Popperian falsificationism: useful idea, or naïve/outdated?

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Popperian falsificationism: useful idea, or naïve/outdated?

Postby Idhan » Sat Apr 04, 2009 5:11 pm UTC

On the Utility of Religion thread, I realized that I was going to make a point that depended on the concept of Popperian falsificationism, or at least Popperian falsificationism as it's perceived in folk culture. Then I realized that I was hesitant to do so, because I had a feeling that simply assuming that paradigm would be regarded as naïve and old-fashioned among the worldly, latté sipping sophisticates of SB (or whatever). I ended up using the concept, with a few scare quotes and disclaimers.

Anyway, what do you think of falsificationism? Is it an enduringly useful way of thinking about the scientific method, or is it an outdated, naïve model that was debunked by Kuhn, Feyeraband, etc?

My observation, as neither a scientist nor a philosopher, is that scientists tend to accept falsificationism as a reasonable philosophy of science, and talk about things like the falsifiability of theories ("string theory is unfalsifiable pseudoscience!") with little critical questioning of falsificationism as a paradigm. Philosophers, on the other hand, seem to generally regard falsificationism as outdated and naïve, with little relation to the way actual science is done.

Update: I just thought I'd note that I've never read any Popper, which is why I referred to "Popperian falsificationism as it's perceived in folk culture," which is, not having read Popper, how I perceive it myself. As for my personal views, I tend to side with falsificationism against its critics, but I'm somewhat insecure in that view.
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Indon » Sat Apr 04, 2009 5:44 pm UTC

Well, if not with methods stemming from falsification, how else do we test ideas to see which ideas are better than others?
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby diotimajsh » Sat Apr 04, 2009 6:29 pm UTC

Idhan wrote:...scientists tend to accept falsificationism as a reasonable philosophy of science, and talk about things like the falsifiability of theories ("string theory is unfalsifiable pseudoscience!") with little critical questioning of falsificationism as a paradigm. Philosophers, on the other hand, seem to generally regard falsificationism as outdated and naïve, with little relation to the way actual science is done.
This. This is exactly how I tend to encounter falsifiability: scads of scientist bloggers and writers (sometimes atheists and skeptics too) use it to criticize nebulous theories. [Edit: Why did I repeat "atheists and skeptics" here? Redundancy removed.] Whereas many philosophers are all, "C'mon guys, this is a problematic way to delimit science from non-science. Surely we can do better."

My opinion is kind of a mix of the two. Falsifiability is a handy guideline to ensure that theories are actually making testable predictions, but it's not necessarily definitive of all good theories or science in general. I guess I see it as more of a useful heuristic than a litmus test for Genuine ScienceTM. There may be times when it's best for science allow the use of unfalsifiable theories, depending on how they' functioning in other explanatory capacities.
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby JoshuaZ » Sat Apr 04, 2009 10:29 pm UTC

Well, most scientists in practice are neo-Popperian and presumably their opinion counts for something...

The main issue that philosophers have with falsification is that you can construct more or less pathological cases where it doesn't work. The most serious objection IMO is that of Quine who observed that it isn't ever completely clear which hypothesis should be rejected after an experiment. Roughly speaking, hypotheses always exist as part of a network of hypotheses and you can reject or modify different ones. By appropriately modifying existing hypotheses you can prevent the direct falsification of a single specific hypothesis.

I'm a fan of Lakatos's proposed test for pseudoscience which says more or less that an idea is pseudoscience if it doesn't lead to useful/interesting new ideas but only to additional ad hoc hypotheses to keep the original idea intact. Young Earth Creationist, astrology, and most other topics that are described as pseudoscience fit this bill.

There's a more serious overarching problem here: philosophers want everything to be just perfect and to have consistent logic. If not, they declare something to be useless. But that's not how life works. Even if the criteria Lakatos and Popper aren't perfect they work very well. Rejecting them for that reason would be akin to rejecting all evidence in front of us due to the Grue paradox and its variants. Real life more or less requires some degree of pragmatism. We should thus be aware that Popperianism isn't perfect. But it is good enough for almost all practical purposes.

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby qetzal » Sat Apr 04, 2009 11:07 pm UTC

Upfront disclosure: I'm a scientist, not a philosopher. Just so my biases and background (or lack thereof) are clear.

