A curious thing happened to me earlier today. I went to my local convenience store around six in the morning. At that hour, there was no one else in the store except myself and a new clerk -- a young woman I'd never seen before.
She looked like she was having trouble waking up -- no one else being around -- so I charitably decided to help her wake up by engaging her in a stimulating conversation about the truth-values of logical operands in a propositional calculus -- a "wake up and take notice!" topic if ever there was one.
I went on about them for about ten minutes but it wasn't enough. She actually appeared sleepier than before I had begun talking! Poor thing must have been out partying the night before. So I quickly changed the topic to something absolutely guaranteed to thrill. A topic that amounts to logic's equivalent of "Shock and Awe": The question of when it's best to induce, and when its best to abduce, a conclusion!
Well, another ten happy minutes went by when she suddenly and without warning did the strangest darn thing I've ever seen a store clerk do -- new or not!
She opened the cash register, took out all the cash, abruptly shoved it at me, and began screaming, "Here! Take it! Take it all! Anything to get you out of my store! Anything! Just leave!"
Naturally, I was shocked and appalled. Shocked and appalled that her words could not possibly be interpreted as a logical argument for my leaving her store. At best, she was making a mere appeal to greed -- which as you must already know is a fallacy. Nevertheless, I composed myself and quickly exited, but only after refusing the money -- I didn't want to give her the impression I could fall for such an illogical argument.
So now I'm wondering. Do I have any grounds for reasonably believing her behavior reflects that she had a sudden psychological fit of some sort? Perhaps some kind of seizure? There seems no other possible cause to it.
Well, I just thought I'd share a peculiar moment from my morning with you before getting into the much more exciting question of the practical differences between induction and abduction.
An Obvious Statement
Without doubt, one of the most famous statements in the long history of logic appears to us as a deceptively obvious premise. Naturally, I refer to the famous claim, "All men are mortal".
The statement seems so obviously true to us that we seldom if ever ask ourselves, "How do we actually know all humans are mortal?" Yet, it is only if and when we do ask that question that the thrills begin.
You see, there are only three kinds of logic -- deduction, induction, and abduction. Of the three, only induction and abduction have any chance at all of providing us with an empirical answer to our question. Poor old deduction by her very nature cannot.
Yet, induction and abduction when applied to the question produce very difference grounds for asserting its claim that all men are mortal. Very different grounds.
To induce or to abduct? That is the question.
To induce that all men were mortal, we might begin by compiling a huge database of births and deaths, searching the database for -- say -- "people over the age of 150 who are still living", and then when we find no one in that category, generalizing to the conclusion that "all humans die before the age of 151." i.e. "All humans are mortal".
But to abduce that all men are mortal, we would do something that is in a key way very different. We might begin the same way -- with searching a large database for anyone who had lived over 150 years. But then, instead of reaching a conclusion based on generalization --- we would reach a conclusion based on reasoning from the data to the most likely or best explanation.
To explain what reasoning to the best explanation means, try thinking of it this way:
By the way, in the above case of the exploding store clerk, we cannot induce that she had a fit because we have no data set of store clerks having fits to show us the probability of her behavior being caused by a fit. However, we can abduce that she had a fit because that is the only reasonable cause of her behavior -- and hence, the most likely, best, or most probable explanation for it.
I mean, really? Can you think of any other reason she would have been so desperate for me to leave her store? I sure can't.
Last, there's a hot debate in logic about what is required for induction to show us the cause of something -- and whether it even can show us the cause of something. But I won't get into that debate here for fear of over-exciting my audience. There are only so many thrills a person can take in a single day, and I'll wager most of you are near your limit after having read this exciting post.
Questions? Comments?
She looked like she was having trouble waking up -- no one else being around -- so I charitably decided to help her wake up by engaging her in a stimulating conversation about the truth-values of logical operands in a propositional calculus -- a "wake up and take notice!" topic if ever there was one.
I went on about them for about ten minutes but it wasn't enough. She actually appeared sleepier than before I had begun talking! Poor thing must have been out partying the night before. So I quickly changed the topic to something absolutely guaranteed to thrill. A topic that amounts to logic's equivalent of "Shock and Awe": The question of when it's best to induce, and when its best to abduce, a conclusion!
Well, another ten happy minutes went by when she suddenly and without warning did the strangest darn thing I've ever seen a store clerk do -- new or not!
She opened the cash register, took out all the cash, abruptly shoved it at me, and began screaming, "Here! Take it! Take it all! Anything to get you out of my store! Anything! Just leave!"
Naturally, I was shocked and appalled. Shocked and appalled that her words could not possibly be interpreted as a logical argument for my leaving her store. At best, she was making a mere appeal to greed -- which as you must already know is a fallacy. Nevertheless, I composed myself and quickly exited, but only after refusing the money -- I didn't want to give her the impression I could fall for such an illogical argument.
So now I'm wondering. Do I have any grounds for reasonably believing her behavior reflects that she had a sudden psychological fit of some sort? Perhaps some kind of seizure? There seems no other possible cause to it.
Well, I just thought I'd share a peculiar moment from my morning with you before getting into the much more exciting question of the practical differences between induction and abduction.
An Obvious Statement
Without doubt, one of the most famous statements in the long history of logic appears to us as a deceptively obvious premise. Naturally, I refer to the famous claim, "All men are mortal".
The statement seems so obviously true to us that we seldom if ever ask ourselves, "How do we actually know all humans are mortal?" Yet, it is only if and when we do ask that question that the thrills begin.
You see, there are only three kinds of logic -- deduction, induction, and abduction. Of the three, only induction and abduction have any chance at all of providing us with an empirical answer to our question. Poor old deduction by her very nature cannot.
Yet, induction and abduction when applied to the question produce very difference grounds for asserting its claim that all men are mortal. Very different grounds.
To induce or to abduct? That is the question.
To induce that all men were mortal, we might begin by compiling a huge database of births and deaths, searching the database for -- say -- "people over the age of 150 who are still living", and then when we find no one in that category, generalizing to the conclusion that "all humans die before the age of 151." i.e. "All humans are mortal".
But to abduce that all men are mortal, we would do something that is in a key way very different. We might begin the same way -- with searching a large database for anyone who had lived over 150 years. But then, instead of reaching a conclusion based on generalization --- we would reach a conclusion based on reasoning from the data to the most likely or best explanation.
To explain what reasoning to the best explanation means, try thinking of it this way:
- You begin with an observation, such as "No one in my data set lives past 150".
- Next, you ponder or research the issue in order to come up with a set of possible explanations or causes for your observation.
- Then you figure out which possible explanation or cause is the most likely or best explanation.
- Last, you announce to the world that you have discovered the best, most likely, or most probable explanation or cause of your observation and collect your Nobel Prize.
By the way, in the above case of the exploding store clerk, we cannot induce that she had a fit because we have no data set of store clerks having fits to show us the probability of her behavior being caused by a fit. However, we can abduce that she had a fit because that is the only reasonable cause of her behavior -- and hence, the most likely, best, or most probable explanation for it.
I mean, really? Can you think of any other reason she would have been so desperate for me to leave her store? I sure can't.
Last, there's a hot debate in logic about what is required for induction to show us the cause of something -- and whether it even can show us the cause of something. But I won't get into that debate here for fear of over-exciting my audience. There are only so many thrills a person can take in a single day, and I'll wager most of you are near your limit after having read this exciting post.
Questions? Comments?
