The most significant applications of deductive reasoning are mathematics and philosophy, but making a comic strip about either of those would be difficult.

Wrong. Apologies but this misapprehension always gets me peeved. Deductive reasoning is the process by which one infers a conclusion with certainty, as opposed to inductive reasoning, which only infers a conclusion with probability. Nothing about specifics or generalities comes into it, at all, ever.

Yes, the most significant use might have been from maths and physics, but the most famous use of deductive reasoning is indeed in the crime world. THink Sherlock Holmes etc.

Come to think of it, that panel somewhat reminds me of the old 1970's sitcom Barney Miller, wherein one of the detectives was taking a phone call about a stolen car... he asks the caller for a description of the vehicle, repeating each detail (so we audience members know what he is hearing) as he jots it down on a form. As he repeats the ever-increasingly tasteless details that the caller is giving him, he finally says "maybe it wasn't stolen... maybe it ran away!"

Hey, when I went to confirm my post (which as I type this, is awaiting moderation), a pop-up in a flashing seizure-inducing frame announced "Congratulations--you've won!" and said that I was the 100,000 visitor. It also stated amid the flashing that it was not a joke.

I thought it more important to finalize my post/comment, rather than to click on the flashing ad. But hey, instead of the usual flurry of "first!" claimants you usually get, I claim "one hundred thousandth!"

Note from scott: Sorry about that. I'm not supposed to have those kinda ads here. I'll look into it.

Inductive reasoning is where you observe a pattern, and figure out what the following steps in the pattern would be. Great for math, because math is nothing but patterns. You got a series of numbers up to N, then you induce N+1.

Deductive reasoning is the complete opposite. You have a conclusion, and you try to guess what the pattern is. Impossible to do with math, at least without any clues, because there's literally an infinite number of ways to get a conclusion.

When it comes to people, though, the cases are opposite. With deductive reasoning, you have a conclusion (the pink RAZR is missing), and you have to find the series of events that lead to that conclusion (boss is a scatterbrain, boss would rather have other people do his work for him, boss likes to put small objects in places where he would easily lose them). Inductive reasoning isn't as good, because it involves a bunch of assumptions from trying to see patterns. You take a look at other people who also own pink RAZRs (13 year old girls) and people have lost things (usually because of a theft), and conclude that your boss's pink RAZR was stolen by a 13 year old girl.

So yeah, sorry to say that you got it wrong. Unless that was your intention. But that's not your style, so probably not. It's still a funny comic though.

@The Rugi: No, induction in math is, confusingly, entirely deductive reasoning. Inductive reasoning is separate from mathematical induction, despite the two sharing a common name. As Wikipedia correctly explains, "In fact, mathematical induction is a form of rigorous deductive reasoning." So, your first two paragraphs are entirely wrong. However, you are correct that Scott got it wrong.

hey chaps, 'deduction' and 'induction' do have technical meanings in logic and contemporary epistemology, but just because they have specialist meanings there, doesn't mean that those are the only meanings! They even have have different meanings in other specialist disciplines! Mathematical induction, as mentioned by The Rugi is not very much like enumeratio simplex, which is the thing normally called 'induction' in first-year philosophy classes. Electrical induction is something different again. 'Deduction' sometimes just means 'that which is deducted', e.g. a tax deduction.

Doyle didn't screw everyone up. He used it in an ordinary English sense, which has been around for at least 500 years. Newton refers to his reasonings as 'Deductions from Phenomena' in the Philosophiae Naturalis Principia Mathematica, and what he's doing there certainly isn't logical deduction as we know it.

Scott is a pretty capable user of ordinary American English, and he doesn't need to bow to specialist usage until Basic Instructions starts having titles like 'How to Prove Consistency of First-Order Logic'.

@ The Rugi. You have it backwords, all mathematics is, is deductive reasoning, because it only deals with truths that a given set of definitions and assumptions necessarily entail. For example, If 0 does not equal one, and if zero is not greater than 1, then it necessarily follows that 0 is less than 1. Everyone has known that mathematics relies on deductive reasoning since Euclid wrote The Elements. Before anyone else mentions XKCD, I am aware of it, it is not the worst comic I have seen by any stretch of the imagination, but something about it that I can not put my finger on frustrates me.

@Gregory Borgosian, @The Rugi: The Rugi's characterisations of inductive and deductive reasoning are actually fairly apt. Gregory is right in the sense that a proof in mathematics is the result of deductive reasoning, but The Rugi has it quite right that the conclusion is in most cases the starting point, not the end point, of the deductive investigation. Mathematicians don't very often start with a set of axioms and randomly start proving a whole lot of results until they find something interesting (although I'm sure this happens some times - maybe quite a bit now we have computers). The mathematician already suspects or hopes (or maybe even knows!) the intended result is true, or at least thinks it's worth investigating, and that's where the deductive proof-work starts. So how do they find the intended result? Well, often it's as The Rugi says - they've spotted a pattern, and they wonder whether it's true in all cases.