On the one hand, I agree that science does not typically proceed the way Popper envisioned, by a strict process of hypothesis and falsification. I also agree there is more to science than just falsification, both in practice and in principle.

OTOH, I do think that all true scientific theories must be falsifiable. If a 'theory' is not falsifiable, then no possible empirical observation could ever contradict it. If so, it can't possibly make useful predictions. A theory is only useful if it tells us we can expect to observe X, not Y, under specified circumstances. But any theory that does so is automatically falsifiable (simply by observing Y, not X).

I realize some things are commonly called theories even though they may be non-falsifiable (e.g. String Theory). But honestly, I think it's wrong to call them theories.

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby doogly » Sun Apr 05, 2009 7:12 am UTC

Practicing scientist, not a philosopher.
Popper's falsifiability is pretty good stuff, but Popper did not like things like Bohr's instrumentalism (according to wiki.) I think Bohr's ideas have a lasting popularity. There is a strong sense that in the Bohr v Einstein "what is reality like" discussions, Bohr wound up the winner. But also in science in practice you are allowed to think different things at different times. One example is in quantum mechanics - you can be Copenhagen for one problem and and then switch to a many worlds points of view for an extra insight, and there is no jealous quantum mechanic in the sky who will smite you for switching idols. You might have a favorite, but acknowledge they are functionally equivalent. I think a lot of these philosophical models for truth wind up being functionally equivalent and just a more or less convenient way of evaluating a theory, when what you are interested in doing is evaluating a theory. This is what we are mostly interested in doing, rather than establishing a unified model of science.
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby AFedchuck » Mon Apr 06, 2009 8:04 pm UTC

I think one thing to point out first is that Popper's falsification is more nuanced than the science bloggers seem to suggest - his most important works don't suggest that you throw out a theory because one experimental result 'disproved' it - he was well aware of the fallibility of experimental evidence (to both error and theoretical) and suggested that tenacity was necessary.
qetzal, your point about falsifiablity is true, but only to a very limited extent. Falsifiability, as I understand it, is more than simply believing that unless a theory makes predictions it is not science, it specifies that negative evidence is more important than positive evidence (in some people's eyes it is the only admissible evidence). There are whole host of other conditions on what science is.
JoshuaZ, I'm not sure that scientists' view of science counts for anything - do goldfish have a useful view of their life? To phrase that in a slightly less provocative fashion, scientists aren't sociologists or philosophers of science and so their evidence is likely to be anecdotal and also very positive towards science. Further, when you ask someone do they carry out "the scientific method" they are likely to say yes, as the limited education scientists receive on how science work is also neo-Popperian. That's not to say scientists have nothing to say, but I'd take personal accounts as not so useful. After all, it isn't scientists who came up with the ideas that we're talking now, is it?
I acept that real-life needs compromises, but why plump for Popper over the other philosophies? If they provide better descriptions, why not use them? I think part of the reason that scientists like the simplified view of Popper is that it elevates them above the need to recognise that science is in many ways extremely human, with all the human faults. As pointed out earlier, naive falsification isn't the criterion used by scientists to choose whether something is science or not, so why should it be used at all? I find it the obsession with "Pop-popper" in the blogosphere slightly worrying and frustrating, because although denouncing pseudo-science and creationism are ridiculous and needed to be countered, the intelligent outsider will recognise the double-standards and may well think that the rational scientists are in fact being as duplicitous as those they are trying to combat.

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby doogly » Mon Apr 06, 2009 8:12 pm UTC

AFedchuck wrote: do goldfish have a useful view of their life?

Yes, I think so. Chances are very good they grok goldfishery better than I could.

AFedchuck wrote: After all, it isn't scientists who came up with the ideas that we're talking now, is it?

I suggested Bohr's view as possibly better / more common in practice, and he is definitely a scientist.
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby qetzal » Mon Apr 06, 2009 10:31 pm UTC

AFedchuck,

I agree that falsifiability has a more limited application than falsificationism (aka Popperianism, at least as far as I understand it). That was my point. While falsificationism (the philosophy) does not adequately describe how science proceeds in the real world, falsifiability (the property) is an essential element of all 'proper' scientific hypotheses and theories.

