Mnemonics to remember Xductive reasoning

[RabbitWho]

Hello, you're looking absolutely fantastic today.

I think I get this for now:

Inductive Reasoning:
Nobody has every seen a cat in space. Therefore there are no cats in space.

Deductive Reasoning
Given that I think all cats are nice, and given that my cat is a cat, it can be deduced that I think my cat is nice.

Abductive Reasoning
My cat hasn't got testicles. Therefore, by abductive reasoning, the possibility that it is female is reasonable. Actually he's neutered.


But how do I remember which is which, any mnemonics? Concrete applications in daily life?

Also can you check that I have it right?



Thanks

 

[chiro]

Hey RabbitWho.

I think you have it right. Here are my own explanations:

Inductive: Try and extrapolate something that is beyond the domain of your knowledge by using something that is within your knowledge. One of the earlier famous cases of this was with Newton and Gravity and later with ElectroMagnetism where this too was seen as a fundamental force. What you are extrapolating is not within your domain of knowledge.

Deductive: Start with general properties to prove specific ones. If you have general assumptions, then you want to use these and transform them as necessary to arrive at a specific conclusion that maintains all initial assumptions.

So for concrete examples, induction is something like physics (and science in general to a large extent) where we observe a tiny fraction of things and try to generalize it beyond that tiny fraction of observation. Deduction is basically the axiom -> proof thing that mathematicians use when they already have set the axioms and want to prove something more specific than the axioms themselves. Abductive is hypothesis testing.

In short: inductive -> what some of science (particularly physics) does, deductive -> what mathematicians often do.

 

[RabbitWho]

Thanks! That's really helpful.

 

[MLP]

Two observations.

1. All deductive reasoning does not proceed from the general to the specific, at least not in any straightforward way. Consider the following valid, deductive argument that appears to go from the specific to the general.

Only Alice and Bill are on the hill.
Alice has blue eyes.
Bill has blue eyes.
Therefore, everyone on the hill has blue eyes

2. Valid inductive arguments, but not valid deductive ones, can be made invalid by the addition of more information. Consider the following argument.

95% of all who smoke two packages of cigarettes daily over an extended period have contracted lung disease.
Jones has smoked two packages of cigarettes over an extended period.
Therefore, Jones will contract lung disease.

If we add the additional piece of information that Jones is a member of the lucky 5% that smoke two packages of cigarettes but do not contract a lung disease, the above argument is no longer valid.

 

[RabbitWho]

95% of all who smoke two packages of cigarettes daily over an extended period have contracted lung disease.
Jones has smoked two packages of cigarettes over an extended period.
Therefore, Jones will contract lung disease.

If we add the additional piece of information that Jones is a member of the lucky 5% that smoke two packages of cigarettes but do not contract a lung disease, the above argument is no longer valid.

I don't think that's a valid argument unless you say "Jones will most likely contract lung disease" instead. I don't think it can be valid when there is such uncertainty in it.

I could be wrong though, this is new to me.

What about this:Every person who smokes two packages of cigarettes daily over an extended period has some lung problems.
Jones has smoked two packages of cigarettes over an extended period.
Therefore, Jones will have lung problems.Oh wow, look! Jones hasn't got lung problems! He's the first one ever!

What would you say now, that the argument was invalid? Or that the argument was still valid with the information that you had at the time but that the information turned out to be wrong. So now the argument is still valid but it's incorrect.

 

[MLP]

Hi RabbitWho,

I am okay with your amendment. We could even go further and require that the conclusion be "Jones has a 95% chance of contracting lung disease".

I am appealing to our pre-analytic notion of what a valid inductive argument is since I know of no precise definition of inductive validity that's universally accepted.

The point I was making stands though.

Best Regards

 

[MLP]

Let 'S' be 'x smokes two packs of cigarettes over an extended period'
Let 'L' be 'x has lung problems'
Let 'a' be 'Jones'

Then the argument

(\forallx)( Sx \rightarrow Lx)
Sa
Therefore, La

is deductively valid. So if it turned out that \negLa, I would say we must give up one of the premises.