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Induction and Deduction

Jack Flak

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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.
 

redacted

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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

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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

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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.
 

redacted

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

This is exactly my point.
 

Jack Flak

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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).
 

redacted

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^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

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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

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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.
 

redacted

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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 :)
 

Jack Flak

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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.
Nor did I say that, or think that. (I may have taken issue with other conclusions in the thread.)
 

redacted

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I didn't think you thought that. I was just frustrated because I couldn't word my position in a way that was clear to all y'all.
 

Orangey

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Well, "well-known" is a bit relative. I guess you could say it's well-known to the few people who care about informal logic :). But yeah, it's called the "reconstructive deductivist" position because the idea is to reconstruct informal (and typically so-called inductive, conductive, or abductive) arguments into syllogisms by making the unstated premise explicit. Basically what you described.

I was going to say more, but I think I need to go to sleep for now (lest I type out something totally incoherent and regret it later).
 

Orangey

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Nor did I say that, or think that. (I may have taken issue with other conclusions in the thread.)

I was really referring to those who posted elementary definitions of "deductive" and "inductive" as though doing so should clear up any confusion (the assumption being that dissonance has his definitions "incorrect").
 

The_Liquid_Laser

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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.

Heh, I've never heard of informal logic until your mention of it. After doing a quick scan of Wikipedia, it sounds like what I'd call "poor man's logic". I.e. a person can make a reasonable argument without formally studying logic, or they can use colloquial language rather than formal language and still have a reasonable argument. It sounds something like this to me. (I may be off.)

dissonance said:
One hidden premise in all induction is "the future resembles the past".

This has been bugging me since I've read it. It's quite possible to have induction without an assumption like this. Although for an INxJ the majority of their personal induction probably does use this assumption.
 

Magic Poriferan

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Heh, I've never heard of informal logic until your mention of it. After doing a quick scan of Wikipedia, it sounds like what I'd call "poor man's logic". I.e. a person can make a reasonable argument without formally studying logic, or they can use colloquial language rather than formal language and still have a reasonable argument. It sounds something like this to me. (I may be off.)

Well, my logic class talks substantially more about informal logic than formal logic. We did cover a lot of important things for formal logic, but my professor explained that through most of life. It's honestly a more practical skill than formal logic. Not that I dislike formal logic, but it's a bit ivory tower.


This has been bugging me since I've read it. It's quite possible to have induction without an assumption like this. Although for an INxJ the majority of their personal induction probably does use this assumption.

While that's true, I think we can agree that a strong inductive argument does usually work on the premise of some kind of repetition or large numbers. This is known as induction by enumeration. It is simple. and almost surely the most common form of inductive logic used. Sadly, it might be the most common form of logic used by humans in general.

It is true however that there are other kinds of inductive argument, Dissonance, but I would return to Laser by pointing out that they are all very similar to induction by enumeration. Reasoning by analogy, for instance, is still based on the notion that something happening before tells us what will happen now. The fact is, and I think this might be what Dissonance was trying to say, is that for induction to be useful on any complex level almost always requires it to be concatenated with deduction again. The value of statistics heavily lies in the concept of inductive logic, but to get them right, you'll need mathematical reasoning, which is deductive. To ultimately prove that your inductive arguments make more sense than someone else's, you'll have to run the premises through a test of cogency, which will again require deduction.
 

Orangey

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Heh, I've never heard of informal logic until your mention of it. After doing a quick scan of Wikipedia, it sounds like what I'd call "poor man's logic". I.e. a person can make a reasonable argument without formally studying logic, or they can use colloquial language rather than formal language and still have a reasonable argument. It sounds something like this to me. (I may be off.)

You've never heard of it? Most critical thinking and even intro to philosophical logic classes are based around informal logic. The study of fallacies? That's part of informal logic.

I don't know what you mean when you say that a person "can make a reasonable argument without formally studying logic, or they can use colloquial language rather than formal language and still have a reasonable argument." It is indeed the study of reasoning in natural language...the type that would be used in everyday examples of argument. People don't reason formally unless they're talking specifically about an issue within a formal language (that is, if we happen to be formal philosophers). Everything else is couched in natural language and in discourse.

The usefulness of studying formal logic (in terms of being able to reason better as a result of having studied it) is yet to be determined...but I would not be surprised if most people didn't really find it useful for "real" argument. The application of formal logic to "real world" argument is its own philosophical issue. In fact, there are some logicians that question whether formal notions of validity even really serve as good models by which to judge correctness in reasoning.
 

redacted

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I was really referring to those who posted elementary definitions of "deductive" and "inductive" as though doing so should clear up any confusion (the assumption being that dissonance has his definitions "incorrect").

Thank you!

This has been bugging me since I've read it. It's quite possible to have induction without an assumption like this. Although for an INxJ the majority of their personal induction probably does use this assumption.

Do you have an example? I honestly can't think of one. Applying any trend assumes this, including gravity, making 3d representations out of 2d info, etc.
 

The_Liquid_Laser

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You've never heard of it? Most critical thinking and even intro to philosophical logic classes are based around informal logic. The study of fallacies? That's part of informal logic.

All of my logic training comes from a mathematical context, so that is why I'm not familiar with it. Formal logic is very useful within the context of mathematics, but it's true that it's too rigorous to use formally among most people.

dissonance said:
Do you have an example? I honestly can't think of one. Applying any trend assumes this, including gravity, making 3d representations out of 2d info, etc.

Example: I hear that five of the people who are taking a piano class are Mary, Betty, Jennifer, Rachel, and Heidi. I conclude that only females take piano class.
 

redacted

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Example: I hear that five of the people who are taking a piano class are Mary, Betty, Jennifer, Rachel, and Heidi. I conclude that only females take piano class.

Ah. I see what you're saying.

I guess I would say it's still a hidden premise because you wouldn't make that inference if you hadn't made similar guesses and been right in the past.

Say you're in a universe with 8 possible worlds:
000
001
010
011
110
111
100
101

If you're trying to make an algorithm for guessing the third number from the first two, it's never going to be better than the opposite algorithm. This is a universe in which the future is not necessarily like the past. But if you chop off one of the possible worlds, you can make an algorithm that works, because you assume that the future is like the past, and you're right some of the time.

See what I'm saying?

Maybe my wording of the premise was a bit misleading.
 
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