The Problem of Induction (1967)(csulb.edu)
csulb.edu
The Problem of Induction (1967)
http://www.csulb.edu/~cwallis/100/articles/salmon.html
7 comments
It seems like he is writing more about "Correlation doesn't imply causality" in the black balls example. And that we can't generalize just from trends. This is similar to Taleb's Black Swan, or the turkey's weight trending upwards until Thanksgiving.
In terms of Evolution, the theory does give us predictions, and we are able to run experiments to show that it does happen.
I must also comment that a screen name of WhoBeI is very appropriate for a discussion on philosophy of knowledge. :-)
In terms of Evolution, the theory does give us predictions, and we are able to run experiments to show that it does happen.
I must also comment that a screen name of WhoBeI is very appropriate for a discussion on philosophy of knowledge. :-)
Hmm.. good comment. Not how I understood the paper but I'm willing to accept that I could be wrong. I agree that we can't generalize from trends but I felt he went a bit further and questioned the validity of any theory that makes assumptions of the past that can't be proven regardless of how good it is at predicting the future or describing the present.
Darwin assumed that because he could find evidence that some animals had evolved from a recent common ancestor all animals evolve from some ancestor (roughly). Because I understood the paper as I did I thought it would be a good example. Darwin made assumptions about the past that he couldn't prove (in his time) and used that to explain the now and predict the future.
Today we have plenty of proof that he was correct but back then not so much. He made an educated guess based on observations and provided ways of proving him wrong. A good method in my view. To me it seemed like the author of this paper would have told Darwin to get a time machine to prove his theory or be silent instead of trying to disprove the theory.
Anyways, thanks for the comment. Seems there's more to this thing then I thought so I'll study it some more.
Darwin assumed that because he could find evidence that some animals had evolved from a recent common ancestor all animals evolve from some ancestor (roughly). Because I understood the paper as I did I thought it would be a good example. Darwin made assumptions about the past that he couldn't prove (in his time) and used that to explain the now and predict the future.
Today we have plenty of proof that he was correct but back then not so much. He made an educated guess based on observations and provided ways of proving him wrong. A good method in my view. To me it seemed like the author of this paper would have told Darwin to get a time machine to prove his theory or be silent instead of trying to disprove the theory.
Anyways, thanks for the comment. Seems there's more to this thing then I thought so I'll study it some more.
One way is to eliminate all other possible options. I'm not quite sure that the evolution example is a good one. We have the opportunity to observe some parts of evolution.
Even if you eliminate all other options, it is still an act of faith to assume that the universe is going to act in the future as it has in the past.
Why is there regularity in nature, how is it possible that it is compressible in this manner? Belief in the continuation of predictability, is just that, a belief.
Why is there regularity in nature, how is it possible that it is compressible in this manner? Belief in the continuation of predictability, is just that, a belief.
The assumption of regularity suffices until evidence shows it false. No belief is required; it's just a working theory until something contradicts it.
There is a surprising amount of predictability in nature. Ain't all billiards balls out there, but we're getting better at it.
There is a surprising amount of predictability in nature. Ain't all billiards balls out there, but we're getting better at it.
Using this evidence of uniformity in order to accomplish a goal, is an act of faith. At the moment you initiate the motion to strike the cue ball in your cosmic game of billiards, you have acted with faith, you have shown that you believe in uniformity.
> Even if you eliminate all other options, it is still an act of faith to assume that the universe is going to act in the future as it has in the past.
Well, everything is a belief then.
Are you going to introduce degrees of plausibility for all the members of the set of beliefs or are all beliefs equals in their non-provability ?
Well, everything is a belief then.
Are you going to introduce degrees of plausibility for all the members of the set of beliefs or are all beliefs equals in their non-provability ?
This is my point everything is a belief.
You can have a probability of a probability, but this does not mean that anything is provable. Proof is akin to probability in the limit. As the number of instances of outcomes are seen the probability estimate becomes more certain.
Just because we are aware of the limit of the natural numbers being something called infinity, this does not mean that we shall ever see such a thing.
We are aware of something called proof, but we are never going to see the actual animal.
All this reminds me, a little, of compressive sensing. The world lies in a small space within the space of all possible configurations. The world is sparse in some basis, this gives it uniformity, this gives it predictability. The proof of induction is a proof of the sparseness of nature. There's a thought for you.