And strictly speaking proofs in mathematics over the last 2000 years often aren't deductive in the sense of logical deduction. They do make the occasional appeals to intuition — usually in very general ways that the mathematically-trained won't differ on, to be sure. One way of seeing the history of mathematics is the progressive elimination of the need of appeals to intuitions in proofs, although I don't think this was really adopted as an explicit goal until Frege, Russell and Hilbert in the late 19th and early 20th centuries.

All three types of reasoning are required for good detective work, but only deduction can be used to actually prove anything as true.

Abduction is basically a guess (or more formally, a hypothesis), a is derived from b with no basis other than b can sometimes follow from a. This is where you start in the reasoning process - the RAZR is missing, what are the possible explanations? Someone stole it is one way the RAZR would be missing, the guy simply lost it is another.

Induction is used to evaluate the abductions and allows us to gather evidence for the final deduction - b is implied by a (but b does not necessarily follow from a). These are things you expect to see if a is true. If someone stole the phone, what would you expect to see? What about if the guy simply lost it? This gives us a whole lot of a's that we know are true. Now we can deduce the answer.

Deduction is the proof - a is true, and b must follow from a. The guy misplaced his phone, therefore his phone was missing. Once you have the proper evidence, deduction is very, very easy. The trick is getting all of the proper evidence.

In real life, getting enough evidence for deductive reasoning is often not possible, so crimes are "solved" on the basis of very strong inductive reasoning instead of the unshakable deductive reasoning. This is why criminal court cases are adjudicated to the standard of "reasonable doubt" instead of "beyond all doubt".

A.C. Doyle's books were simply set up to allow Sherlock to find all of the evidence he needed to perform deductive reasoning, is all. Just because it isn't realistic doesn't mean it is wrong.

In common language we tend to call this entire process "Deduction".

## Reader Comments (28)

My sister acts like the dude in the last panel.

I didn't even know that they still produced RAZRs. I had thought that all the thirteen year olds that had them had grown.

The most significant applications of deductive reasoning are mathematics and philosophy, but making a comic strip about either of those would be difficult.

Panel 4 is excellent.

Wrong. Apologies but this misapprehension always gets me peeved. Deductive reasoning is the process by which one infers a conclusion with certainty, as opposed to inductive reasoning, which only infers a conclusion with probability. Nothing about specifics or generalities comes into it, at all, ever.

Otherwise, great post.

@Gregory Bogosian

Yes, the most significant use might have been from maths and physics, but the most famous use of deductive reasoning is indeed in the crime world. THink Sherlock Holmes etc.

Making a comic about mathematics and philosophy is certainly possible! http://www.xkcd.com/

Panel 3 made this one my new favorite. :D

Actually, what you're using here is called inductive reasoning. A.C. Doyle kinda screwed everyone up on that one.

I had a pink RAZR when I was thirteen.

Panel 4 halted work for a good ten minutes. FTW!

@Marshall

I said that it was difficult, I didn't say that it was impossible.

I rather liked panel 2 myself.

Come to think of it, that panel somewhat reminds me of the old 1970's sitcom Barney Miller, wherein one of the detectives was taking a phone call about a stolen car... he asks the caller for a description of the vehicle, repeating each detail (so we audience members know what he is hearing) as he jots it down on a form. As he repeats the ever-increasingly tasteless details that the caller is giving him, he finally says "maybe it wasn't stolen... maybe it ran away!"

Hey, when I went to confirm my post (which as I type this, is awaiting moderation), a pop-up in a flashing seizure-inducing frame announced "Congratulations--you've won!" and said that I was the 100,000 visitor. It also stated amid the flashing that it was not a joke.

I thought it more important to finalize my post/comment, rather than to click on the flashing ad. But hey, instead of the usual flurry of "first!" claimants you usually get, I claim "one hundred thousandth!"

Note from scott: Sorry about that. I'm not supposed to have those kinda ads here. I'll look into it.

@Marshall: Except that comic isn't any good.

@induction vs. deduction:

Sorry guys, you're both wrong. What you're looking at here is abduction.

Inductive reasoning is where you observe a pattern, and figure out what the following steps in the pattern would be. Great for math, because math is nothing but patterns. You got a series of numbers up to N, then you induce N+1.

Deductive reasoning is the complete opposite. You have a conclusion, and you try to guess what the pattern is. Impossible to do with math, at least without any clues, because there's literally an infinite number of ways to get a conclusion.

When it comes to people, though, the cases are opposite. With deductive reasoning, you have a conclusion (the pink RAZR is missing), and you have to find the series of events that lead to that conclusion (boss is a scatterbrain, boss would rather have other people do his work for him, boss likes to put small objects in places where he would easily lose them). Inductive reasoning isn't as good, because it involves a bunch of assumptions from trying to see patterns. You take a look at other people who also own pink RAZRs (13 year old girls) and people have lost things (usually because of a theft), and conclude that your boss's pink RAZR was stolen by a 13 year old girl.

So yeah, sorry to say that you got it wrong. Unless that was your intention. But that's not your style, so probably not. It's still a funny comic though.

