further testing revealed it to be wrong.  This happens a lot in science.

Now you have deductive and abductive reasoning in your toolkit. That just leaves inductive reasoning.  What nefarious plot will Sheeplock and Dachson find themselves in that requires such logic?  You’ll have to wait and find out.  Since the Farnston’s didn’t need their extra non-Humbold’s champagne our duo was more than happy enough to take it off their hands.  They’re probably a little less logical now.

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