Flawed Understanding of Deduction/Induction - where does it come from?

[MathHelp]

Hi everyone.

So I understand deduction to be any argument where the conclusion is certain to follow from the premises assuming those premises are true. With induction, the conclusion is only likely if the premises are true.

But I have noticed that in some academic circles, specifically related to criminology/criminal profiling that people seem to think things like:

1. "Induction is reasoning from the specific to the general" 

2. "Induction is when a conclusion is made using generalisations and probability" (those are types of induction, but not the only kind).

3. "Deduction is drawing conclusions from the physical evidence" (What?!?!?!?!?)

4. "Deduction is reasoning from the general to the specific". 

In each of these examples, I am referring to situations where a criminology textbook/expert has specifically made the distinction between induction and deduction. So it is not an example where a detective might have been giving an interview and then used the word "deduced" as a synonym for "I reasoned...".

I was wondering if anyone knew what is leading to all the confusion in a subject that is very clear about the definitions.

I would also add that the definitions found in criminology/profiling literature don't seem useful. For example, if you accept their definitions there is nothing more to learn. They don't begin to explain how to improve thinking when you are reasoning from the specific to the general or vis versa. It is as if they just give a definition for the limited purpose of being able to classify their thinking.

 

 

[studiot]

7 hours ago, MathHelp said:

Flawed Understanding of Deduction/Induction - where does it come from?

 

What a pity Imatfaal is no longer active as both a qualified legal professional and a talented amateur scientist he would have been the ideal member to answer this.
Legal people often have very penetrating thought processes and this question is largely about thought processes.

Anyway  deduction / Induction is a good topic to introduce (I will use that word again later) so +1

Both words are very important in many scientific disciplines and, as often happens, each discipline tailors the specific meaning to its own requirements.
Thankfully as far as I know everyone within a given scientific discipline agrees that meaning, unlike some terms.

Thank you for outlining what perhaps some legal system means by it, I was not aware of such a difference between science and the legal world.
But beware that legal systems can vary enormously in different parts of the world so what holds good in one country may not pertain in another.

 

We see that the words are important in English because they appear equally as the noun, verb and adjective, but all spring from the same root the Latin duco to lead.
The Greeks actually developed both concepts before the Romans but the Romans introduced both deductivus and inductivus.

The difference is that Induction is usually associated with introducing (I said I'd use that word again) the consequent, perhaps by some sort of causation or forcing of it. The consequent could stand alone from the introduction, which is important in maths.
Whereas deduction requires no such additional help, the consequent being inherent in the antecedent or premise(s).
Which means that so long as you have the antecedent the consequent is there, whether you acknowledge it or not.

Philosophy examines the situation whe

7 hours ago, MathHelp said:

is certain to follow from the premises assuming those premises are true.

Philosophy examines what happens when this is not true, maths does not, except in a few very special circumstances.

Edited December 15, 2022 by studiot

[Genady]

I wouldn't say these understandings are flawed. They are just different and are used for different purposes. BTW, there is also a mathematical induction, where a conclusion is as certain to follow from the premises as in deduction.

[studiot]

5 minutes ago, Genady said:

BTW, there is also a mathematical induction,

That's the whole point in maths.
You need the apparatus of maths to perform the induction.
Either by set theory or setting an equivalent condition or constraint.
There is a whole cadre of mathematicians who refuse to accept any inductive proof as a result.

[MathHelp]

9 hours ago, Genady said:

I wouldn't say these understandings are flawed. They are just different and are used for different purposes. 

I would normally agree but I don't think a conscious decision has been made for a new definition of induction/deduction to be created that better suites their needs.

The reason I think this is for several reasons:

The textbooks/academics/professionals I have come across treat deduction of having the feature of certain conclusions if the premises are true. But they do not define it that way. In one case a textbook gives the following example of the modus ponens rule of implication:

Quote

A

B

C

Therefore D.

This is clearly an inductive argument. The author actually used statements rather than letters but as they relate to crime it would not be appropriate to write what was said here. However, it was similar to this:

Quote

Joe was studying logic on Monday

Joe bought a logic textbook today

Joe is a student

Therefore Joe is enrolled in a logic course at university.

This is clearly an inductive argument and is certainly not a modus ponens deduction. However, even if we are generous and say that other disciplines are allowed to create their own definitions, I would hope you can agree that the conclusion given is not at all certain based on the premises and so the textbook is definitely wrong when it says deductive conclusions under their definition are certain if the premises are certain.

I would agree with you that the FBI definition (based on what a non-FBI profiler told me) that "inductive profiling is profiling based on generalisations and probability" is a definition that seems useful and does not exclude the possibility that FBI profilers work to improve their logical skill by studying induction.

The other problem is that the "deductive" (actually inductive) profilers criticise the FBI "inductive" profilers by saying "they can't know that, what if x, y, z?" which is a criticism that quite literally applies to their own methods.

