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Deductive vs Inductive vs Abductive reasoning

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Aristotle, Argument, Logic, Deductive reasoning, Inductive reasoning, Abductive reasoning, Conductive reasoning, Critical Thinking

In this article I’m going to explain the four different types of reasoning:

You might have heard of deductive and inductive reasoning before, and found it all pretty damn confusing.

In this article I’m going to demystify it and make it easy to understand.

Why do you need to know this?

Every form of argumentation and reasoning falls into one of the following four categories. The better you understand them, the clearer and sharper your thinking and argumentation will be.

“Deduction, induction, and abduction are like three parts of the same puzzle, and all formal reasoning is done using them and only them. Without abduction there is no hypothesis, without induction no testing, and without deduction no way to falsify; i..e. not only is there no logic or reason without these methods, there is no science (and essentially no philosophy). They are simply names for the aspects of human reason.” – FactMyth.com

Let’s begin:

Quick definitions

Let’s quickly define some terms:

Premise

Premises are statements that are presented as the reasons why an argument should be accepted as valid.

Inference

An inference is a logical connection between two statements. To infer is to conclude something from indirect evidence, or from what someone else implied.

Syllogism

A syllogism is an argument that has the form of:

Premise 1: (Major Premise)

Premise 2: (Minor Premise)

Conclusion

Throughout this article I’ll be using the following abbreviations:

P1: (Major Premise)

P2: (Minor Premise)

C: (Conclusion)

Note: Arguments aren’t “true” or “false”

Academics, philosophers and scientists don’t talk about arguments being “true” or “false”, “right” or “wrong” etc.

Arguments aren’t “true” or “false”, only individual statements are.

Argumentation uses different terminology depending on whether an argument is:

  • Deductive
  • Inductive
  • Abductive
  • Conductive

I’ll explain this terminology clearly in this article.

Deductive reasoning

  • Deductive reasoning is a “top-down logic” meaning it starts with a general premise e.g. “All men are mortal”, and leads toward a specific conclusion e.g. “Socrates is mortal” (Deductive reasoning goes from the general to the specific)
  • “Deductive” means the conclusion is “drawn from” the general principle
  • In a deductive argument the conclusion is already contained within the premises, and always follows directly from the premises, without deviating or abstracting in any way. There is nothing in the conclusion of a deductive argument that is not contained within the premises
  • Deductive arguments aim towards certainty. In a deductive argument the conclusion is definitely true if the premises are true, and they necessarily lead to the conclusion

Deductive arguments: Valid, Invalid, Sound

Deductive arguments fall into one of three categories:

  • Valid
  • Invalid
  • Sound

Valid Argument

A valid argument is one where if the premises were true, then they would necessarily lead to the conclusion

Valid arguments don’t require true premises

Note: This doesn’t mean that the premises are true, in fact, both the premises can be false, and the argument can still be valid

A valid argument is simply one where if the premises were true, they would necessarily lead to the conclusion

Valid arguments focus on the structure of the argument, not the truth of the premises

Valid argument example #1

P1: All dogs can fly

P2: Snoopy is a dog

C: Snoopy can fly

Note: Obviously dogs can’t fly, however if the premises were true that all dogs could fly, and that Snoopy was a dog, then it would necessarily lead to the conclusion that Snoopy could fly

Valid argument example #2

P1: All cats can dance

P2: Garfield is a cat

C: Garfield can dance

Note: As far as I know cats can’t dance, however if it were true that all cats could dance, and that Garfield was a cat, then the premises would necessarily lead to this conclusion

Valid argument example #3

P1: All parents are younger than their children

P2: Homer and Marge are parents

C: Homer and Marge are younger than their children

Note: Again, the premises aren’t true, however if it were true that all parents were younger than their children, and that Homer and Marge were parents, than the premises would necessarily lead to this conclusion

Invalid Argument

Any deductive argument that isn’t valid is invalid

I.e. Any argument that isn’t structurally valid, where the premises don’t necessarily lead to the conclusion, is invalid

Invalid arguments can have:

  • No true premises
  • One true premise
  • All true premises and a true conclusion

However, even if both the premises are true, and the conclusion is true, if the premises don’t necessarily lead to the conclusion, then the structure of the argument is invalid, and the argument itself is invalid

Invalid argument example #1

P1: Barcelona is the capital of Spain

P2: Rome is the capital of Italy

C: Tokyo is the capital of Japan

Note: In this example both the premises are true, and the conclusion is true, however the premises don’t necessarily lead to this conclusion, so the argument is invalid