In other words, and responding more directly the 3rd paragraph of the OP, I think it's correct for scientists to emphasize the falsifiability of theories, even if they don't critically question (or even fully understand) falsificationism as a paradigm.

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Philwelch » Tue Apr 07, 2009 4:19 pm UTC

JoshuaZ wrote:The main issue that philosophers have with falsification is that you can construct more or less pathological cases where it doesn't work. The most serious objection IMO is that of Quine who observed that it isn't ever completely clear which hypothesis should be rejected after an experiment. Roughly speaking, hypotheses always exist as part of a network of hypotheses and you can reject or modify different ones. By appropriately modifying existing hypotheses you can prevent the direct falsification of a single specific hypothesis.


This is probably the biggest observation of Quine.

In an experimental context the logic supposedly goes as follows:

If the theory is true, the experiment will produce the predicted results.

In practice, the logic is actually as follows:

If the theory is true, and the experiment is well constructed, and we didn't make any mistakes, the experiment will produce the predicted results.

This puts you in a sticky quandary. If you really wanted, you could develop this fanatical belief that you're really bad at doing experiments, so in your mind the theory's still true—you're just shitty at doing lab work. And even if you're exceptionally careful, some sort of error will creep into the results and cast doubt on any conclusions you might want to draw. I suspect some Bayesian model of inference would, however, get us around this problem.

JoshuaZ wrote:There's a more serious overarching problem here: philosophers want everything to be just perfect and to have consistent logic. If not, they declare something to be useless. But that's not how life works. Even if the criteria Lakatos and Popper aren't perfect they work very well...Real life more or less requires some degree of pragmatism.


It's kind of patronizing to think that philosophers don't realize this—I'd hazard a guess that most of the English-speaking tradition in philosophy was an attempt to wrestle with this fact, albeit in various contexts.

This also misses the point of philosophical criticism. Philosophers, at least in the English-speaking tradition, aren't so interested anymore in debunking imperfect and inconsistent ideas for the sake of discrediting them. Philosophy is actually a lot like software. You have some philosophers who build a framework of logic that we may safely rest our thinking upon, and you have other philosophers who keep finding bugs in that framework of logic. The real question is thus: can Popperian falsificationism be patched well enough to work, or should we throw it out and start using another codebase?
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby JoshuaZ » Fri Apr 10, 2009 3:49 am UTC

Philwelch wrote:
JoshuaZ wrote:The main issue that philosophers have with falsification is that you can construct more or less pathological cases where it doesn't work. The most serious objection IMO is that of Quine who observed that it isn't ever completely clear which hypothesis should be rejected after an experiment. Roughly speaking, hypotheses always exist as part of a network of hypotheses and you can reject or modify different ones. By appropriately modifying existing hypotheses you can prevent the direct falsification of a single specific hypothesis.


This is probably the biggest observation of Quine.

In an experimental context the logic supposedly goes as follows:

If the theory is true, the experiment will produce the predicted results.

In practice, the logic is actually as follows:

If the theory is true, and the experiment is well constructed, and we didn't make any mistakes, the experiment will produce the predicted results.


But it's even worse than that. Even if I perform the experiment correctly I don't know which hypothesis to reject. Maybe my basic theory was correct but some auxiliary implicit hypothesis was incorrect. For example, let's say a

Philwelch wrote:This also misses the point of philosophical criticism. Philosophers, at least in the English-speaking tradition, aren't so interested anymore in debunking imperfect and inconsistent ideas for the sake of discrediting them. Philosophy is actually a lot like software. You have some philosophers who build a framework of logic that we may safely rest our thinking upon, and you have other philosophers who keep finding bugs in that framework of logic. The real question is thus: can Popperian falsificationism be patched well enough to work, or should we throw it out and start using another codebase?


If that's the test, then it works just fine for almost all everyday uses. As others have observed if a hypothesis isn't falsifiable then it has serious problems. It may be that falsification is a necessary but not sufficient condition for a theory to be scientific.

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Outchanter » Fri Apr 10, 2009 9:45 am UTC

Philwelch wrote:In practice, the logic is actually as follows:

If the theory is true, and the experiment is well constructed, and we didn't make any mistakes, the experiment will produce the predicted results.

