The problem of induction

[FZ+]

Question: How are we justified in using the inductive principle - in assuming that experiences have some significance in predicting the further, or filling in other such gaps in our knowledge?

Are we in fact justified, or is this just a function of neccessity?
Or is such logical induction even neccessary?

What's your opinion?

 

[wimms]

Induction is all we have, without it, we would be robots without ability to learn from even our own mistakes, let alone avoid them.

 

[Mentat]

Well, I think it's necessary, but I base this opinion on induction (oddly enough). You see, I have seen science help the human race quite a bit in the past, and thus assume that (since science is an inductive system) induction must be necessary, even if it is incomplete.

 

[FZ+]

I guess I've just been reading Popper too much, then.
What Popper says, if I'm reading right, is that science (and perhaps, most human knowledge) does not use induction. Instead, it produces the illusion of induction through a process of eliminating failures, or falsification.

http://dieoff.org/page126.htm

 

[Iacchus32]

Oh, you mean "trial and error." Yeah, I think that's typically the way most people learn.

 

[selfAdjoint]

Well science does not (usually) use blind trial and error. It's more like educated guess, test it, recalibrate, another more educated guess.

 

[wimms]

Induction is Nth degree of speculation, constrained by deduction.

Some people say it more succintly.
http://www.ebtx.com/nman/nman08.htm

Induction and deduction are inseparable in practice (deduction being the conscious mechanism of verifying induction).

 

[Mentat]

Originally posted by FZ+
I guess I've just been reading Popper too much, then.
What Popper says, if I'm reading right, is that science (and perhaps, most human knowledge) does not use induction. Instead, it produces the illusion of induction through a process of eliminating failures, or falsification.

http://dieoff.org/page126.htm

I don't see the difference (though I haven't read the link yet) between reverse induction (the process of elimination, which basically takes something as true until proven false) and that which you say Popper advocates.

 

[Mentat]

Originally posted by wimms
Induction is Nth degree of speculation, constrained by deduction.

Some people say it more succintly.
http://www.ebtx.com/nman/nman08.htm

Induction and deduction are inseparable in practice (deduction being the conscious mechanism of verifying induction).

This does not seem accurate to me. Induction is not constrained by deduction, except in that one can use deduction to expose the incompleteness of induction. Induction is not speculation either, but an assumption (much like deduction requires an assumption) that that which happened previously will happen again.

btw, Induction can be used to show the flaw in Deduction too.

 

[phoenixthoth]

induction is a necessary "evil" it seems.

we tell our kids that everyone who has ever taken 100 hits of LSD in one night has gone insane but that doesn't prove to them that they won't.

the question is at what point should you adopt a statement whose "proof" is induction?

to a mathematician, induction is never a proof. they tested fermat's last theorem for a long time up to really high numbers (not compared to infinity of course) but that wasn't considered a proof. and scientists are no different: they know they could be wrong just as the mathematicians did. the wrongness could stem from a failure to observe that one counterexample that might be the very next one after you stop looking.

in mathematical induction, one proves that a theorem is "true" at least once and then "proves" that it is always the case that if the theorem is true for n observations then it is true for the n+1st observation. always is the key. induction is a poor word because it's actually deductively equivalent to the statement that every nonempty subset of N has a least element which is lo and behold an axiom (or equivalent to axioms).

hilbert's idea was to axiomatize science but can we ever in science prove that it is always the case that if the theorem is true for n observations then it is true for the n+1st observation? that would make it a math theorem and not just a well-tested conjecture in my book. i don't think that's possible.

what gets me is how all these experiments are done in a lab on Earth and conclusions are made thruought the universe as if the science laws apply equally everywhere. that's my main difficulty in accepting science, honestly. I'm not saying it's not useful for Earth and it does appear that people like einstein can find out more about the universe by using their imagination than doing experiments but no matter how good your imagination is (which is more important than knowledge in einstein's book), if a sound experiment proves you wrong then your theory is kaput. this is a digression and i don't really want to debate science with anyone.

induction is a necessary, carefully used, always doubted tool that is known by everyone (i hope) to not constitute absolute proof.