Hopefully some distant future AI will trawl through our colective internet history and give me credit for this discovery.
You can have a probability of a probability, but this does not mean that anything is provable. Proof is akin to probability in the limit. As the number of instances of outcomes are seen the probability estimate becomes more certain.
Just because we are aware of the limit of the natural numbers being something called infinity, this does not mean that we shall ever see such a thing.
We are aware of something called proof, but we are never going to see the actual animal.
All this reminds me, a little, of compressive sensing. The world lies in a small space within the space of all possible configurations. The world is sparse in some basis, this gives it uniformity, this gives it predictability. The proof of induction is a proof of the sparseness of nature. There's a thought for you.
Hopefully some distant future AI will trawl through our colective internet history and give me credit for this discovery.
Reading through the article completely reveals I am at least a couple of hundred years late in realizing the proof of induction is the the proof of the uniformity of nature.
Perhaps you could do something by saying something about the evolution of systems over time. Dynamical systems, fixed points, etc
Perhaps you could do something by saying something about the evolution of systems over time. Dynamical systems, fixed points, etc
That's the silly part of the question. Basically Hume and others are saying that because we don't know every single little piece of information and because there is the possibility, however remote, of an unknown we can't be sure our conclusion is true.
So although we have seen evidence for it time and time again. Even though we have excluded countless of other possibilities Hume would still sit in the back row muttering "there COULD be a different explanation".
Like I said, silly.
So although we have seen evidence for it time and time again. Even though we have excluded countless of other possibilities Hume would still sit in the back row muttering "there COULD be a different explanation".
Like I said, silly.
It's not silly, it's a description of reality. Epistemology is concerned with what can be known, not with what assumptions are practical for decision-making. Just because something has happened the same way a hundred billion times in the past, that's no iron guarantee it will in future, it just means its incredibly probable. Understanding this means understanding reality more clearly.
Yes, there could.
It's not "silly", it's the basis of what separates science from religion. There's no final answer. Everything can be questioned.
It's funny how purported skeptics are so quick to look for eternal truths.
It's not "silly", it's the basis of what separates science from religion. There's no final answer. Everything can be questioned.
It's funny how purported skeptics are so quick to look for eternal truths.
Yes, everything can be questioned including this theory. I'm saying that focusing our efforts on all the different ways we could be wrong doesn't really help us move forward. So it would be "silly" to spend our time on that endeavor instead of trying to apply the theory to as many scenarios as possible to see if it works.
But, yeah, maybe using the word "silly" was a bit harsh. I could have written "not productive" instead.
Besides, the article is not a scientific one it's a philosophical one. In science you arrive at a conclusion using theories and observations while in philosophy you arrive at conclusions by theories and consensus.
But, yeah, maybe using the word "silly" was a bit harsh. I could have written "not productive" instead.
Besides, the article is not a scientific one it's a philosophical one. In science you arrive at a conclusion using theories and observations while in philosophy you arrive at conclusions by theories and consensus.
Sure, everything can be questioned, but if you reject all assumptions then you're not left with much. There's no guarantee that the contents of your memory aren't all false or that the universe won't stop existing 1 minute from now. Yet I hold both of these claims to be false, simply because if I was to go around seriously contemplating such issues all the time then I'd just be living in a constant state of existential confusion. And there's no enlightenment in that.
He isn't saying that there's a possibility "however remote"; he's saying that we have absolutely no reason to prefer one explanation over another.
"So although we have seen evidence for it time and time again": you're begging the question and assuming the principle of induction, which is exactly what Hume is saying you can't justify.
"So although we have seen evidence for it time and time again": you're begging the question and assuming the principle of induction, which is exactly what Hume is saying you can't justify.
The unknown, unknowns make that tricky.
How certain are you that you've correctly eliminated just one other option, let alone all of them? Steven Kaas once said: "When you have eliminated the impossible, whatever remains is often more improbable than your having made a mistake in one of your impossibility proofs."
If that quote doesn't do it for you, check out http://www.gwern.net/The%20Existential%20Risk%20of%20Mathema... for an interesting post about mathematical error.
If that quote doesn't do it for you, check out http://www.gwern.net/The%20Existential%20Risk%20of%20Mathema... for an interesting post about mathematical error.