This puts you in a sticky quandary. If you really wanted, you could develop this fanatical belief that you're really bad at doing experiments, so in your mind the theory's still true—you're just shitty at doing lab work. And even if you're exceptionally careful, some sort of error will creep into the results and cast doubt on any conclusions you might want to draw. I suspect some Bayesian model of inference would, however, get us around this problem.

Exactly. Reality is probabilistic, so there's no one-shot method that can give you a sure answer after one experiment, or even a finite number of experiments. But given enough time you can get arbitrarily close.

Redundant thought of the day: when the null hypothesis is true, it will still be rejected (at the 5% level) in roughly 1/20th of experiments performed. If we took that as an inerrant falsification, we'd lose a good portion of useful ideas.

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby trece8 » Wed May 13, 2009 10:10 pm UTC

Hi, I'm studying a scientific career, and I like examining thoroughly all kinds of stuff, (but?) I think it could be helpful to share my view to you:

Scientific theories are things that predict outcomes of measurements. They have a given probability of success for prediction of each measurement ( more than 50% ) in a certain range of applicabilty.

So, there are no "false" theories, because we can't know the "true" ones. It's not important to have just one theory about each topic (atoms, clouds, why i pee yellow)... that's all that Popper's about (having zero or one theory about each phenomenon).
The important thing is that the measurements of repeatable experiments "fit" in a theory, no matter how stupid/cool it sounds. If a theory that models the Earth as a yellow chipmunk makes me predict 90% of the roulette outcomes in a casino, I'd congratulate its scientist mastermind LOUDLY. It doesn't matter what the shape of the Earth that theory says it is... it is obviously outside its range of applicability. It doesn't matter that 10% of the time it doesn't work: that doesn't make the other 90% less efficient.

...and if another guy comes with a theory for the casino that says that I'm an asshole and predicts it with 80% accuracy, I'd congratulate him too!

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby folkhero » Thu May 14, 2009 7:38 am UTC

I generally agree with Duhem's and Quine's arguments against Popper along with Kuhn's account of normal vs. revolutionary science. If an experiment doesn't give the expected result, all we know is that at least one of our theories and assumptions are wrong. In the reality of current modern science usually the assumption that is wrong is that the equipment was working properly, or that the the procedure was done properly, or that some outside influence that hadn't been considered, or that was considered negligible turned out to not be negligible. I'm not trying to knock on scientists, the margins of error that they deal with is so small that even the best in the world are going to make mistakes some of the time. We don't throw out well tested theories unless we keep running into problems with it and someone comes up with an alternative that can account for the theory seemed to work so well in other equations.

Let's look at an example: the planet of Mercury moves in a way that Newtonian mechanics can't explain, but fits perfectly with the theory of relativity. This was known well before relativity was thought up, but scientists didn't abandon Newton's theory of gravity because it worked every single other place that they looked on the earth and in the solar system. They really couldn't throw out Newton without an alternative because it was so foundational that they would have to postpone nearly all the physics research going on until the issue could be resolved.

Having said that, I think falsification can be somewhat useful in some situations. I think its a good rule of thumb, or red flag in the demarcation between science and pseudoscience. If a theory can't doesn't make falsifiable predictions, it should throw up some huge red flags. If it can't make any predictions, or its predictions can't -in principle- be falsified, then the theory isn't really scientific at all. If a theory makes predictions that we don't know how to falsify, but is not constructed in a way that would make falsification impossible, then it becomes a sticky situation. Maybe a little further exploration of the theory, or some advancement in technology or another scientific theory will make the theory falsifiable; maybe that day will never come and the theory will always be in a sort of limbo (I'm looking at you string theory).

Fortunately, we do have tools other than falsifiability to measure these theories in limbo. Unfortunately, these tools tend to be more subjective than the sort of things scientist usually like working with. We can judge a theory by its plausibility (how well does the story told by the theory mesh with our current understanding of the world?), its simplicity (I'm trust you're all familiar with Occam's razor), its fecundity (does exploration of this theory lead to new theories or a better understanding of existing theories) and its elegance (hard to really define, but when you see it, it makes a theory very compelling).
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Philwelch » Thu May 14, 2009 4:57 pm UTC

folkhero wrote:Let's look at an example: the planet of Mercury moves in a way that Newtonian mechanics can't explain, but fits perfectly with the theory of relativity. This was known well before relativity was thought up, but scientists didn't abandon Newton's theory of gravity because it worked every single other place that they looked on the earth and in the solar system. They really couldn't throw out Newton without an alternative because it was so foundational that they would have to postpone nearly all the physics research going on until the issue could be resolved.


