Deductive vs Inductive vs Abductive reasoning

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

• Deductive reasoning
• Inductive reasoning
• Abductive reasoning
• Conductive reasoning

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

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

The premises are the statements that are presented as the reasons why the conclusion of an argument should be accepted as valid.

Inference

An inference is a conclusion reached on the basis of evidence and reasoning.

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
• In a deductive argument the conclusion is definitely true if the premises are true, and they necessarily lead to the conclusion
• A deductive argument cannot have true premises and a valid inference but a false conclusion

Deductive arguments: Valid, Invalid, Sound

Deductive arguments fall into one of three categories:

• Valid
• Invalid
• Sound

Valid Argument

A deductive argument is valid argument if it has a form that would make it impossible for the premises to be true and the conclusion false, or if the conclusion follows necessarily from the premises.

Valid arguments don’t require the premises or the conclusion to be true

The validity of an argument has nothing to do with whether or not the premises or the conclusion are actually true or not. It only has to do with what would follow from the premises if they were true. A valid argument can have false premises and a false conclusion.

A deductive argument can be valid even if both the premises and the conclusion are false.

A deductive argument can be invalid even if both the premises and the conclusion are true.

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

Valid arguments focus on the form and structure of the argument, not the truth of the premises or the conclusion.

Valid argument example #1

P1: All dogs can fly

P2: Snoopy is a dog

C: Snoopy can fly

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

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

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 example #1

P1: Madrid is the capital of Spain

P2: Rome is the capital of Italy

C: Tokyo is the capital of Japan

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

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

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 the 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

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

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

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

Inductive reasoning (Using past experiences to make future predictions)

• Inductive reasoning is using past experiences to make future predictions
• Inductive reasoning deals 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 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 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 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 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…

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

Why?