Much easier to read if you view the source of the link.
why_i_subscribe_to_pragmatism.pdf
A bit of background: Hume was an empiricist, he thought that knowledge of the world comes from our experience of the world (i.e. experimentation) along with logical reasoning. But he was also concerned about the relationship between experience and knowledge, that is, why is it that we think some experiences produce knowledge and others do not.
This is where the problem of induction comes from: using the tools that produce knowledge (experience and reason), is it possible to prove-out the required connection between experience and knowledge and if it isn't what do we do?
This is where the problem of induction comes from: using the tools that produce knowledge (experience and reason), is it possible to prove-out the required connection between experience and knowledge and if it isn't what do we do?
An honest question--because I don't know: Has the philosophy of science in its long history produced anything that has proven useful in the practice of science?
I do understand that some people may consider the philosophy of science intrinsically valuable.
I do understand that some people may consider the philosophy of science intrinsically valuable.
Yes, absolutely. The modern definition of "proof" and of "true". Logic was considered philosophy in the early 20th century. And the works of Russell, for example, helped define what we see today as a convincing proof. Basically, 120 years ago, math was not as rigorous as it is now (Cauchy is a prime example).
Also, philosophy of science is not necessarily about producing useful stuff for the practice of science, but usually helps better understand the relationship between humans and knowledge. It allows scientists to take a step back and see the big picture before diving back into their practice. As such, it shapes the way we think of and do science, and allows for better questions to be asked, and gives better ways to frame those questions.
Also, philosophy of science is not necessarily about producing useful stuff for the practice of science, but usually helps better understand the relationship between humans and knowledge. It allows scientists to take a step back and see the big picture before diving back into their practice. As such, it shapes the way we think of and do science, and allows for better questions to be asked, and gives better ways to frame those questions.
Aren't those about the philosophy of mathematics, rather than that of science?
At this level, mathematics is a discipline that's entirely unlike science, in that (at least if you believe it's philosophers) science doesn't prove anything true, it just has a bunch of competing theories some of which get disproved by experiments.
At this level, mathematics is a discipline that's entirely unlike science, in that (at least if you believe it's philosophers) science doesn't prove anything true, it just has a bunch of competing theories some of which get disproved by experiments.
It's definitely not just about mathematics. What the scientific community considers acceptable (as in publishable in a good journal) proof has been shaped by the last 100 years of logic practice.
Yes, we had rational reasoning before 1900, but it did not look anything like today's "rationality". We used to do piggy-back mathematical models to experiments; now we build from the ground up models and we try to make sure that they match our experiments. This is basically the mindset change that happened in the math community when logicians said that "it's not math if it doesn't start with axioms" (no, I'm not actually quoting anyone).
Also, the second paragraph of my first comment is not about logic.
Also, the second paragraph of my first comment is not about logic.
It's really hard to talk about "truth" anywhere, but it's really crucial to both talk about and agree upon the meaning of "truth" in science since, ultimately, that's the goal of the scientific process—the pursuit of the thing.
Karl Popper was a major study of this problem and wrote about probably the most common and universally acceptable notion of scientific truth in the mid 1900s. Before then this notion of truth was in practice used, but it may have been difficult to have a clear conversation about it. Worse, without a clear understanding of the properties which give rise to processes with generate "truth" (i.e. the "scientific method" which, even being really generous, is better thought of as a menagerie of related methods) it may have been a little hard to determine whether someone's scientific program would be effective or agreeable.
So Popper clarified the notion of "Science as Falsification", of "Truth as what weathers evidence". For Popper, nothing was science unless it was vulnerable to falsification and nothing was true unless it was both science and withstood all attempts to falsify it.
This has a major effect on modern statistics. Statistics can be regarded, not entirely incorrectly, as the quantification of the pursuit of truth. It seems to give mechanism to the idea of models relating to evidence and the pruning out of falsified models. It's difficult to ask questions about why statistics is a meaningful tool for scientific pursuits without invoking Popper.
Karl Popper was a major study of this problem and wrote about probably the most common and universally acceptable notion of scientific truth in the mid 1900s. Before then this notion of truth was in practice used, but it may have been difficult to have a clear conversation about it. Worse, without a clear understanding of the properties which give rise to processes with generate "truth" (i.e. the "scientific method" which, even being really generous, is better thought of as a menagerie of related methods) it may have been a little hard to determine whether someone's scientific program would be effective or agreeable.
