Hume and Induction...

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Hume and Induction...

Postby Gigafrost » Mon Apr 07, 2003 5:50 pm

First of all, I'd like to identify Induction for y'all. Induction is pretty much a generalization of events. It comes in two forms: I've seen alot of green emeralds, therefore all emeralds are green; The sun will rise tomorrow because it's risen every day.

In addition, I'd like to identify what Deduction is. It is the use of logic and tautologies such that the conclusion *has* to be true if the premisses are true.

Alot of our decisions and knowledge are based upon Induction; it is what we do naturally. Hume saw a problem with Induction, and what he saw is pretty damaging. His arguement was that Induction was not rational, and that would mean that almost everything we know is not justified, and we would then know next to nothing. Basically, his two arguements go like this:


Proof 1: The Principal of the Uniformity of Nature
1. All Inductions have as a hidden premiss that the universe is uniform (aka, the future will resemble the past at time...known as "the Principle of the Uniformity of Nature", henceforth said as PUN).
2. In order to be rational, an arguement must have all its premisses be rational.
3. In order for induction to be rational, PUN must also be rational.
4. If PUN is rational, then it can be rationalized with either deduction or induction.
5. PUN cannot be proven with Induction because it would be circular reasoning \ begging the question.
6. PUN cannot be proven with Deduction because the universe is not, by definition or by logic, required to be uniform.
7. Therefore, PUN is not rational.
8. Therefore, Induction is not rational.

Proof 2: Reliability
1. Induction can be rationally justified if it is shown to be reliable.
2. To show it is reliable, you must provide an inductive or deductive arguement for the reliability.
3. Induction cannot be argued for reliability with Induction, again because of the question-begging.
4. Induction cannot be argued for reliability with logic and definitions
5. Therefore, Induction cannot be shown to be reliable.
6. Therefore, Induction cannot be rationally justified.


So, this leaves us in a weird place. Are we able to counter both of these proofs?

Well, Strawson argued that Induction is, by definition, a rational activity. He says that this doesn't save Induction from reliability, but it's still rational. Sober's (the author of the textbook) arguement against this is the example of a recipe: if you have a recipe for a cake that you argue is an excellent (rational) recipe, yet you have no reason for thinking that the recipe would result in a nice cake (reliablitiy), that would sound silly.

I would argue that Induction is, by definition, a rational activity. It is the rational use of PUN. But this doesn't change the fact that the results are dependant on PUN and the knowledge is gone, so that kind of leads to a dead end.

Next, Max Black argued that it wouldn't be question begging to prove induction with induction. He says that:

1. Induction has been highly reliable in the past.
2. Therefore, Induction will be highly reliable now.

is a valid proof of it. The problem with this is it opens the way for non-sensical proofs. Take the example of counter-induction. It works the opposite way Induction does. Here's a proof of counter-induction using counter-induction:

1. Counter-Induction has been highly unreliable in the past.
2. Therefore, counter-Induction will be highly reliable now.

Quite problematic, eh? Well, after thinking about this some, I've wondered if there is any merit to analyzing why Counter-Induction would be flawed in a way that induction wasn't. A couple of ideas I've had are:

1. In order to prove and disprove Counter-Induction using Counter-Induction, the opposite condition must first be true. In other words, Counter-Induction seems to be self-contradicting.
2. The arguement for counter-induction has that counter-induction is both true and false. This shows contradictions that would allow you to assume anything you want.
3. Counter-Induction cannot work with PUN, so perhaps it works with the Prinicpal of the dis-uniformity of nature? One potential problem with this, though, is that by being dis-uniform, it would become uniform in that sense. So, counter-induction either has no supporting principals, or it has a component that can be considered inductive, which is contradictory to the definition of counter-induction.

To end, Sober offers some of his own ideas. To begin with, he talks about background assumptions. If you assume that the universe is uniform then there's no problem with induction. You can also assume in-between inductions to solve this problem. When talking to somebody, if you are looking to construct a rational arguement for another person, you are free to use whatever the both of you hold to be true.

Also, Sober discusses how Hume is trying to disconnect beliefs about the future with beliefs about the present and how it is similar to Descartes' attempt to connect indubitable beliefs with present and past observations. If you believe these connections are deductive, you are lead to skepticism. So, you're forced to believe in your own connections between them.

Anywho, I've got to go to class, so thoughts\comments\arguements\etc...
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Postby Gigafrost » Mon Apr 07, 2003 9:21 pm

Alrighty, back home from class, so I'm going to add some more onto the thoughts.