It was even more interesting than that!

At this point, there was a well established method of discovering planets by observing their gravitational effects on neighboring planets. So it was conjectured that there was yet another planet even closer to the sun than Mercury. This planet was named Vulcan, and was considered extremely difficult to observe due to its proximity to the sun. There were even 19th century "observations" of Vulcan by astronomers, though other astronomers didn't observe it. In true Quinean fashion, we held onto one idea (Newtonian mechanics) by supposing other facts that would make it consistent with our observations (planet Vulcan).

As soon as relativity came out, though, Mercury's orbit made perfect sense. Since we had other theoretical and experimental confirmations of relativity, and since relativistic laws mathematically converged to Newtonian laws, in true Quinean fashion we again refactored our suppositions until the world made consistent logical sense once again.
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby trece8 » Thu May 14, 2009 9:59 pm UTC

Before that, when Copernicus proposed a heliocentric cosmology, the previous theory (geocentric with epicycles) predicted way better the results at that time.
But we got more into the Copernicus-way... kinda like the other way around the "Mercury" stuff.
Anyway, it seems any theory can predict results good enough ... it only needs enough modifications. The way of thought is that you keep the theories that seems to be easier to get them to fit the most experimental outcomes it can.

BTW:
Why a lot of people seem to need the UNUSED aspects (of any theory) to make sense?
In theories, there's the part that is called the "model": the story some guy devised to fit all the predicted measurements in. The story doesn't matter at all... he could have thought it other way, but made the same predicted measurements: The model doesn't have anything to do with reality, it is just a simple way to remember the predictions (formulas, reasonings, etc).
Specially, when explaining out-of-the-ordinary things, nobody can picture out-of-the-ordinary things as they are... that's why there is something called "particle/wave" duality and not something like the "hyperspace/chewbacca thoughts" duality. Elemental particles aren't "little balls", aren't "strings", and they probably aren't both balls-and-strings-at-the-same-time neither, ... but you explain their properties by picturing them as that, because in usual life we know how balls and strings work, so by saying "it's a ball" you immediatly understand it can bounce off of things (specially other balls), you can count them and more... (just by saying "ball"), and when you say "it's a wave" (or a string) you understand they can go through things, combine, turn around walls and such.

But thinking a ball and a string are made of little balls (points? condensed clouds?) and strings is like saying that Santa Claus is made of little Santa Clauses... you see it doesn't really explain the "reality" of the Santa Claus, but can make you remember more easily the outcomes of the Santa-made-of-Santas theory.

So, there is no need for ONE model -> there is no need for just ONE theory neither.

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Philwelch » Thu May 14, 2009 10:23 pm UTC

While true, it would be a lot simpler and neater if we had just one theory for everything. So no, not necessary, but worth working for.
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Carnildo » Fri May 15, 2009 2:50 am UTC

trece8 wrote:Before that, when Copernicus proposed a heliocentric cosmology, the previous theory (geocentric with epicycles) predicted way better the results at that time.
But we got more into the Copernicus-way... kinda like the other way around the "Mercury" stuff.


This is an interesting case, because from a predictive standpoint, both models (Copernicus wound up adding epicycles to his model) are correct. The epicycles are simply a form of two-dimensional Fourier analysis, and if you stack up enough of them, the Copernican model produces Kepler's ellipses, while the geocentric model produces the sum of the ellipse of Earth with the ellipse of the planet you're looking at.

The reason for choosing Newtonian gravity over any of the above models is not that it makes better predictions, but that it explains its predictions.

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby doogly » Fri May 15, 2009 3:01 am UTC

Newton's gravity makes predictions; epicycles and whatnot were purely descriptive.
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Carnildo » Fri May 15, 2009 3:58 am UTC

All of them make predictions of the form "where will the planets be at time X?"