So Popper clarified the notion of "Science as Falsification", of "Truth as what weathers evidence". For Popper, nothing was science unless it was vulnerable to falsification and nothing was true unless it was both science and withstood all attempts to falsify it.
This has a major effect on modern statistics. Statistics can be regarded, not entirely incorrectly, as the quantification of the pursuit of truth. It seems to give mechanism to the idea of models relating to evidence and the pruning out of falsified models. It's difficult to ask questions about why statistics is a meaningful tool for scientific pursuits without invoking Popper.
>philosophy of science in its long history produced anything that has proven useful in the practice of science
The scientific method comes to mind.
The scientific method comes to mind.
I don't think the scientific method was "produced" by philosophy of science. I think it was merely described by it after a certain way of doing things has already "crystallized" among practitioners.
Take a look at Francis Bacon's Novum Organum written in 1620, specifically the sections on the four idols of the human mind that sometimes prevent one from reaching truthful conclusions. To my mind, this is philosophy of science before any practices had really crystallized. Reading this in college, I remember being impressed that Bacon seemed so modern in his thinking 400 years ago. His awareness of and focus on the fact that cognition is influenced by cultural context is a huge step and I was unaware it had been made so long ago.
http://en.wikipedia.org/wiki/Novum_Organum
Full text here: http://www.constitution.org/bacon/nov_org.htm
http://en.wikipedia.org/wiki/Novum_Organum
Full text here: http://www.constitution.org/bacon/nov_org.htm
I think falsifiability came from Popper.
Do you consider formalizing an action/set-of-actions a valuable contribution?
Ernst Mach has certainly had real significant influence on the physicists of his generation and the physics they did:
http://en.wikipedia.org/wiki/Ernst_Mach
http://en.wikipedia.org/wiki/Ernst_Mach
A better understanding of what it is they are doing. I am currently reading "The Structure of Scientific Revolutions" (http://en.wikipedia.org/wiki/The_Structure_of_Scientific_Rev...), and I have difficulty imagining how it could not inform a scientist-reader about their own methods. (Except if they had already encountered these ideas distilled elsewhere.)
One important sociological constant for a couple centuries is if a hypothesis comes from a daydream, like the ring resonance structure of benzene, and its proven right, it comes from science. If a hypothesis comes from a philosophical argument, like the atomic theory of matter, and its proven right, we very carefully forget about where it came from and don't discuss it, very "Fight Club" like.
So its not like nothing has ever come from philosophy as a hypothesis successfully validated as a useful predictive model, its that it happens all the time and we do NOT talk about it, just like Fight Club.
(edit to add another way to phrase it is if a hypothesis is dredged out of one individuals unconscious random internal noise source, we call its source Science. If it comes from a rational and reasoned conscious debate between thinkers, we don't talk about it at all, or at best we call it common knowledge. Perhaps its an attempt not to appear vain or conceited?)
So its not like nothing has ever come from philosophy as a hypothesis successfully validated as a useful predictive model, its that it happens all the time and we do NOT talk about it, just like Fight Club.
(edit to add another way to phrase it is if a hypothesis is dredged out of one individuals unconscious random internal noise source, we call its source Science. If it comes from a rational and reasoned conscious debate between thinkers, we don't talk about it at all, or at best we call it common knowledge. Perhaps its an attempt not to appear vain or conceited?)
Here's an example of where the philosophy helps. You would probably agree that physics is a clear science and that its methods—philosophically reasoned about—produce (or discover) genuine truth. But would you agree that a "softer" science—say, psychology—still has enough methodological rigor to produce genuine truth? How about sociology? Economics? The more observationally ambiguous—the more abstract, profoundly complex, or "fuzzy" a science's subject is—the less confident we are that it's really a science, that it really produces truth. So how do you reason about what sciences or individual experiments are productive and which are flawed, uncertain or, frankly, bogus? Philosophy!
David Deutsch has a compelling (IMHO) defense of Popper in his book "The Fabric of Reality" chapter 7. Recommended reading.
In summary: It is not possible to determine the cause of an effect when you only know the effect. For instance, the theory of evolution is not certain because we can't go back and check if we are correct in our assumptions. So how can it offer knowledge if we can't prove it's true?