Basically, another thought I had for proving these proofs against Induction wrong involves putting Deduction through the same trials. The hope is to either prove the logic wrong or to see why exactly Deduction can dodge the treatment. Although I haven't worked it out in detail, I think the result would be the reassurance that Deduction is a sort of "necessary" inference, IE, it is an inference that is rational in every possible world, while Induction is a "contingent" inference, IE, only rational in worlds where the universe is uniform, with us having good reason to believe that the universe is uniform.

Today in class we talked about another supposed problem with Induction...the grue problem of induction. Basically, it works like this...

First, you define the color grue...
X is grue if and only if either x is green and has been examined before 2010, or x is blue and hasn't been examined before 2010.

Now, let's say you've seen 100,000 emeralds, all of which are green. You'd then end up with this arguement:

I have seen 100,000 emeralds, all of which have been green
-----------------------------
Therefore, by induction, all emeralds are green.
-----------------------------
Therefore, all emeralds are also grue.
-----------------------------
Therefore, we have seen all emeralds before the year 2010.

Kind of a startling conclusion, hmmm? Well, I think my instructor made too big a deal out of it. Pretty much, after thinking about it alot, I see that the transition from green to grue is a logical fallacy.

G(x) says "for the given emerald 'x', it has the property of being Green"
R(x) says "for the given emerald 'x', it has the property of being gRue"
E(x) says "for the given emerald 'x', it has the property of being examind before 2010"
AxG(x) says "for all emeralds 'x', they have the property of being green"

Also, I'm going to use the following symbols for logical "operations":

<-> means "iff" or "is equivalent to"...think of it as "both sides are the same thing"
-> means "implies"...basically, it says that if the left piece is true, then the right one has to be true. Believe me, it's different...
~ means "not"...pretty much, if something is "true" or "false" then if it has a ~ attached to the left, it returns the opposite
^ means "and"...it's true if both the left and the right side of it are true...
v means "or"...it's true if either side is true...

So, we can construct the definition of Grue...

AxR(x) <-> Ax( (G(x)^E(x)) v (~G(x)^~E(x)) )

Now, the above arguement claims...

AxG(x) -> Ax( (G(x)^E(x)) v (~G(x)^~E(x)) )

But if you'll notice, the E(x) appear out of nowhere in that formula! If you look closer at the requirement to be a grue, you'll see that there something has to have one or the other of these properties...

G(x)^E(x)
~G(x)^~E(x)

Both of them require that the examination be mentioned, yet the examination of the emeralds has not been generalized! This is where the grue problem originates from...the instructor was talking about how it brings up the problem of "when" we should induct, so maybe I've got an answer...

The examination of the emeralds has to be generalized in order for the grue logic to work, yet this seems silly. Why is that? Well, first off, it is doing something very interesting in that it is saying that a sample *is* the overall population, and that is contradictory to what Induction is! In addition, Induction would eventually confirm this generalization to be wrong, as if we assumed we've seen all the emeralds there are to see, but then somebody shows us more emeralds, then inductively, we can conclude that the induction for the examination of *all* emeralds is wrong because it's been wrong 100% in the past!
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Postby Gigafrost » Wed Apr 09, 2003 5:14 pm

Originally posted at another message board
The problem is that the world is not necessarily rational/logical and that we simply do not understand it all.


Exactly! If the world itself is not necessarily rational or logical, then neither are the conclusions and beliefs we gather based upon it, and if induction, which requires the world to have some ration, does not work, then almost everything we know is not justified. This is why the problem with induction is seen as a skepticism problem...it denies that we are justified in believing anything from induction, and in so doing, it is denying us any ability at all to argue that we know most of the things we know.



*this is where my post turns to other thoughts I've had*



So, we have to find some way to justify induction, and the simplest way to do that is to state that induction is, by definition, rational. The problem then is that we've got to prove that the universe has enough uniformity to justify the results of using induction. Thinking about it some, I think I can make a convincing arguement that shows that there is enough uniformity to justify induction. It follows like this:


If the universe did not have enough uniformity to justify induction, then most good inductive activities would result in a false answer.
But most good inductive activities don't result in a false answer.
----------
Therefore, it is not the case that the universe does not have enough uniformity to justify induction.
----------
Therefore, the universe has enough uniformity to justify induction.


Because this is a deductive arguement, in order to disagree with the conclusion you'd have to disagree with one of the premisses, so to cover that...

Premiss #1: If the universe did not have enough uniformity to justify induction, then most good inductive activities would result in a false answer.
My defense for it:
Of course, this is hard to justify because if the universe had no uniformity then at times it would seem like it did (because being non-uniform is being uniform, in a sense). It would be a completely random universe. Now a world like that would not agree with the above statement, since it'd be random if most were false or not. However, once you start getting closer to a uniform idea of the universe, you'll find that the above if statement is *way* more likely to be true, since there are then more and more uniformities and disuniformities (and the if statement works with either of those). So, in order to believe that the if statement above has 0 chance of being right, you would have to believe that the universe is totally random...that events happen with and without causes. That the sun may or may not rise tomorrow for any or no reason. I believe that most people will find it hard to believe the sun will randomly not rise on a day...