Invalid argument example #2

P1: All NBA players play basketball

P2: My friend plays basketball

C: My friend is an NBA player

Note: In this example both the premises are true, however they don’t necessarily lead to this conclusion. Just because all NBA players play basketball, that doesn’t mean that everyone who plays basketball is an NBA player. This is an example of the logical fallacy affirming the consequent (Just because all P are Q, that doesn’t mean all Q are P)

Invalid argument example #3

P1: Tiger Woods is one of the greatest golfers of all time

P2: Tiger Woods has won over 15 major championships

C: Tiger Woods is the greatest athlete of all time

Note: Tiger Woods maybe the greatest golfer of all time, the GOAT, but that doesn’t necessarily mean that he’s the greatest athlete of all time. The premises don’t necessarily lead to this conclusion

Sound argument

A sound argument is a valid argument with all true premises

The structure of a sound argument is valid, and the premises are true

Sound arguments are the strongest form of argument

Sound argument example #1

P1: A Billionaire has more money than a homeless person

P2: Jeff Bezos is a Billionaire

C: Jeff Bezos has more money than a homeless person

Note: Both the premises are true, and they necessarily lead to the conclusion

Sound argument example #2

P1: China has a population of 1.4 Billion

P2: Israel has a population of 9 Million

C: China has a greater population than Israel

Note: Both the premises are true, and they necessarily lead to the conclusion

Sound argument example #3

P1: LeBron James is 6′ 8″

P2: Kevin Hart is 5′ 4″

C: LeBron James is taller than Kevin Hart

Note: Both the premises are true, and they necessarily lead to the conclusion

Inductive reasoning

  • Inductive reasoning is a “bottom-up logic” in which conclusions are drawn from several observations and lead toward a general premise (Inductive reasoning goes from the specific to the general)
  • “Inductive” means the observations are “drawn into” a general principle
  • Inductive arguments deal with probability not certainty. In an inductive argument if the premises are true, it’s highly likely the conclusion will be true, but it’s not 100% guaranteed e.g. If you fall out of a Skyscraper you will probably die but it’s not 100% certain
  • Inductive reasoning can abstract and deviate from the information contained in the premises. Conclusions can rely upon inferences and contain new information not contained in the premises
  • Inductive reasoning is less certain that deductive reasoning, but it’s more practical and useful in day to day life. We use inductive reasoning to make future predictions based upon our past experiences e.g. the sun will come up tomorrow, the laws of physics will continue to hold, effects will continue to follow causes etc.

Inductive arguments: Strong, Weak, Cogent

Inductive arguments fall into three categories:

  • Strong
  • Weak
  • Cogent

Strong argument

An inductive argument is strong if the conclusion probably follows from the premises

Strong argument example #1

P1: Most sprinters are faster than most bodybuilders

P2: Usain Bolt is a sprinter, Arnold Schwarzenegger is a bodybuilder

C: Usain Bolt is probably faster than Arnold Schwarzenegger

Strong argument example #2

P1: Magician David Blaine can hold his breath underwater for 17 minutes

P2: I don’t think I could hold my breath underwater for 60 seconds

C: David Blaine could probably hold his breath underwater longer than me

Strong argument example #3

P1: James Holzhauer is one of the greatest Jeopardy contestants of all time

P2: Paris Hilton wasn’t known for being the sharpest tool in the shed

C: James Holzhauer would probably beat Paris Hilton in a game of Jeopardy

Note: All three of the above examples are almost virtual certainties, however there still exists the slightest possibility, no matter how infinitesimal, that the conclusion could be wrong

Weak argument

An argument is weak if the either one of the premises are untrue, or if the conclusion is unlikely to follow from the premises

Weak argument example #1

P1: Cancer is one of the leading causes of death

P2: My grandmother died

C: My grandmother must have died of cancer

Note: The conclusion doesn’t necessarily follow from these premises. The cause of death could have been cancer, diabetes, heart disease, stroke, any number of things, not necessarily cancer

Weak argument example #2

P1: Alex Jones said the Sandyhook massacre was a staged hoax

P2: Conspiracy theorists say things like the earth is flat, and the world is run by shape-shifting reptilians

C: All conspiracy theories are bullshit

Note: This is a giant leap in logic that isn’t warranted by the premises. Just because most conspiracy theories are bullshit, that doesn’t mean they all are

Weak argument example #3

P1: My sister went to see the faith healer Benny Hinn to heal her broken ankle

P2: The faith healing didn’t work, my sister still has a broken ankle

C: It must be because she didn’t have enough faith

Note: This argument is weak because it presupposes that Benny Hinn (or “God” working through Benny Hinn) really can heal people. It also concludes that the only reason she wasn’t healed was because she “didn’t have enough faith”, when in reality she probably wasn’t healed because Benny Hinn can’t really heal people and the whole thing is an act.