Maybe we're all thinking Inception?

@Gregory Bogosian

There actually is a comic about math, philosophy, and velociraptors. It's called xkcd.

@The Rugi: No, induction in math is, confusingly, entirely deductive reasoning. Inductive reasoning is separate from mathematical induction, despite the two sharing a common name. As Wikipedia correctly explains, "In fact, mathematical induction is a form of rigorous deductive reasoning." So, your first two paragraphs are entirely wrong. However, you are correct that Scott got it wrong.

@Everyone

Induction, Deduction, or Abduction(nice one hahaha), the comic's still a great laugh.

hey chaps, 'deduction' and 'induction' do have technical meanings in logic and contemporary epistemology, but just because they have specialist meanings there, doesn't mean that those are the only meanings! They even have have different meanings in other specialist disciplines! Mathematical induction, as mentioned by The Rugi is not very much like enumeratio simplex, which is the thing normally called 'induction' in first-year philosophy classes. Electrical induction is something different again. 'Deduction' sometimes just means 'that which is deducted', e.g. a tax deduction.

Doyle didn't screw everyone up. He used it in an ordinary English sense, which has been around for at least 500 years. Newton refers to his reasonings as 'Deductions from Phenomena' in the

Philosophiae Naturalis Principia Mathematica, and what he's doing there certainly isn't logical deduction as we know it.Scott is a pretty capable user of ordinary American English, and he doesn't need to bow to specialist usage until Basic Instructions starts having titles like 'How to Prove Consistency of First-Order Logic'.

@ The Rugi. You have it backwords, all mathematics is, is deductive reasoning, because it only deals with truths that a given set of definitions and assumptions necessarily entail. For example, If 0 does not equal one, and if zero is not greater than 1, then it necessarily follows that 0 is less than 1. Everyone has known that mathematics relies on deductive reasoning since Euclid wrote The Elements. Before anyone else mentions XKCD, I am aware of it, it is not the worst comic I have seen by any stretch of the imagination, but something about it that I can not put my finger on frustrates me.

Dammit. I was hoping to learn about destructive reasoning. Or maybe reading comprehension.

@Gregory Borgosian, @The Rugi:

The Rugi's characterisations of inductive and deductive reasoning are actually fairly apt. Gregory is right in the sense that a proof in mathematics is the result of deductive reasoning, but The Rugi has it quite right that the conclusion is in most cases the starting point, not the end point, of the deductive investigation. Mathematicians don't very often start with a set of axioms and randomly start proving a whole lot of results until they find something interesting (although I'm sure this happens some times - maybe quite a bit now we have computers). The mathematician already suspects or hopes (or maybe even knows!) the intended result is true, or at least thinks it's worth investigating, and that's where the deductive proof-work starts. So how do they find the intended result? Well, often it's as The Rugi says - they've spotted a pattern, and they wonder whether it's true in all cases.

And strictly speaking proofs in mathematics over the last 2000 years often

aren'tdeductive in the sense of logical deduction. They do make the occasional appeals to intuition — usually in very general ways that the mathematically-trained won't differ on, to be sure. One way of seeing the history of mathematics is the progressive elimination of the need of appeals to intuitions in proofs, although I don't think this was really adopted as an explicit goal until Frege, Russell and Hilbert in the late 19th and early 20th centuries.Hmmm, Basic Instructions seems more like a place for....abductive reasoning.

http://en.wikipedia.org/wiki/Abductive_reasoning

Well alright! Thanks my fellow sleuth! I say, I thoroughly enjoyed that one! Seriousyly. Ripping with laughter!

Yay! Someone is wrong on the internet! ;)

All three types of reasoning are required for good detective work, but only deduction can be used to actually prove anything as true.

Abduction is basically a guess (or more formally, a hypothesis), a is derived from b with no basis other than b can sometimes follow from a. This is where you start in the reasoning process - the RAZR is missing, what are the possible explanations? Someone stole it is one way the RAZR would be missing, the guy simply lost it is another.

Induction is used to evaluate the abductions and allows us to gather evidence for the final deduction - b is implied by a (but b does not necessarily follow from a). These are things you expect to see if a is true. If someone stole the phone, what would you expect to see? What about if the guy simply lost it? This gives us a whole lot of a's that we know are true. Now we can deduce the answer.

Deduction is the proof - a is true, and b must follow from a. The guy misplaced his phone, therefore his phone was missing. Once you have the proper evidence, deduction is very, very easy. The trick is getting all of the proper evidence.

In real life, getting enough evidence for deductive reasoning is often not possible, so crimes are "solved" on the basis of very strong inductive reasoning instead of the unshakable deductive reasoning. This is why criminal court cases are adjudicated to the standard of "reasonable doubt" instead of "beyond all doubt".

A.C. Doyle's books were simply set up to allow Sherlock to find all of the evidence he needed to perform deductive reasoning, is all. Just because it isn't realistic doesn't mean it is wrong.

In common language we tend to call this entire process "Deduction".