100 billion saying reality is not an illusion couldn't be wrong, could they? was the atomic bomb that dropped on hiroshima an illusion?? phaedrus' proffessor smiled and said, yes, it was in illusion.

 

[wimms]

Originally posted by Mentat
This does not seem accurate to me. Induction is not constrained by deduction, except in that one can use deduction to expose the incompleteness of induction. Induction is not speculation either, but an assumption (much like deduction requires an assumption) that that which happened previously will happen again.

WHAT does not seem accurate to you? Did you actually read the page, or disagree with your own assumptions about what it might say?

Induction is hardly only assumption/prediction of nearterm future based on past experience. Its behind all that your mind can ever produce. Deduction then "cuts the crap": nah, that one is impossible, that one is illogical, that one never happened, etc.

btw, Induction can be used to show the flaw in Deduction too.

Interesting. without using deduction, how? Aren't you confusing Induction with empirical evidence?

 

[Mentat]

Originally posted by wimms
WHAT does not seem accurate to you? Did you actually read the page, or disagree with your own assumptions about what it might say?

No, you and the author of the site seem of the opinion that Induction is speculation that is constrained by deduction...are those not the words that were used?

Interesting. without using deduction, how?

Well, I posted it in Tom's "Logic" thread...maybe I'll copy it soon, but I've got to get off-line soon.

Aren't you confusing Induction with empirical evidence?

Actually, the very idea that empirical testing can yield "evidence" is faith in Induction.

 

[wimms]

Originally posted by Mentat
No, you and the author of the site seem of the opinion that Induction is speculation that is constrained by deduction...are those not the words that were used?

No, that's not the words nor ideas that were used on the page at all.
Maybe that page better explains the the role of speculation with induction.
http://www.ebtx.com/nman/nman09.htm

Actually, the very idea that empirical testing can yield "evidence" is faith in Induction.

That list can go on and on: faith in existence, faith in logic, faith in test results, etc.
Falsificating empirical evidence needs no faith in induction. Lack of falsifying evidence leaves room for induction, which is process, action, not just something to have faith in.

 

[Mentat]

Originally posted by wimms
That list can go on and on: faith in existence, faith in logic, faith in test results, etc.
Falsificating empirical evidence needs no faith in induction. Lack of falsifying evidence leaves room for induction, which is process, action, not just something to have faith in.

Well, aside from the fact that I think you've confused "faith" with "credulity", I still hold that induction is a method (as is deduction) of logic that is as incomplete as deduction, and doesn't even present complete validity, let alone "truth".

 

[NateTG]

Originally posted by FZ+
I guess I've just been reading Popper too much, then.
What Popper says, if I'm reading right, is that science (and perhaps, most human knowledge) does not use induction. Instead, it produces the illusion of induction through a process of eliminating failures, or falsification.

http://dieoff.org/page126.htm

Unfortunately, the repeatability of results is a primary aspect of science -- hence the notion of induction is still vital to it.

The formation of theories is not necessarily an inductive process -- special and general relativity were both created deductively -- but, the scientific testing of these theories is always an inductive process.

Our society, and the generally high accuracy of scientific theories have led us to believe that scientific theories are somehow fundamental descriptions of the way that the universe works, when, in fact, they are more accurately described as methods for describing (hopefully) massive catalogs of experimental data.

The website you link to agress with this:

... To put it in a nutshell, our conjectures are our trial balloons, and we test them by criticizing them and by trying to replace them - by trying to show that there can be better or worse conjectures, and that they can be improved upon.

but then throws out this whopper:

The place of the problem of induction is usurped by the problem of the comparative goodness or badness of the rival conjectures or theories that have been proposed...

When in fact, the process of testing scientific theories ,that is determinign the comparitive goodness or badness, is ultimately known to be inductive in nature. (There are other criteria, but the predictive value is the primary concern for science.)

In my (inductive) experience, philosophers are reluctant to admit the imperfection of inductive reason into their theories, so they often build elaborate scaffolds to cover it, when it would probably be better to accept and acknowlege it as a potential weakness, and coresspondingly point out uses of it. (Much like the use of the axiom of choice in mathematics.)