Logic vs emotion

[IndigoRose]

My preference for a dichotomy would be between "logical" and "intuitive", because intuition really stands for a decision basis that you might at first have a great deal of trouble quantifying, but if you do, it's the better and more logical basis.

Intuitive is such an emotionally loaded word for some people. The dichotomy for me is situations where I use deduction, and situations where I use induction ... but one does not become the other. They are serving two different purposes.
IndigoRose

 

[BillHoyt]

The dichotomy for me is situations where I use deduction, and situations where I use induction ... but one does not become the other. They are serving two different purposes.
IndigoRose

You are drawing too strong a dichotomy here and you err when you say "one does not become the other." Induction is the engine that delivers new premises to deduction. Deduction is incapable of creating new truths; it can only uncover truths latent within the premises.

 

[IndigoRose]

You are drawing too strong a dichotomy here and you err when you say "one does not become the other." Induction is the engine that delivers new premises to deduction. Deduction is incapable of creating new truths; it can only uncover truths latent within the premises.

Induction can supply you with a new theory. Deduction can assist you in analysing it. One does not become the other. I am not sure where you see an error.
IndigoRose

 

[BillHoyt]

Induction can supply you with a new theory. Deduction can assist you in analysing it. One does not become the other. I am not sure where you see an error.
IndigoRose

"Theory" is a scientific construct. "Induction" is a logical construct. Deduction does not assist in analyzing induction.

I go to a field in New England and see hundreds of orange day lillies. I drive further west and stop at another New England field and see dozens of orange day lillies. Onto New York, where I stop at a huge field and see thousands of orange day lillies. It is the same in Ohio. And Indiana. Everywhere I go I see orange day lillies and only orange day lillies. I induce: "All day lilllies are orange."

That is a conclusion of the induction, and a premise to any deduction. Now I dig up a dozen day lilly tubers, from many different fields, and plant them in my yard. They are about to bloom. I deduce:

All day lillies are orange
These plants about to bloom are day lillies
Therefore these plants about to bloom are orange.

Induction is the logic engine that supplies new premises to deduction.

 

[IndigoRose]

Induction is the logic engine that supplies new premises to deduction.

We are saying the same thing, so I don't understand why you see an error. The process of producing the premise is different than the process that proves the premise.
IndigoRose

 

[BillHoyt]

We are saying the same thing, so I don't understand why you see an error. The process of producing the premise is different than the process that proves the premise.
IndigoRose

I'm hoping that this post makes it clear we're not saying the same thing. I think you have the misconception that deduction proves the initial premises. It doesn't. Go back over the example I posted. Induction created the universal premise about day lillies. Deduction predicted instances of day lillies based on the premise. It said that these day lilllies, as yet unblooming, will be orange. That is simply a prediction about specific cases.

 

[IndigoRose]

I think you have the misconception that deduction proves the initial premises.

No, I don't, and I don't know where you got that idea.
IndigoRose

 

[BillHoyt]

No, I don't, and I don't know where you got that idea.
IndigoRose

Perhaps it might serve the discussion better for you to address the substance of my post?

 

[IndigoRose]

Perhaps it might serve the discussion better for you to address the substance of my post?

You said, "I think you have the misconception that deduction proves the initial premises." and I disagreed with your assumption.
IndigoRose

 

[BillHoyt]

You said, "I think you have the misconception that deduction proves the initial premises." and I disagreed with your assumption.
IndigoRose

Well, then I must misunderstand this statement of yours: "The process of producing the premise is different than the process that proves the premise." You wrote it in response to my statement: "Induction is the logic engine that supplies new premises to deduction. " Please explain what you meant, then.

 

[IndigoRose]

Well, then I must misunderstand this statement of yours: "The process of producing the premise is different than the process that proves the premise." You wrote it in response to my statement: "Induction is the logic engine that supplies new premises to deduction. " Please explain what you meant, then.

