Problem of induction - impossible to solve, and thats deductively certain!!

[GrowingSmaller]

The problem of induiction I dont really understand it too well but may have a soluiton. A proof that it cant be justified.

The issue is - and I am not that familiar so forgive any mistakes - can inductive reasoning be justified?

Like the sun will rise tomorrow becase it has in the past, we can accept it as cogent argument, but we cant say that the future will resemble the past except by analogy, so were using inductive reasoning to establish inductive reasoning. But that would be circular reasoning.

If its a priori uncertain reasoning, woulnt there be a a priori situation where induction necessarily fails? Whatever observations we have?

And that is, IMHO....: in justifying induction itself


We need a mathematical approach, it one that knows in advance that induction will fail us and where. Or wont.

Theres a possible world in which the sun will always rise. But theres no possible world in which induction is justified, because (being inductive, probablistic) it necessarily fails somewhere.

So in asking why induction fails, its like asking why does 2+2 does not equal 10.

So its impossible to "slove" the problem, thats true deductively, across all possible worlds, and the opposite view is absurd. Being inductio, it has to fail. And that failure is in justifying induction.

 

[SkyWriting]

The problem of induiction I dont really understand it too well but may have a soluiton. A proof that it cant be justified.The issue is - and I am not that familiar so forgive any mistakes - can inductive reasoning be justified?

It can be justified for the sake of convenience, but it is logically incorrect.

...one cannot reliably surmise past events
from physical evidence unless there is
only one plausible explanation for that
evidence.

In your example, the sun will likely rise tomorrow
but the sky may be cloudy, or you may die, or
the earth may explode. Some of these interfering
events are more likely than others, but each will
mess up your predictions. Life lives on faith.

 

[Bob Crowley]

First of all, we need to be aware that mathematical induction and philosophical induction are different. Mathematical induction is more rigorous, and is based on deductive reasoning.

From the little I've read about it, philosophical induction tends to be based on experience eg. the sun rising tomorrow, railway controls doing what they're supposed to (the drivers of two trains in Germany had their inductive faith in railway technology shattered recently), and virgins normally don't get pregnant (there's been at least one episode where inductive reasoning didn't fit the bill - mind you it would appear to be the only exception, if you discount virgins who undergo IVF. Joseph had to be reassured that his inductive reasoning was false on this occasion).

I drive for a living. Part of my inductive philosophy in regards to driving is that I find that most drivers don't brake suddenly and hard on the freeway when there is no reason to do so. I stake my health and life on it to some extent. I assume, based on past experience, that I'm not going to be caught unawares by this issue.

We use inductive philosophy all the time to filter out unlikely scenarios, otherwise we'd be spending all our time worrying if the car is going to start tomorrow, will a sink hole swallow the house tonight, and could an elephant escape from the local zoo and trample me to death on my way to work.

But it's not philosophy. It's really observation based on experience which we use to make decisions. It may not be personal experience - it might be based on statistics, or the experience of others. I've got no interest in bungee jumping, but if it came to the crunch, it appears that most attempts end safely.

Now for my next question - is inductive philosophy of any relevance to Christian apologetics, and if so, how.

I'll leave it to someone better versed in formal logic to answer that one. I haven't got enough philosophical training to make an inductive guess with regards to the role of philosophy in apologetics.

 

[essentialsaltes]

It's important to keep in mind what Bob Crowley said about the difference between mathematical induction and philosophical induction. A common example of failed philosophical induction comes from the world of math (but it's not mathematical induction).

Into how many pieces can you cut a circle by connecting dots on the circumference?

One dot, one piece
Two dots, two pieces
Three dots, four pieces
Four dots, eight pieces

I'm a little afraid to post the image for five dots here...

But you can count it yourself -- 16 pieces.

Obviously, if you have six chords, the number of pieces will be--- what? 31!?!?!

(Actually, using mathematical induction, you can arrive at the correct result (as opposed to the naive guess from limited philosophical induction).)

 

[Tinker Grey]

I'm not sure what the problem of induction is.

If there cannot be absolute certainty ... well, there can be certainty enough.

I may not be philosophically certain the sun will rise tomorrow (i.e., that the earth will continue rotating at a speed approximately that of today such that the sun will appear to come over the horizon), but I am practically certain. Is that not enough?

 

[Chris B]

Obviously, if you have six chords, the number of pieces will be--- what? 31!?!?!

(Actually, using mathematical induction, you can arrive at the correct result (as opposed to the naive guess from limited philosophical induction).)

Nice. Didn't know that one.

If there are no loose ends or missing factors (a decent lemma) then mathematical induction is solid.
for instances such as "there will be a dawn tomorrow" we are more stuck on stacking up probabilities, directly or indirectly.
Fortunately for dawns we can do a bit better than just counting them, as they sit in a model of the soar system which has provided a range of observations and predictions to support its reliability.

It doesn't squeeze *all* uncertainty out of existence, though.
That's difficult to impossible, a lot of the time.

 

[Chris B]

I'm not sure what the problem of induction is.