Cogent arguments

A cogent argument is a strong argument with all true premises

Cogent arguments are the strongest form of inductive arguments, and the 2nd strongest argument after a sound argument

Cogent argument example #1

P1: The odds of winning the Mega Millions Lottery are approx. 1 in 300 million

P2: I bought a ticket to the Mega Millions Lottery

C: I probably won’t win the Mega Millions Lottery

Both the premises are true, and it’s a strong argument because it’s almost certain that you won’t win the Mega Millions Lottery

Cogent argument example #2

P1: The United States has the most powerful military in the world

P2: Mongolia has one of the smallest militaries in the world

C: If the United States went to war with Mongolia, the US would probably win

Cogent argument example #3

P1: Brian Shaw is the current title holder of the “World’s Strongest Man”

P2: My friend doesn’t even lift weights

C: Brian Shaw is probably stronger than my friend

Uncogent argument

Any inductive argument that is weak is uncogent by default.

For a more detailed description: Inductive Reasoning

Not to complicate things but let’s quickly look at…

The problem of induction

The problem of induction in a nutshell:

We don’t know if inductive reasoning leads us to knowledge.

Why?

Inductive reasoning presupposes:

  • The laws of nature will remain uniform (the “principle of uniformity”)
  • The future will resemble the past e.g. the sun will come up tomorrow, the laws of physics will continue to hold, effects will always follow causes etc.

All inductive reasoning has us making future predictions based on past experiences and observations e.g. every time we drop something we assume it’ll fall to the ground, because that’s what happened every other time.

However as David Hume the famous Scottish Philosopher noted in his famous “Problem of Induction” in 1739, there is no way to justify this. Just because the laws of nature were uniform in the past, that doesn’t mean they necessarily must be in the future.

The only way to justify believing that the future will resemble the past, and that the laws of nature will remain uniform, is that’s how it was in the past. In other words: In the past the future resembled the past, so in the future it will continue to resemble the past. That’s circular reasoning.

Long story short: We have no good answer to the problem of induction. However, just because we’re not sure that inductive reasoning leads us to certain knowledge about reality, it’s not going to stop us from using it because it’s practical and useful, and it works more often than not.

For a more detailed breakdown: The Problem of Induction

Abductive reasoning

  • Abductive reasoning is “inference to the best explanation”, it’s simply taking an educated guess at the “most likely” explanation for an observation, or set of observations, given the limited data and evidence you have
  • If you have conflicting evidence, or multiple competing hypothesis, you go with the simplest and most likely explanation, the one with the best evidence
  • Abductive reasoning, like inductive reasoning, isn’t perfect and doesn’t guarantee that the conclusion is correct even if the premises are correct, however it’s very useful because we’re always working with limited, data, evidence, information etc.

Abductive argument example #1

P1: Two prisoners are locked up together, one a violent serial killer, the other a child molestor

P2: The next morning a prison officer walks by the jail cell to see the serial killer standing over the dead body of the child molestor who has blood oosing out of his head

C: The serial killer murdered the child molestor

Note: Yes it could be that the child molestor somehow commited suicide, or died of a sudden heart attack or stroke and hit his head on the concrete as he fell down, however it seems more likely that he was murdered by the serial killer

Abductive argument example #2

P1: Children are assigned homework from their teacher and asked to hand it in the following morning

P2: One child who doesn’t pay much attention in class and never does his homework, claims the next day that his dog ate his homework

C: The child didn’t do his homework

Note: It could be that the child’s dog really did eat his homework, however it seems more likely that he didn’t do his homework and is using the “dog ate my homework” as an excuse

Abductive argument example #3

P1: You tell a secret to only one person

P2: The next day everyone knows your secret

C: That person told other people your secret

Note: It could be that other people somehow guessed your secret, however it’s more likely that that person betrayed your trust and told other people your secret

For a more detailed description: Abductive Reasoning

Conductive reasoning

Note: Not all academics, philosophers, scientists etc. accept conductive arguments as a valid form of reasoning, however I will share it here for your reference