Induction, going from the specific to the general, supplies a hypothesis, or a premise. That process of producing hypotheses is different than the deduction used to prove a hypothesis.
IndigoRose

 

[BillHoyt]

Induction, going from the specific to the general, supplies a hypothesis, or a premise. That process of producing hypotheses is different than the deduction used to prove a hypothesis.
IndigoRose

Induction proves induction. Period. End of story. Deduction does not prove induction. How many times must I repeat myself? I provided an example of both previously. Induction produces new premises. Deduction is NOT used to then prove those premises. Induction did that already.

If you still don't get this, then please provide examples.

 

[IndigoRose]

Induction proves induction.

No, induction does not prove the hypothesis it creates.

Deduction does not prove induction.

I did not say that deduction proves induction

Induction produces new premises.

Yes, I said that already, several times.

Deduction is NOT used to then prove those premises.

I *am* saying that induction is used to create a hypothesis. I am *not* saying that deduction proves a premise.
IndigoRose

 

[BillHoyt]

No, induction does not prove the hypothesis it creates.



I did not say that deduction proves induction



Yes, I said that already, several times.



I *am* saying that induction is used to create a hypothesis. I am *not* saying that deduction proves a premise.
IndigoRose

You obviously have no idea what you are talking about. Provide examples or citations or stop wasting our time and go away.

 

[IndigoRose]

You obviously have no idea what you are talking about. Provide examples or citations or stop wasting our time and go away.

You said, "I think you have the misconception that deduction proves the initial premises." and I disagreed with your assumption.

IndigoRose

 

[BillHoyt]

"Induction can supply you with a new theory. Deduction can assist you in analysing it."

Wrong.

"Induction, going from the specific to the general, supplies a hypothesis, or a premise. That process of producing hypotheses is different than the deduction used to prove a hypothesis. "

Wrong.

I have asked you to provide examples or citations. Please do so. If you fail to do so with your next post, then this is my last post to you on this topic.

 

[IndigoRose]

BillHoyt's premise: "I think you have the misconception that deduction proves the initial premises"

Your premise is incorrect. I do not think that. Since your premise is incorrect, that is as far as it needs to go.
IndigoRose

 

[IndigoRose]

[No message]

 

[drkitten]

"Induction can supply you with a new theory. Deduction can assist you in analysing it."

Wrong.

"Induction, going from the specific to the general, supplies a hypothesis, or a premise. That process of producing hypotheses is different than the deduction used to prove a hypothesis. "

Wrong.

I have asked you to provide examples or citations. Please do so. If you fail to do so with your next post, then this is my last post to you on this topic.

This is verging on the silly, but it's also typical of your rather short-sighted view of the practical aspects of mathematical thought.

Have you ever noticed that lots of even numbers (greater than four) appear to be the sum of two odd primes?

6 = 3 + 3
8 = 5 + 3
10 = 3 + 7 = 5 + 5
12 = 7 + 5
100 = 97 + 3 = 93 + 7 = 89 + 11 = ...

Induction suggests a hypothesis : Every even number (greater than 4) is the sum of two odd primes. (This, of course, is the famous Goldbach conjecture.)

Induction, as shown, will generate the hypothesis, but to prove the hypothesis will require deductive reasoning. If you figure out a suitable deductive argument "proving the hypothesis," let me know. I -- and most of the number theory community -- would be interested.

q.e.d.?

(Edited to fix rather embarassing typo.)

 

[IndigoRose]

Have you ever noticed that lots of even numbers (greater than four) appear to be the sum of two odd primes?

6 = 3 + 3
8 = 5 + 3
10 = 3 + 7 = 5 + 5
12 = 7 + 5
100 = 97 + 3 = 93 + 7 = 89 + 11 = ...

Induction suggests a hypothesis : Every even number (greater than 4) is the sum of two odd primes. (This, of course, is the famous Goldbach conjecture.)

Induction, as shown, will generate the hypothesis, but to prove the hypothesis will require deductive reasoning. If you figure out a suitable deductive argument "proving the hypothesis," let me know. I -- and most of the number theory community -- would be interested.

q.e.d.?

I like your example. Thanks.
IndigoRose