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby doogly » Fri May 15, 2009 4:12 am UTC

But not, "what would some other planet's orbit look like?"
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Outchanter » Fri May 15, 2009 10:39 am UTC

In addition, Newton's theory made predictions like "how quickly will an apple accelerate toward the earth?" It was called the universal law of gravitation for a reason - it provided a uniform description of both orbiting bodies up there and falling objects down here. Epicycles on the other hand... ;)

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby trece8 » Sat May 16, 2009 6:12 pm UTC

Philwelch wrote:While true, it would be a lot simpler and neater if we had just one theory for everything. So no, not necessary, but worth working for.


Not really. The point is not just one theory, is just an "easier" theory.
While just one theory would be an easy way to remember the results, it can be really really difficult to apply it.
For example: nobody uses quantum mechanics to know how much time will it take the chicken to cross the road. The idea is laughable, because nobody in the history of science will ever make a model of a chicken based on quantum mechanics. QM says that it can model a lot, but not really. It is so difficult to apply that you'll never see that model (nor the standard model) applied to human-scale things properly.
Just ONE "everything" theory is a neat idea if you think you can actually simulate the entire universe. The problem is: you can't. You'd need more matter than what you want to simulate (and that's a lot, probably more than what's available).

So, the point really is "easy to learn" theories, not a "unique" theory.
Given a certain prediction rate, wouldn't you choose many reaaaaaaaaally easy-to-learn theories than just one (in which you perhaps are not able to derive all its logical consequences)?
I think you would. And if you wouldn't: why?

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Philwelch » Sat May 16, 2009 8:45 pm UTC

trece8 wrote:Just ONE "everything" theory is a neat idea if you think you can actually simulate the entire universe. The problem is: you can't. You'd need more matter than what you want to simulate (and that's a lot, probably more than what's available).

So, the point really is "easy to learn" theories, not a "unique" theory.
Given a certain prediction rate, wouldn't you choose many reaaaaaaaaally easy-to-learn theories than just one (in which you perhaps are not able to derive all its logical consequences)?
I think you would. And if you wouldn't: why?


Why? Mathematical beauty. And it turns out that in most of physics, the "complicated" theories just have a lot of terms that reduce to 0 or 1 upon certain limits, thus yielding the simpler theories.
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby trece8 » Sun May 17, 2009 4:50 am UTC

Philwelch wrote:Why? Mathematical beauty. And it turns out that in most of physics, the "complicated" theories just have a lot of terms that reduce to 0 or 1 upon certain limits, thus yielding the simpler theories.


Before I forget about the "mathematical beauty", I have to tell you:
1. Nobody knows what is it. And if it exists, it means different things for different people. So, the phrase doesn't mean anything useful.
2. The "ultimate formula" for the universe could easily be " 1=x ", for example. Some people could vote that as "oh so neat", but it would be obnoxiously intrincate and useless. Science doesn't look for beauty: art does. And science is not art, btw.
3. Science is not math, and math is not science, so "mathematical beauty" has nothing to do with that. Math is an instrument of science, perhaps the most important after measuring, but an instrument. As the Stratocaster is to Hendrix, Jimi didn't need that to be a musician, nor was the purpose of Jimi to make a better guitar.

The "complicated" theories don't really reduce to other theories, because you don't need only differential equations, you need hypothesis over your phenomenon. The only way that I'll start to trust you there would be for you to deduce thermodynamics from ONLY string theory or QM (but being unable to introduce hypothesis as the form and distribution of molecules, and walls or such, only QM or string theory).

A sidenote: Things about "big" things doesn't have to be deduced from things about "little" things. It can be well the other way around (like relativity), so... why doesn't thermodynamics derive into string theory, in your way of thought?

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Outchanter » Sun May 17, 2009 10:08 am UTC

I think the main motivation for unifying physics is that what are generally considered the most successful theories in physics so far are themselves unifications of previous ideas.

trece8 wrote:Before I forget about the "mathematical beauty", I have to tell you:
1. Nobody knows what is it. And if it exists, it means different things for different people. So, the phrase doesn't mean anything useful.

While beauty is by definition subjective, what most people mean when they refer to mathematical elegance is something along the lines of Occam's razor, or parsimony. And there are some ways of formalizing that.