  • A conductive argument has multiple independent premises that are convergent, that don’t depend or rely on each other. Each premise counts separately in support or against the conclusion. If one or more premises were removed from the argument, the argument would still stand
  • Conductive arguments may even include “counter-premises” that go against the conclusion
  • A popular example of a conducive argument are the lists of pros and cons that people use to make decisions

Conductive argument example #1

  • P1: Thailand is a popular holiday destination
  • P2: I’m in the mood to go on holiday
  • P3: Thailand has cheap accommodation, food, entertainment etc.
  • P4: The weather in Thailand is nice right now
  • P5: Flights to Thailand are cheap
  • C: I’ll go on holiday to Thailand

Conductive argument example #2

  • P1: The All Blacks are the favorites to win the 2019 Rugby World Cup
  • CP2 (Counter Premise): The All Blacks used to be Rugby World Cup chokers (choking in 1991, 1995, 1999, 2003, 2007)
  • P3: The All Blacks have won the last two Rugby World Cups back-to-back (2011, 2015)
  • P4: The All Blacks boast an 89% winning percentage since 2012
  • CP5: Ireland has beaten the All Blacks in two of the last three games
  • P6: The All Blacks overall winning record against Ireland is 28-2
  • C: The All Blacks will win the 2019 Rugby World Cup

Conductive argument example #3

  • P1: Donald Trump is the odds on favorite to win the 2020 election
  • CP2: A new Glengariff Group poll has both Bernie Sanders and Joe Biden leading Trump in a hypothetical 2020 matchup by 53% to 41%
  • P3: I don’t trust polls. Remember the bullshit statistics that said Hillary Clinton was going to win in a landslide and had a 90% to 99% chance of winning the 2016 US Election?
  • C: Donald Trump will win the 2020 election

Things to watch out for in an argument

Before we conclude, I quickly want to point out some things to look out for when you’re evaluating an argument.

Ask yourself:

  • Are the premises true?
  • Are the premises relevant to the conclusion? (If you can remove a premise without making a difference to the conclusion, then the premise is irrelevant)
  • Do the premises necessarily lead to the conclusion?
  • Are all terms clearly defined so everyone is on the same page?

You should also watch out for:

  • Ambiguous language
  • Hidden premises
  • Definitional retreats
  • Non sequitur – statements that don’t follow from the previous statement
  • Red herring – statements used to distract from the issue at hand
  • Shifting of the burden of proof – the burden of proof always lies on the one making a claim e.g. if I claim to be able to read minds or predict the future, then it’s up to me to provide evidence that I can, it’s not up to you to provide evidence that I can’t
  • Weasel words

If you want an in-depth breakdown: How to win an argument

Summary

Let’s recap a few points:

Deductive reasoning

Deductive reasoning is a “top-down logic” meaning it goes from a general premise to a specific instance

Deductive arguments aim towards certainty. In a deductive argument the conclusion is definitely true if the premises are true, and they necessarily lead to the conclusion

Deductive arguments fall into one of three categories:

  • Valid – a valid argument is simply one where if the premises were true, they would necessarily lead to the conclusion
  • Invalid – any deductive argument that isn’t valid is invalid
  • Sound – a valid argument with true premises

Words associated with deductive reasoning:

“Definitely”

“Certainty”

“Necessarily”

Inductive reasoning

Inductive reasoning is a “bottom-up logic” in which conclusions are drawn from several observations and lead toward a general premise (Inductive reasoning goes from specific instances to general premises)

Inductive arguments deal with probability not certainty. In an inductive argument if the premises are true, it’s highly likely the conclusion will be true, but it’s not 100% guaranteed. The conclusion from an inductive argument can be wrong, even if the premises are true

Inductive arguments fall into three categories:

  • Strong – an inductive argument is strong if the conclusion probably follows from the premises
  • Weak – any inductive argument that isn’t strong is weak
  • Cogent – a cogent argument is a strong argument with all true premises

Words associated with inductive reasoning:

“Probably”

“Most likely”

“Chances are”

Abductive reasoning

Abductive reasoning is “inference to the best explanation”, it’s simply taking an educated guess at the “most likely” explanation for an observation, or set of observations, given the limited data and evidence you have

Conductive reasoning

Conductive arguments have multiple independent premises that are convergent, that don’t depend or rely on each other. Each premise counts separately in support or against the conclusion. If one or more premises were removed from the argument, the argument would still stand

I hope this article simplifies things!

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