Premiss #2: But most good inductive activities don't result in a false answer.
My defense for it:
This is the harder of the two to defend, imo, since the definition of a "good inductive arguement" can be hard to nail down. In addition, people can just as easily argue that I don't know that most result in a non-false answer. I'll tackle the "non-false" wording...it's important because I'm not saying that the inductions are all true...I'm saying that they're not pointing in the wrong direction. The importance of this is that I'm saying the results of the good inductive activities are reliable indicators of what the truth might be. Induction isn't designed to be exact, so it is unfair to expect the answers to be exact.

I am not going to attempt to nail down what a "good inductive arguement" is because of how much it varies, but I would say that one way of finding good inductive arguements would be to find out what made certain inductions go wrong. Simple things like noticing that the sample size was way too small (for example, you only looked at 1 crayon and decided that all crayons were that color), or maybe the sample size was biased (for example, you ask all your friends what they think of you and you conclude that everybody thinks you're a nice friend).

Anywho, that thought's finished...I think...
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Postby Gigafrost » Thu Apr 10, 2003 1:55 am

Phew. If you've been wondering why there have been so few replies here, and you probably have, it's because it's very long and deals with equations and so on and so forth.

Yeah, I've been putting alot of thought into this.

Wait a minute one of the perps, Sober used an assupmtion.

Doesn't
he
needs to first prove this assumption before he can use it?

Not necessarily, but if he has a questionable premiss\assumption then he'll need to defend why he made it in order for people to believe him. The thing about deduction is that in order for it to really be deductive, the conclusion *has* to logically follow from the premisses. That doesn't mean the premisses have to be true, though, and that's the best way to destroy a deductive arguement...that is, to explain how a premiss isn't necessarily true...

how can you declare counter-induction as a dis-uniform principle, but then by it becoming uniform by following those laws, be considered entirely fasle just because of that fact? How can you explain something like that without describing rules for which it lives by. It would then become something unexplainable, and thus beyond our reach, correct? If there is something that is false in all senses but one, can it be called true? Nope, its still false. But damnit, this is a dead end in the fact that if something is true in all senses but one, it effectively becomes false. Bad example. Nothing can be drawn from Counter induction, like much can be drawn from induction. The thing you seem to be questioning here is if induction is true/false, compared to deduction. Deduction is the use of true/false statements to get an answer. Can you use deduction to define induction, or the rules of it, or how about counter-deduction. You’re using one of the methods being compared, and because it cannot be put into question when it is not as still standing as induction (ie you’re putting fingerprints all over the only evidence we have).

I think one of the important things you've talked about was that counter-induction, by being the reverse of induction, would have uniformity, and that would sort of make it self-contradicting...I think that's what you said...so hopefully we're just rewording the same thing, there?

And, actually, I'm trying to prove that induction is true\rational... and i think part of the biggest problem you've presented is that Hume tried to analyze Induction with Deduction and that might very well be the reason why this problem has occured...because Induction is not Deduction...

As for fingerprints all over the evidence...I'm kind lost what you mean...

Here’s a good question. How can you define deduction, using induction. Turn it around, giga, and you’ll find it as impossible as defining induction through deduction.

It sounds like your question is very similar to my thoughts about "putting deduction through the same trials"...because, as you said, it even puts the rationality of deduction into question. I attack that below...

Can induction be described/proved through induction? Or deduction through deduction?

Well, I talked about Induction "proving" Induction some...but not Deduction proving Deduction. The funny thing is, if you can't prove induction with induction, then likewise you can't prove deduction with deduction without running into the same problems, so then the only way to prove deduction would be with induction, which isn't supposed to be rational, which would mean that deduction isn't rational, which throws everything out of balance!

Is there any other mode of thinking in which to solve these answers?

Maybe Abduction, which is you have an observation and you come up with some hypothesis that tries to explain it, and you choose the hypothesis that most explains the observation...although I haven't quite explored using it...yet...

I find thinking of something in a certain way, with a certain mentality, may get your answer, but you will have to start over with a different thought process to get your answer many times for the deeper questions. Like I said in the “lost people” thread, that different languages stress different ways of thinking, and learning entirely different languages may make you more apt to answer these questions. Or at least I theorize.