If there cannot be absolute certainty ... well, there can be certainty enough.

I may not be philosophically certain the sun will rise tomorrow (i.e., that the earth will continue rotating at a speed approximately that of today such that the sun will appear to come over the horizon), but I am practically certain. Is that not enough?

"If there cannot be absolute certainty ... well, there can be certainty enough."
Certainly to the point where agonising over the uncertainty is counterproductive, and a better methodology is to treat the high probability as a provisional certainty.

Problems only crop up there where the uncertainty that is actually there matters in particular circumstances.
Then it can get messy, for instance in the clash of two (apparent) absolutes.
Or the "impossible" happens because in fact it was only very unlikely.

 

[Tinker Grey]

"If there cannot be absolute certainty ... well, there can be certainty enough."
Certainly to the point where agonising over the uncertainty is counterproductive, and a better methodology is to treat the high probability as a provisional certainty.

Problems only crop up there where the uncertainty that is actually there matters in particular circumstances.
Then it can get messy, for instance in the clash of two (apparent) absolutes.
Or the "impossible" happens because in fact it was only very unlikely.

Indeed. There are two questions, I think, regarding justification. One is whether one is justified in one's belief. The other is whether one was justified in some belief that was shown false.

My answer to the first is that I am if experiences preceding the question substantiate the belief. The answer to second is that I was justified in that the experiences preceding being shown false substantiated the belief. That I now need to reformulate a belief to incorporate the new information is called learning. It's a good thing.

 

[quatona]

The problem of induiction I dont really understand it too well but may have a soluiton. A proof that it cant be justified.

"Can´t" or "can"?

The issue is - and I am not that familiar so forgive any mistakes - can inductive reasoning be justified?

Depends on the purpose, and on the nature of the resulting claim.

Like the sun will rise tomorrow becase it has in the past, we can accept it as cogent argument, but we cant say that the future will resemble the past except by analogy,

So where´s the problem - as long as you don´t make an absolute truth claim?
"Unless there´s a dramatic change in the cosmological setup, the sun will rise tomorrow. Such changes occur rarely - if ever -, so, for all practical intents and purposes, I am working from the premise that the sun will rise tomorrow."

so were using inductive reasoning to establish inductive reasoning. But that would be circular reasoning.

When it comes to foundations of our reasonings, this will always be a problem: Either we establish them circularly, or we are earning ourselves the reproach of being inconsistent.

If its a priori uncertain reasoning, woulnt there be a a priori situation where induction necessarily fails? Whatever observations we have?

And that is, IMHO....: in justifying induction itself


We need a mathematical approach, it one that knows in advance that induction will fail us and where. Or wont.

Theres a possible world in which the sun will always rise. But theres no possible world in which induction is justified, because (being inductive, probablistic) it necessarily fails somewhere.

So in asking why induction fails, its like asking why does 2+2 does not equal 10.

So its impossible to "slove" the problem, thats true deductively, across all possible worlds, and the opposite view is absurd. Being inductio, it has to fail. And that failure is in justifying induction.

Sorry, you´ve lost me here.

 

[GrowingSmaller]

Now for my next question - is inductive philosophy of any relevance to Christian apologetics, and if so, how.

I'll leave it to someone better versed in formal logic to answer that one. I haven't got enough philosophical training to make an inductive guess with regards to the role of philosophy in apologetics.

There are inductive aologetics or theologicial arguments. For example the argument from design is an argument from analogy IIRC.

 

[GrowingSmaller]

I'm not sure what the problem of induction is.

Not that qualified, but its about the warrant we have for using inductive reasoning as a whole. We can use induction for all kinds of everyday (and mathematical) decisions. But what, philosophically, is the warrant we have for induction. Some say "it works" is good enough. But i heard that itself is an inductive arguument, "it worked in the past so it will work in the future". Then, if induction is the justification of induction, you have circular reasoning...

 

[GrowingSmaller]

Sorry, you´ve lost me here.

Yep I am half lost myself. Its a bit of a dodgy batton of an argument.

 

[Chris B]

There are inductive aologetics or theologicial arguments. For example the argument from design is an argument from analogy IIRC.

Which can be useful and illuminating or can be completely invalid.
A classic case is the story of the blind men and the elephant.
It is valid up to a point, but pressed too far (generalised) it contains a terrible and fatal flaw.

 

[KCfromNC]

I'm not sure what the problem of induction is.

The problem is that some philosophers assume that things you can't deductively prove using made up rules and made up assumptions are somehow suspect, even though those things work really well here in reality.

 

[quatona]

There are inductive aologetics or theologicial arguments. For example the argument from design is an argument from analogy IIRC.

Such arguments suffer from a serious problem, imo: They are dealing with a supposedly unique and extraordinary event and with a situation and conditions that are allegeldy fundamentally different than anything within our experience. To argue inductively or by analogy means contradicting the defining particularities of the issue in question.

 

[GrowingSmaller]

I see what you mean, Quatona. If the thing argued for is totally dissimilar to the world, how can an analogy work?