It was a cold snowy December morning in London. A nasty blizzard was afoot on this dreary winter morning. “That’s a nasty blizzard. Isn’t it, Watson?” exclaimed Sherlock as I entered the cozy living room of our apartment at Baker Street after my customary morning walk. My entry seemed to have rudely interrupted his mid-morning siesta. He was still lying curled up on the couch next to his dark man cave with all the lights turned off and the blinds shut tight as he startled me with this innocuous but insightful pronouncement.
“With all the blinds shut and the lights turned off, you can hardly hear even a whisper from the street outside or catch a glimpse of what the weather is like outside. Moreover, I just picked up the morning newspaper from Mrs. Hudson. So, you had no direct way to know there was a snowstorm raging outside this morning. How did you figure that out, Holmes?” I asked, perplexed and amazed by his conclusion.
“Elementary, my dear Watson. I know that you wear your heavy boots only when it snows badly. I saw you were wearing your heavy boots as you entered. Therefore, it must be snowing heavily outside. It’s all about a valid and sound deductive argument, my friend!”
“Now I get it, Holmes,” I spoke as I walked sheepishly into the kitchen.
“Oh no! What a mess. Who spilled the milk here?” I cried out as I deftly avoided stepping into a dirty puddle on the floor.
“Hmm, let me try my hand at explaining this by applying some of your deductive logic to ascertain how this could have happened. There is only one window in the kitchen, and it seems to be partly open. I left the milk jug on the table and you were sleeping when I left for my morning walk and it had just started snowing. No one else visited us because our landlord, Mrs. Hudson, was here the whole time and she said no one entered the apartment or left it when I was gone. All cats like milk and our next-door neighbor, Mr. Abernathy, is the only one in our block who has a cat. So, it’s certain that his cat must have spilt the milk. Is my conclusion right following a similar line of reasoning?”
“My dear Watson, not quite. The wind from the blizzard could have knocked the jug off. So even if all your premises are true, the conclusion could be false, so that is an invalid deductive argument my friend.” chuckled Holmes to my consternation.
“Alright. Let me try and make this a valid argument: Suppose I found a cat’s whisker in the spilt milk. It is well-known that I possess the amazing skill of “cat whiskerology”. Using this powerful skill, I identify that the whisker came from a Cheshire cat. Our neighbor Mr. Abernathy has a Cheshire cat and that is the only domestic cat in our neighborhood. I see this neighbor’s Cheshire cat perched on his balcony next to our window. And Mrs. Witherspoon, whose apartment faces our kitchen window and whose truthfulness and veracity I have come to rely upon, claims she witnessed a Cheshire cat jumping into our kitchen and leaving with milk dripping from its face and observed the cat left milk-stained paw prints on our windowsill. So, I conclude Mr. Abernathy’s Cheshire cat spilt the milk. Would that make it a valid and sound argument?” I asked.
Holmes grinned, “Unfortunately, while it is a valid argument it still is not sound, my dear fellow, since you are no expert in ‘cat whiskerology’!”.
“Darn it, Holmes. Let me try something else. Suppose we can identify the breed of a cat by testing the genetic material of its whiskers. And upon matching the material of the whiskers found in the milk with samples of materials from all known breeds of cats, I determine that it closely matches the patterns of a Cheshire cat. So, I conclude that this belongs to a Cheshire cat. Will that be a valid argument?”
“No Watson. What you just presented here is a strong inductive argument. The genetic material test is never 100% accurate, there could be errors in how you collected the samples or you could have some contamination in the sample or testing materials. So, what you can reasonably conclude with high confidence (let’s say higher than 75%) is that the whisker belonged to a Cheshire cat. In essence, what you have here is a strong inductive argument,” explained Holmes.
“Hmm. So then is there such a thing as a weak inductive argument, can you explain how that is different from a strong inductive argument?” I asked Holmes.
“Suppose we assume all of the above premises are true and in addition to the above premises, it is true that Cheshire cat’s genetic material is very close to that of human mustaches, hair from lion’s mane, a monkey’s hair or sheepdog’s fur. So, it is equally probable that what you tested could be a Cheshire cat’s whisker or hair or fur from any of the other animals. In this case, it would make your conclusion less likely (less than 50% probability) and make it a weak inductive argument. Does that make sense?”
“Whew! I never knew that studying how a jug of milk ended up getting spilled could transform into a fascinating study of logical reasoning and make me a better logician!” I said.
“Yes, Watson, from a drop of water a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other. Come on Watson, all this talk is making me thirsty for milk, let us ring up Mrs. Hudson and ask her to bring us both some milk and scones.”
Just as Holmes rang for Mrs. Hudson, my neighbor’s Cheshire cat leapt in from the kitchen window and slurped up the rest of the spilt milk. I beamed with satisfaction that comes from being vindicated: perhaps the cat from my logical multiverse had indeed materialized as my neighbor’s cat to prove the soundness of my conjecture!
Vishak Srikanth is a high school student from California. He enjoys using his creative energies to express and share his perspectives through his literary endeavors, artwork, scientific research, or musings on current geopolitical or socioeconomic events.