And it's an interesting idea, however the two main cannons of philisophical thinking, Induction and Deduction, are based upon basic human thinking patterns (ie, we naturally categorize things), and necessary truths. The only weird one is abduction, methinks. I think that if Induction, Deduction, or Abduction can't be used to find an answer, though, then it won't be possible to find one.
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Postby TerraFrost » Thu Apr 10, 2003 2:21 am

Giga... i hope your not disappointed by lack of replies here, atm. you *do* have a lot of material posted, and... afaik, while you may be doing this an assingment, i myself have other assingments to do...

and unlike most of the replies you have been recieving, it is my hope to give you a reply that *had* some thought put into it... this, as opposed to some of the sorta "generic" "adlib" replies you have been getting...
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Postby Dracofrost » Thu Apr 10, 2003 3:13 am

Personally, I believe in induction, simply because it works. It's pretty much one of the main basis' of the scientific method, no? It's got us far enough along, right? I mean otherwise we wouldn't be able to go into space or get online or any of those great technological things that wouldn't be possible without science having advanced to the point that it has, right? I'm probably babbling and not adding anything to the debate, but blah...
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Postby Gigafrost » Thu Apr 10, 2003 3:34 am

Terra: It'd be nice to hear any kind of response...I need to develope my ideas more than anything else...even if the responses are "generic" it allows me to better get an idea of what I'm thinking about...if your post ends up being really good and thoroughly thought-out, that's nice! But I certainly don't require that you kill your extra time or anything...and if all I can work with is "generic" posts, then by golly, I'm going to work with "generic" posts... (note that I'm not planning on copying this over to CR for the overall debate, nya?)

Personally, I believe in induction, simply because it works. It's pretty much one of the main basis' of the scientific method, no? It's got us far enough along, right? I mean otherwise we wouldn't be able to go into space or get online or any of those great technological things that wouldn't be possible without science having advanced to the point that it has, right? I'm probably babbling and not adding anything to the debate, but blah...

And, induction certainly seems to work, and Hume argues we're not justified in thinking that because that observation is, itself, an induction. He says we can't prove induction with induction because it's circular reasoning.

So, my suggestion for getting out of that is two-part. First, you assume that induction is, by definition a rational use of "The Principal of the Uniformity of Nature," and then to show that PUN is reliable. To do that, it involves your observation that induction works. You say...

If nature didn't have any uniformity then induction wouldn't work very often.
Induction works often.
Therefore, the universe has some uniformity.

And viola! ^_^ Basically, even though I made it look complicated, I'm trying to give a good reason for you to believe in induction for that same reason... :)
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Postby Gigafrost » Thu Apr 10, 2003 3:39 am

Another post with a very good point:
When it gets this twisted, i like to hide behind Goedel's Thoerem. Not everything valid in a logical system can be proven in said system, provided the system is large enough to be useful.

That said, i have a problem with Hume's arguement.

Proof #2, Reliability. What is reliable? Since Hume has not, apparently, provided the definition he used, let's go by the Dictionary.Com definition. What interests me in these definitions is this one:

2. Yielding the same or compatible results in different clinical experiments or statistical trials.

Come to think of it, any and all measures of reliability are inductive, and rest solely on the PUN. Arguing that we must prove reliabiliy, which is an inductive quality, without using induction is silly. It merely leads into reductio-ad-absurdum arguements, whre any attempt to prove anything is countered with "You can't prove it'll be that way next time"


I didn't think about that...that reliability *is* inductive...hmmm....
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Postby TerraFrost » Sun Apr 13, 2003 12:56 am

I've seen alot of green emeralds, therefore all emeralds are green


there are two sorta conclusions you can draw from a statement like that... the first one goes something like this...

you're defining something for which a definition already exists. if you decided to call everything that has a light wavelength of 510nm as green (well, that actually is what green light is, hehe) then everything that is green is going to have a light wavelength of 510nm. that's a biconditional. with this statement... what makes an emerald an emerald? a certain combination of atoms? the first half of the sentance assumes that you already know what an emerald is. the second half adds something to the definition... an emerald is a combination of atoms *and* is green. that means that something with the same combination of atoms thats red must have some other name... which is entirely possible. i mean, there isn't some universal rule that says every object that has its own name must be fundemental characteristics. you can label objects as brown based on their color. you can label objects as stones based on their physical apperance. there's nothing that says you can't do that.

to tie this back to the orig. statement... if you want all emeralds to be green, than green is what they'll be.

however... if you're saying that because every combination of atoms that you've seen that constitutes an emerald is green, that all combinations of atoms are green... well... aside from being a logical fallacy... it's association (ie. every pizza i've had is tasty, so when i think of pizza, i think "yum"). unless you change the definition, then it's always going to be just that (an association). science isn't based on association. science doesn't say that because all compounds are green that it'll always be green. rather... science actually attempts to say *why* a compound is green. textbooks do association.

