Induction and Deduction

[Jack Flak]

Originally Posted by dissonance

Argh! Can't tell if you're just fucking with me.

You probably are.

I'm not. If you meant to say

The sun has risen every day
Therefore the sun will rise tomorrow

That's induction. If you meant to say

The sun always has and always will rise once per day
Therefore it will rise tomorrow

It's deduction based on a false premise. Because going by the best scientific knowledge available, the sun won't "rise" forever.

[evan]

Grrr, I always have a problem explaining my ideas to INTPs, especially with typing instead of talking.

Do you see my point about induction just being deduction with hidden premises? Or do I really need to think of another way to explain it?

[Jack Flak]

I believe I do fail to understand what you're getting at. I'll read the thread again, if you want to clarify feel free.

After reading the thread:

1. It seems some of you are agreeing that a specific line of inductive reasoning is actually deductive reasoning, which stumps me.
2. It seems the knowledge you seek is something outside the bounds of logical analysis, so I naturally have little interest. We're coming at it from very different perspectives. I see it as a very simple issue. "No, you can't really trust it. The end."

[reason]

Induction is not deduction, by definition.

Deduction: the logical content of the conclusion is a subset of the logical content of the premises.
Induction: the logical content of the premises is a proper subset of the logical content of the conclusion.

The set relation between the logical contents is reversed, and therefore, if induction was deductive, then there would be no induction, only deduction. However, inductive arguments are invalid, that is, the conclusion of an inductive inference can be false even when the premises are true, whereas deductive inferences are valid, that is, the conclusion must be true if the premises are true. In other words, there is a distinct, and important, difference between inductive and deductive inferences, which is qualitive and nontrivial.

I have spent way too long thinking about this, btw.

[evan]

Originally Posted by reason

Induction is not deduction, by definition.

Deduction: the logical content of the conclusion is a subset of the logical content of the premises.
Induction: the logical content of the premises is a proper subset of the logical content of the conclusion.

The set relation between the logical contents is reversed, and therefore, if induction was deductive, then there would be no induction, only deduction. However, inductive arguments are invalid, that is, the conclusion of an inductive inference can be false even when the premises are true, whereas deductive inferences are valid, that is, the conclusion must be true if the premises are true. In other words, there is a distinct, and important, difference between inductive and deductive inferences, which is qualitive and nontrivial.

I have spent way too long thinking about this, btw.

Grr. I must not have explained this correctly.

I know the definitions of induction and deduction. I've taken like 5 classes that have gone over this stuff. (I've also spent way too long thinking about this. And knowing you, I doubt we're gonna end up disagreeing; I just have trouble wording things in such an INTP way for you to understand right away.)

What I'm saying is that induction is actually a deductive process. "New" information that comes from the inductive process is not actually new. It's just restating the premises or some subset of the premises. The premises are hidden, though... they're not formally listed. But they're still there.

When you say, "the sun has risen every day, therefore it will rise tomorrow", that's induction. But really, you are making the same argument in a deductive way if you included the right premises. Like, if you include "things that I've noticed happen everyday will happen tomorrow with X likelihood", and "things that are some threshold of likely can be thought of as true", etc. it would be a deductive argument.

The real difference between induction and deduction is formality. Induction is less formal, because there are a bunch of hidden premises, and the premises are a bit more vague.

But reasoning has to be deductive. We are biological computers. There's no such thing as coming up with "new" information. Our minds are programs instantiated on the hardware of the brain. And computers are only capable of deduction.

Are you a determinist (you gotta be)? It's not like any atom that makes up our body can decide not to follow the laws of physics. If you think of each atom as a function, then you can think of the body as interactions between trillions of these functions. And functions are not capable of induction, or anything "new".

Each conclusion is come to via deduction if you think of every past state of our brain as a premise.

Do you see what I'm saying now?

EDIT:

Originally Posted by reason

if induction was deductive, then there would be no induction, only deduction.

This is exactly my point.

[Jack Flak]

Useful reasoning is very often inductive. We have to rely on our conclusions for our lives to have any significance to ourselves or others (Which is a goal of most humans, and therefore worth thinking about).

[evan]

^Yes you are right. Induction is used by us every second, multiple times. Coming up with a 3d representation of the world based on the 2d image on our retinas is an inductive problem that we solve all the time. Or choosing words to represent the concepts in our head, etc. etc.

But this thread is not going in the direction I want.

I'm trying to show that inductive arguments are a subset of deductive arguments. They're just informal, since the premises aren't all listed.

Someone please, hear me?

There is no such thing as coming up with new information. All you can do is come up with new ways to say the information you already have.

Man, I've repeated myself like 5 times already.

[Jack Flak]

I think I do "kinda" see where you're coming from, after you injected the notion of probablility into one of your deductions. But like I said, it's just not my bag of chips.

[Orangey]

The idea that all inductive arguments are actually deductive arguments with tacit (unstated or assumed) premises is called the "deductivist" position in informal logic. It is a legitimate theory in the field...dissonance is not crazy or incorrect to have made mention of it.

[evan]

Originally Posted by Orangey

The idea that all inductive arguments are actually deductive arguments with tacit (unstated or assumed) premises is called the "deductivist" position in informal logic. It is a legitimate theory in the field...dissonance is not crazy or incorrect to have made mention of it.

Ah. I wasn't aware this was a well-known position. Good to hear