There does not appear to be any value in learning these definitions of logic as none of the textbooks proceed to teach anything about how to do these uniquely defined methods of logic. In fact, they encourage you to take a logic course...

Quote

Philosophy examines what happens when this is not true, maths does not, except in a few very special circumstances.

Where can I read more about this? 

Quote

BTW, there is also a mathematical induction, where a conclusion is as certain to follow from the premises as in deduction.

Is this difficult for a none-mathematician to understand? I would like to know more about it. 

In any case, I assume that there is some benefit to to the definition?

Edited December 15, 2022 by MathHelp

[studiot]

Try reading through again what I have said to both yourself and Genady very carefully.

A point I was trying to make is that there is plenty of theory that comes before deduction / induction.

None of that is repeated in the definitions or theorems of deduction / induction, but it is all still potentially applicable.

For instance what is a deducton from a premise ?

Its structure is antecedent- connective - conclusion

So here goes

3 plus five makes eight.  Therefore  Uranus  is closer to the Sun than the Earth.

This introduces the idea of sound v unsound reasoning.

The premise is true, there is a connective, yet the conclusion is false

Because the reasoning is unsound.

This also works the other way.

 

 

[Genady]

1 hour ago, MathHelp said:

Is this difficult for a none-mathematician to understand?

I don't know how difficult it is for a none-mathematician to understand mathematical induction, but I don't think they would have any use of it.

Edited December 15, 2022 by Genady

[MathHelp]

2 hours ago, studiot said:

Try reading through again what I have said to both yourself and Genady very carefully.

A point I was trying to make is that there is plenty of theory that comes before deduction / induction.

None of that is repeated in the definitions or theorems of deduction / induction, but it is all still potentially applicable.

For instance what is a deducton from a premise ?

Its structure is antecedent- connective - conclusion

So here goes

3 plus five makes eight.  Therefore  Uranus  is closer to the Sun than the Earth.

This introduces the idea of sound v unsound reasoning.

The premise is true, there is a connective, yet the conclusion is false

Because the reasoning is unsound.

This also works the other way.

 

 

Oh, I understand all that. I thought you were meaning that there is an area in philosophy outside the subject of logic that deals with a fascinating situation where a sound deduction leads to in incorrect conclusion (which is obviously impossible - but you never know with philosophy).

But certainly, I understand that a sound deduction means that the premises are true and the argument is also valid.

It appears that you are making the same point as me. That is that there is plenty of theory (methods/techniques) that are involved in both deduction and induction. This is the very reason why I think the definitions being used by some criminologists/profilers (not talking about lawyers here actually, as I have only been reading the criminology stuff) are not useful. 

The FBI seems to be using a made up definition of inductive profiling that is consistent with inductive logic (two very specific types of induction). So I don't have a problem with what I have been told about their definition. It seems practical. If you are an FBI Profiler and you want to become better at making inductions, you can pick up a logic/statistics textbook and learn about things like Mills Methods, likelihood versus probability, and arguments from analogy.

But if you do "deductive" (not deductive as defined by logicians) profiling and you want to improve your "deductions" you have no starting point. You can't pick up a textbook on deduction and study it - because the logic they are using is actually induction. At the same time, they don't know that what they are doing is induction so they don't know where to find better information. The definitions they are using are therefore a hinderence. 

Edited December 16, 2022 by MathHelp

[wtf]

14 hours ago, Genady said:

I wouldn't say these understandings are flawed. They are just different and are used for different purposes. BTW, there is also a mathematical induction, where a conclusion is as certain to follow from the premises as in deduction.

Worth pointing out that mathematical induction is a deductive process. It's one of the Peano axioms and follows in ZF from the axiom of infinity. Proofs using mathematical induction are deductive, not inductive in the scientific or philosophical sense. 

Edited December 16, 2022 by wtf

[MathHelp]

36 minutes ago, wtf said:

Worth pointing out that mathematical induction is a deductive process. It's one of the Peano axioms and follows in ZF from the axiom of infinity. Proofs using mathematical induction are deductive, not inductive in the scientific or philosophical sense. 

That's true, it is literally a "argument from mathematics" but I think the point that they were trying to make is that in the field of mathematics people have used the word "induction" to mean something quite specific that is not the same as what a logician means. 

You could say something similar about the "deductive" criminal profilers. Deductive profiling is actually an inductive process.

The difference is that I assume that mathematicians have a good reason for creating their concept of induction (which is actually deduction) while "deductive" criminal profilers appear to have created their definitions out of ignorance. As far as I can tell they believe that a logician would completely agree with how they define deduction. 

The definition of "deductive criminal profiling" does not appear to have any purpose or benefit. It does not involve learning any skills that would help the profiler reason better. Criminal Profiling textbooks tend to offer a definition and then go on to argue how much better deduction is than induction. But they don't teach people how to actually make deductions according to their definition of what a deduction is. Not only that, a normal logic textbook is not helpful because a logic textbook would not classify what deductive profilers do as being deductive.