For example, the Kolmogorov Complexity of a deterministic stream of data is defined as the shortest computer program needed to produce it. That may seem trivial but it's actually a very deep idea which goes a long way toward 'explaining' why numbers like e and pi (which can be approximated to arbitrary accuracy using fairly simple programs) are special compared to almost all other transcendentals. In general, Kolmogorov Complexity can't be computed, but it can in many cases be upper bounded by finding an appropriate program or (a special case of this) using a standard compression algorithm, which gives an upper bound related to entropy.

And Rissanen's Minimum Description Length principle applies that idea to statistical models. In practice, the way all model selection methods work is that when there isn't enough data to justify a more complex theory, model selection methods will favour the simpler theory. But as you gather evidence for a particular complex theory which isn't explained well by the simpler theory, you'll switch over. The difficulty is deciding the exact tipping point.

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby btilly » Sun May 17, 2009 4:38 pm UTC

Carnildo wrote:This is an interesting case, because from a predictive standpoint, both models (Copernicus wound up adding epicycles to his model) are correct. The epicycles are simply a form of two-dimensional Fourier analysis, and if you stack up enough of them, the Copernican model produces Kepler's ellipses, while the geocentric model produces the sum of the ellipse of Earth with the ellipse of the planet you're looking at.

If you stick only to predictions about the positions of the planets, sure. However the Copernican system predicted the phases of Venus, while the Ptolemaic did not. So once telescopes allowed Galileo to see that in 1610, the Copernican system had more predictive power.

Some of the other major distinguishing characteristics were that the Copernican system explained why Mercury and Venus were always near the Sun, the Ptolemaic system had something called the equant which the Copernican system did not, the Copernican system had slightly more epicycles (how much depended on whose mathematics you believed), and only the Ptolemaic system fit with Aristotelian physics.

The last was very important historically, and is why Galileo's interest in astronomy lead to basic experiments on physics.
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Philwelch » Mon May 18, 2009 4:00 am UTC

trece8 wrote:
Philwelch wrote:Why? Mathematical beauty. And it turns out that in most of physics, the "complicated" theories just have a lot of terms that reduce to 0 or 1 upon certain limits, thus yielding the simpler theories.


Before I forget about the "mathematical beauty", I have to tell you


...a number of practical facts that all miss the real point.

Math isn't an instrument, it's a language. Mathematical beauty has nothing to do with the form and everything to do with the beauty of the idea being expressed. And it's not some universal objective thing. But if all of physics can be meaningfully expressed in a form that requires only a single statement, that would strike a lot of people as really, really beautiful.

And if you want something purely practical, it's this: the type of people whom it would strike as really beautiful are probably the same type of people who would discover it anyway. Great achievements are rarely accomplished by people who are working out of a grim sense of utility.

trece8 wrote:The "complicated" theories don't really reduce to other theories, because you don't need only differential equations, you need hypothesis over your phenomenon. The only way that I'll start to trust you there would be for you to deduce thermodynamics from ONLY string theory or QM (but being unable to introduce hypothesis as the form and distribution of molecules, and walls or such, only QM or string theory).


Some of them do reduce. Momentum isn't mass times velocity, it's mass times velocity times the Lorentz factor, but the Lorentz factor reduces to 1 unless you're going fast relative to c.

trece8 wrote:A sidenote: Things about "big" things doesn't have to be deduced from things about "little" things. It can be well the other way around (like relativity), so... why doesn't thermodynamics derive into string theory, in your way of thought?


I don't care what direction the derivation goes into. How did you get the sense that I do?
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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Philosophaster » Wed Jun 10, 2009 8:50 am UTC

JoshuaZ wrote:The main issue that philosophers have with falsification is that you can construct more or less pathological cases where it doesn't work. The most serious objection IMO is that of Quine who observed that it isn't ever completely clear which hypothesis should be rejected after an experiment. Roughly speaking, hypotheses always exist as part of a network of hypotheses and you can reject or modify different ones. By appropriately modifying existing hypotheses you can prevent the direct falsification of a single specific hypothesis.

While this is an important issue, I don't think it is the most decisive objection to Popper's falsificationism (or "deductivism," as he called it), which is that a consistent Popperian would have to deny that there is any rational justification for the continued predictive use of any scientific theory.

According to Popper, inductive inference (drawing conclusions about the behavior of unobserved stuff on the basis of the behavior of observed stuff) plays no role in science, and in fact it has no rational justification at all. In place of inductive inference he attempts to offer an entirely deductive model of scientific reasoning.