Proof 1: The Principal of the Uniformity of Nature
1. All Inductions have as a hidden premiss that the universe is uniform (aka, the future will resemble the past at time...known as "the Principle of the Uniformity of Nature", henceforth said as PUN).
2. In order to be rational, an arguement must have all its premisses be rational.
3. In order for induction to be rational, PUN must also be rational.
4. If PUN is rational, then it can be rationalized with either deduction or induction.
5. PUN cannot be proven with Induction because it would be circular reasoning \ begging the question.
6. PUN cannot be proven with Deduction because the universe is not, by definition or by logic, required to be uniform.
7. Therefore, PUN is not rational.
8. Therefore, Induction is not rational.


i agree. i don't think induction is rational. induction seems to me to be a synonym for association (as i explained above), but... that doesn't mean that it is without merit. to take a page from statistics... if all the emeralds you've seen are green, and you've only seen two, then... 100% of emeralds are green. if you've seen 1000 emeralds, and their all green, then you can safely say that 100% of emeralds are green. now that technically doesn't mean that all emeralds are 100% green. there is some margin of error, all the same. for example... if you've seen two emeralds that are green, 100% are green. that 100% can easily become 66%, though, if you find another emerald thats red. if you've seen 1000 emeralds that have all been green, then statistically, you can safelly assume that the next one you find will be green... and the next one, and the one after that, etc. i mean, if you assume that the emerald right in front of you is going to be red, then there's still a 99.999% chance that it won't be.

of course, that still doesn't mean every emerald is green... nor does it *technically* mean that most emeralds are green. but... if it ended up that most emeralds *weren't* green then... the odds of your first 1000 emeralds being green would be astronomical... and it would be safer to assume that there was some sort of higher power behind it. this higher power doesn't necessarily have to be god, though. it could just be that you're color blind to all colors except green, heh. or perhapes you collected all your emeralds from some creek and that creek had something in the water that turned emeralds green or something. too eliminate this sort of doubt, you really need to chose as wide an area as possible to pick emeralds from, but... no matter what you do, you won't get every area... even if you *did* manage to get the entire Earth, you'd still have to worry about other planets...

so... associations are sound, imho, based on statistics, alone, but... they aren't scientific, nor are they strictly rational, persay.

whew... that much just for like the first two or so paragraphs, hehe :)

now... you'll have to forgive me if i don't reply to everything else you wrote, right now :lila:

also... afaik, you're writting this for a paper... if you get scholarships or whatever because of my ideas, hehe... just point out to them that they are *my* ideas... not that i wouldn't want to become rich and famous, yourself, but... i don't want you to enjoy fame at the cost of my fame :lila:

if it came down to that, hehe... i'm sure you'd find your own fame in something :)

also... my post "scientific theory" sorta applies these things in an almost political sort of way :)
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Postby Nyufrost » Sun Apr 13, 2003 4:05 am

There is just entirely too much material here to reply to sensibly so I can understand why Terra has chosen just one aspect to focus on.

I don't think that *any* of this applies to how ordinary people think in everyday circumstances therefore is quite limiting in what it pertains to so it seems a bit far-fetched to apply such anaysis to everyday events.

Because, if you do that, then pretty much everyone is irrational at almost all times in almost everything they think.

I think another good example of the emerald comparison is a common argument used by many men.

Suzy is unhappy with something JoeBob has done and complains therefore he concludes that Suzy is a bitch with PMS. All of his friends say the same thing about their wives, gf's, female friends and females in general. Therefore, it becomes a generally accepted conclusion among men that any women who complain for any reason are bitches with PMS.

Most of these men have no clue what PMS really is. Of those who do, most of them have absolutely no inkling as to whether the woman is experiencing it or not. All they *know* is she has complained --or said something they don't want to hear-- therefore she must be a bitch and she must have PMS.

So, I would have to say induction is indeed pretty irrational.
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Postby Gigafrost » Sun Apr 13, 2003 5:41 am

Nyufrost wrote:There is just entirely too much material here to reply to sensibly so I can understand why Terra has chosen just one aspect to focus on.

I don't think that *any* of this applies to how ordinary people think in everyday circumstances therefore is quite limiting in what it pertains to so it seems a bit far-fetched to apply such anaysis to everyday events.

Because, if you do that, then pretty much everyone is irrational at almost all times in almost everything they think.

I think another good example of the emerald comparison is a common argument used by many men.

Suzy is unhappy with something JoeBob has done and complains therefore he concludes that Suzy is a bitch with PMS. All of his friends say the same thing about their wives, gf's, female friends and females in general. Therefore, it becomes a generally accepted conclusion among men that any women who complain for any reason are bitches with PMS.

Most of these men have no clue what PMS really is. Of those who do, most of them have absolutely no inkling as to whether the woman is experiencing it or not. All they *know* is she has complained --or said something they don't want to hear-- therefore she must be a bitch and she must have PMS.

So, I would have to say induction is indeed pretty irrational.

Alrighty, I'll tackle this first since it's smaller...hehehe...

Pretty much, the example you gave is not an example of Induction, but of bad induction. Of *course* it'll be irrational, and people will use it irrationally. How is it bad? It's biased, that's how, and bias ruins induction's results. In your example, the sample size was also too small, and that is another thing that throws induction's results off. Now, I know that some of this was attemptedly analyzed in Terra's post, but forget that for this response. I'll respond more deeply to those thoughts later.

In any case, Induction goes much deeper than your example. If It's irrational, then so is almost every observation we've made for science. Gravity? Doesn't exist on other planets. DNA exists? Not in things we haven't looked at yet. Will the sun rise tomorrow? No reason to believe it will.

Basically, that's the problem. If you say induction is irrational then so is *every* conclusion we've come to because of observations, which would be pretty much everything. But do you believe the sun will rise tomorrow? Then there has to be times where Induction would be rational or else our world will collapse around us. That's the problem that I'm trying to solve...

TerraFrost wrote:there are two sorta conclusions you can draw from a statement like that... the first one goes something like this...

you're defining something for which a definition already exists. if you decided to call everything that has a light wavelength of 510nm as green (well, that actually is what green light is, hehe) then everything that is green is going to have a light wavelength of 510nm. that's a biconditional. with this statement... what makes an emerald an emerald? a certain combination of atoms? the first half of the sentance assumes that you already know what an emerald is. the second half adds something to the definition... an emerald is a combination of atoms *and* is green. that means that something with the same combination of atoms thats red must have some other name... which is entirely possible. i mean, there isn't some universal rule that says every object that has its own name must be fundemental characteristics. you can label objects as brown based on their color. you can label objects as stones based on their physical apperance. there's nothing that says you can't do that.

Well, there seems to be some assumptions you're working with here that make it a problematic discussion, specifically, that emeralds have a definition and is a combination of atoms and such. The point of the example is not why it's green or what it is. The idea is that we've got alot of somethings we identify as emeralds and we have no idea what properties they have, but all the ones we see are green. If we assume that it's made of atoms in a certain order and such then we're making assumptions about the nature of reality. Induction isn't supposed to be dependant on reality.

Of course, this might be exactly what you were trying to do with this...or not. It's hard to say...

to tie this back to the orig. statement... if you want all emeralds to be green, than green is what they'll be.

however... if you're saying that because every combination of atoms that you've seen that constitutes an emerald is green, that all combinations of atoms are green... well... aside from being a logical fallacy... it's association (ie. every pizza i've had is tasty, so when i think of pizza, i think "yum"). unless you change the definition, then it's always going to be just that (an association). science isn't based on association. science doesn't say that because all compounds are green that it'll always be green. rather... science actually attempts to say *why* a compound is green. textbooks do association.

Well, regardless of what science does or not, Induction is supposed to be the basis of science, not the other way around. However, I think the main point here does underly something (that maybe you were trying to point out that I couldn't pull out...). Pretty much, the results of induction aren't supposed to be a sure thing. It says around what you'd expect. So in the emerald case, you'd expect every emerald you see afterwards to be green. That doesn't mean you'll see a red emerald, but that the specific emerald won't have the ability to be called an "emerald." It would seem that induction is a labeling system for the "norm" example and a measurement for how often you could expect to run into that.

I think a good example of this would be pizza. Let's establish that pizza tastes good. Then, when we eat pizza that tastes good, we call it pizza. But when it tastes bad, we call it bad pizza. If it tastes extra good then it's really good pizza. But the "bad" and "good" attachments tell you how they differ from the norm, right?

Well, maybe you were hinting at this and I just didn't get it, but that an interesting distinction.


i agree. i don't think induction is rational. induction seems to me to be a synonym for association (as i explained above), but... that doesn't mean that it is without merit. to take a page from statistics... if all the emeralds you've seen are green, and you've only seen two, then... 100% of emeralds are green. if you've seen 1000 emeralds, and their all green, then you can safely say that 100% of emeralds are green. now that technically doesn't mean that all emeralds are 100% green. there is some margin of error, all the same. for example... if you've seen two emeralds that are green, 100% are green. that 100% can easily become 66%, though, if you find another emerald thats red. if you've seen 1000 emeralds that have all been green, then statistically, you can safelly assume that the next one you find will be green... and the next one, and the one after that, etc. i mean, if you assume that the emerald right in front of you is going to be red, then there's still a 99.999% chance that it won't be.