If you have a theory that gravity follows the inverse square law and you make lots of observations that fail to falsify this theory, you can, on Popper's account, logically make the statement "The theory that gravity follows the inverse square law has not yet been falsified." But the problem is that there are any number of theories that haven't yet been falsified. If we want to have a *reason* to accept one not-yet-falsified theory over another, then we need some positive account of what constitutes evidence *for* a theory, not just why we should *reject* a theory. Further, even if a theory both is not yet falsified and has even made lots of correct predictions in the past (Popper calls this "corroboration"), why should we assume that it will continue to make correct predictions in the future? That would be an inference from the observed to the unobserved, which is an inductive inference and precisely the thing Popper thought was off-limits to science. Thus on Popper's account of scientific practice, we can have no *rational* justification for the continued use of even our best-corroborated theories. There is, on his account, no rational justification for using the inverse square law rather than an "inverse cube law" to predict the path of a planet tomorrow. For the consistent falsificationist the fact that a theory have not yet been falsified in the past does not give rational license for their continued use, and so the Popperian is stuck in the present with no epistemological warrant for thinking scientific theories will be of any use two minutes from now.

The idea that we should continue using non-falsified, well-corroborated theories for practical purposes is an inductive one, and cannot be accounted for under falsificationism.

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Re: Popperian falsificationism: useful idea, or naïve/outdated?

Postby Dil » Fri Sep 04, 2009 5:26 am UTC

Philosophaster wrote:
JoshuaZ wrote:The main issue that philosophers have with falsification is that you can construct more or less pathological cases where it doesn't work. The most serious objection IMO is that of Quine who observed that it isn't ever completely clear which hypothesis should be rejected after an experiment. Roughly speaking, hypotheses always exist as part of a network of hypotheses and you can reject or modify different ones. By appropriately modifying existing hypotheses you can prevent the direct falsification of a single specific hypothesis.

While this is an important issue, I don't think it is the most decisive objection to Popper's falsificationism (or "deductivism," as he called it), which is that a consistent Popperian would have to deny that there is any rational justification for the continued predictive use of any scientific theory.

According to Popper, inductive inference (drawing conclusions about the behavior of unobserved stuff on the basis of the behavior of observed stuff) plays no role in science, and in fact it has no rational justification at all. In place of inductive inference he attempts to offer an entirely deductive model of scientific reasoning.

If you have a theory that gravity follows the inverse square law and you make lots of observations that fail to falsify this theory, you can, on Popper's account, logically make the statement "The theory that gravity follows the inverse square law has not yet been falsified." But the problem is that there are any number of theories that haven't yet been falsified. If we want to have a *reason* to accept one not-yet-falsified theory over another, then we need some positive account of what constitutes evidence *for* a theory, not just why we should *reject* a theory. Further, even if a theory both is not yet falsified and has even made lots of correct predictions in the past (Popper calls this "corroboration"), why should we assume that it will continue to make correct predictions in the future? That would be an inference from the observed to the unobserved, which is an inductive inference and precisely the thing Popper thought was off-limits to science. Thus on Popper's account of scientific practice, we can have no *rational* justification for the continued use of even our best-corroborated theories. There is, on his account, no rational justification for using the inverse square law rather than an "inverse cube law" to predict the path of a planet tomorrow. For the consistent falsificationist the fact that a theory have not yet been falsified in the past does not give rational license for their continued use, and so the Popperian is stuck in the present with no epistemological warrant for thinking scientific theories will be of any use two minutes from now.

The idea that we should continue using non-falsified, well-corroborated theories for practical purposes is an inductive one, and cannot be accounted for under falsificationism.


I see you have made a few good points here. But I always thought falsification was to do with 'evaluating' as opposed to 'doing' science. If a hypothesis cannot be proved to be false, then you cannot be doing science. Popper made no attempts to explain what he called the 'psychology of science', or how one comes up with a hypothesis, or how to justify 'thinking a scientific theory will be of any use two minutes from now.' Yes, falsification assumes inductive logic is valid, and so does most things, if you think about it a bit about them.

Actually, you're making a general criticism of his theory on how science is to be conducted, while I am saying his demarcation was valid. Correct me I'm accidentally creating a red herring.


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