So, you're saying it'll only be somewhat right, correct? But what Hume's proof did is it established that there's no rational reason to think about it being even somewhat correct. Take the example of the sun rising. We think there's a good reason the sun will rise tomorrow, but what Hume established was that there's no reason to believe it will. Even if we've seen it rise for the past 20 years, there's still no reason according to Hume. Not a 99% chance, not a 50% chance, not even a 1% chance.

of course, that still doesn't mean every emerald is green... nor does it *technically* mean that most emeralds are green. but... if it ended up that most emeralds *weren't* green then... the odds of your first 1000 emeralds being green would be astronomical... and it would be safer to assume that there was some sort of higher power behind it. this higher power doesn't necessarily have to be god, though. it could just be that you're color blind to all colors except green, heh. or perhapes you collected all your emeralds from some creek and that creek had something in the water that turned emeralds green or something. too eliminate this sort of doubt, you really need to chose as wide an area as possible to pick emeralds from, but... no matter what you do, you won't get every area... even if you *did* manage to get the entire Earth, you'd still have to worry about other planets...

so... associations are sound, imho, based on statistics, alone, but... they aren't scientific, nor are they strictly rational, persay.

Now, it might not be strictly rational, but Hume argued that it had no rationality at all. Statistics themselves are induction. Even with associations, that doesn't tackle the problem that it's using the assumption of the Principal of the Uniformity of Nature (PUN), so even though we've made interesting observations about induction, we're still stuck. :\

whew... that much just for like the first two or so paragraphs, hehe :)

now... you'll have to forgive me if i don't reply to everything else you wrote, right now :lila:

also... afaik, you're writting this for a paper... if you get scholarships or whatever because of my ideas, hehe... just point out to them that they are *my* ideas... not that i wouldn't want to become rich and famous, yourself, but... i don't want you to enjoy fame at the cost of my fame :lila:

if it came down to that, hehe... i'm sure you'd find your own fame in something :)

also... my post "scientific theory" sorta applies these things in an almost political sort of way :)


Hehehe, when I write my paper I'm going to make sure ideas that weren't mine are marked as not mine, but by people's on-line names. I, personally, don't have any interest in stealing other peoples' ideas and I plan on using everybody's "screen names" if I use their ideas in the paper. I'll have to start writing it first, though, before I know how much I've got to pad it with other ideas, yes?

But, that said, your ideas aren't a total waste of time in that case, either. It helps me question my own ideas and strengthen my arguements (to me, anyways) for when I actually write about my own idea... :)
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Postby TerraFrost » Sun Apr 13, 2003 6:49 am

Well, there seems to be some assumptions you're working with here that make it a problematic discussion, specifically, that emeralds have a definition and is a combination of atoms and such. The point of the example is not why it's green or what it is. The idea is that we've got alot of somethings we identify as emeralds and we have no idea what properties they have, but all the ones we see are green. If we assume that it's made of atoms in a certain order and such then we're making assumptions about the nature of reality. Induction isn't supposed to be dependant on reality.

Of course, this might be exactly what you were trying to do with this...or not. It's hard to say...


actually, hehe... the point I was trying to make here wasn't about induction at all :)

although thinking about it I guess it sorta could be, heh... is language inductive? because all emeralds we see are green, do we narrow the definition and say all emeralds are whatever they were before and green, too, now?

Well, regardless of what science does or not, Induction is supposed to be the basis of science, not the other way around.


well... i may have misspoken... when i said science i meant theories... not the process through which those theories are... discovered. we don't use induction to explain the world around us. or atleast i've never heard of any scientific theory that said "because it's been this way for x number of times, it'll be this way again". scientific theories come up with reasons... ie. an emerald is green because the resonate at 510hz (i'm just making that up). that's not induction, but it was sorta discovered through induction...

So, you're saying it'll only be somewhat right, correct? But what Hume's proof did is it established that there's no rational reason to think about it being even somewhat correct. Take the example of the sun rising. We think there's a good reason the sun will rise tomorrow, but what Hume established was that there's no reason to believe it will. Even if we've seen it rise for the past 20 years, there's still no reason according to Hume. Not a 99% chance, not a 50% chance, not even a 1% chance.


hume doesn't address probability at all. he just says you can't say it at all. that's what i'm saying, but... i'm saying that the more it has happened in the past the more you can be sure it will happen in the future. you'll never be 100% sure, because you'll never see all the sunrises, but you can be 99.999% sure. hume says in a sorta round about way that you can't assume the world is uniform. statistics doesn't make that assumption, either. if you assume that the next sunrise won't happen (that's 1 sunrise), and then add that together with all the other sunrises that have happened (let's say... 200), then you have 201 sunrises. if the next one were not to happen, then that means that the sun would not have risen .005% of the time. now, if you mix all the sunrises together, and pick one at random, chances are that you're going to get a sunrise. so... chances are the sun will rise tomorrow. we can't be *sure*, but... we can be reasonably sure.

of course, if you think about it, if the sun doesn't rise one day, then it probably will never rise any day after that, probably... perhapes some a dragon ate it, or something. now... the dragon could have eaten the sun on any day, but... out of 201 days, the chances of the dragon eating the sun on any one of those days is .005%.

in proof 1, you had this line:

5. PUN cannot be proven with Induction because it would be circular reasoning \ begging the question.

circular reasoning \ begging the question only apply to a binary world... ie. saying something is true because it is true, or saying something is false because it is false.

statistics isn't a binary world. statistics is a world with an infinte number of possibilities, neither of which are true or false. say 0 is false, and 1 is true... statistics is everything in between. .001, .999, etc. the only thing hume is saying is that you can't have 1 or 0. that's the only thing hume can say, using a binary proof like that.

Now, it might not be strictly rational, but Hume argued that it had no rationality at all. Statistics themselves are induction. Even with associations, that doesn't tackle the problem that it's using the assumption of the Principal of the Uniformity of Nature (PUN), so even though we've made interesting observations about induction, we're still stuck. :\


well... i don't think statistics does use PUN, as I explained above. PUN states that because you see something one way it *will* be that way the next time you see it. statistics *doesn't* say that. statistics does not say *at all* what anything is going to be the next time you see it - only what it will *probably* be, to some percentage.

given your examples of induction:

I've seen alot of green emeralds, therefore all emeralds are green; The sun will rise tomorrow because it's risen every day.


statistics would have them say "i've seen alot of green emeralds, therefore all emeralds are probably green" and "the sun will probably rise tomorrow because it's risen every day". i see those as fundementally different than your examples...

now, here's your definition of PUN:

1. All Inductions have as a hidden premiss that the universe is uniform (aka, the future will resemble the past at time...known as "the Principle of the Uniformity of Nature", henceforth said as PUN).


thats sorta a recursive definition, and almost circular reasoning, in and of itself, heh...

PUN requires induction, and induction requires PUN.

but anyways, i think by saying that statistics is different than induction that i'm saying that it's different than PUN, too :)

Hehehe, when I write my paper I'm going to make sure ideas that weren't mine are marked as not mine, but by people's on-line names. I, personally, don't have any interest in stealing other peoples' ideas and I plan on using everybody's "screen names" if I use their ideas in the paper. I'll have to start writing it first, though, before I know how much I've got to pad it with other ideas, yes?


you can use my real name, instead, since you know it :)

although if you post it online, use my nickname in the online version :)
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Postby Nyufrost » Sun Apr 13, 2003 9:44 am

Gigafrost wrote:But do you believe the sun will rise tomorrow? Then there has to be times where Induction would be rational or else our world will collapse around us. That's the problem that I'm trying to solve...

Then perhaps you should look at induction as taking something you know and building a solid base for it from the bottom up.

You know the sun has risen every day of your life and you have facts to support the truth that it has risen every day for at least 3000 years. Therefore, you can conclude it will rise tomorrow based on inductive thinking since the "theory" has been tested and proven continuously over eons of time. However, the sun could indeed fail to rise tomorrow. Therefore, induction is not reasonable. Believing something does not always make it true.
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Postby TerraFrost » Sun Apr 13, 2003 11:11 pm

i've come with an explanation as to why using statistical data sets isn't circular reasoning :)

a tautology is where A->B is always true. in this case, A is a data set (ie. three sun rises in a row equals three 1's in a data set, for succesful sunrise). to account for the fact that we can't be sure about the next element in that set, we'll add another element to that set to account for that uncertinty. an element that is sorta both 0 and 1. or... to explain differently, we'll have two different sets. one with the previous elements and an extra 0 and one with an extra 1. you now run through each element of the set, and apply the conditional. if even one conditional statement in both the data sets results in a 1, the statement is true. this represents an unlikely chance, but a chance all the same. and... we are guaranteed atleast one 1, because we introduced an element that was both 0 and 1, so to speak. a 0 on the left hand side of a conditional statement will always result in that conditional statement being true... after all, the only false statement that can result from a conditional is when a 1 is on the left hand side, and a 0 is on the right hand side (1->0). thus... the statement will always be true, and it is indeed a tautology.

i guess the sentianal logic equiv of it would be something like...

E(x)->true. the element that's simultanoiusly 1 and 0 guarantees this...

so anyways... it seems to me as if circular reasoning with statistical data sets is indeed a tautology. :)
Last edited by TerraFrost on Sun Apr 20, 2003 12:49 am, edited 1 time in total.
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Postby Nyufrost » Fri Apr 18, 2003 11:06 pm

Gigafrost wrote:It'd be nice to hear any kind of response...
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