What Makes a Good Scientific Hypothesis?

What Makes a Good Scientific Hypothesis?
Unisonus
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Posted Oct 17, 2006 - 8:33 PM:
Subject: What Makes a Good Scientific Hypothesis?
I'm going to ask two questions:

(1) What are the essential characteristics of a scientific hypothesis?

(2) Given two rival hypotheses (H1 and H2) for an event E, how do we decide which is better?

Here are two of the most popular answers, and my objections:

(1) A scientific hypothesis for E is any falsifiable proposition which gives us the causal history of E, or otherwise aids in our understanding of E in some significant fashion.

However, the falsifiability criterion is flawed. Let us distinguish between two kinds of statements:

Falsifiable: "Water boils at 100 degrees Celsius".

Unfalsifiable: "Thor likes jelly doughnuts".

However, the following statement is also falsifiable:

"Water boils at 100 degrees Celsius and Thor likes jelly doughnuts".

Any conjunction of a falsifiable proposition P with any other proposition Q is itself falsifiable; if P is falsified, then (P & Q) is falsified. Hence, the falsifiability criterion does not proscribe unfalsifiable statements from being within the purview of science.

(2) H1 is better than H2 if the probability of E given H1 is greater than the probability of E given H2:

Pr(E|H1) > Pr(E|H2)

Suppose for instance, an incredibly hot chick knocks on my door (E). There are two rival hypotheses:

H1: She is at the wrong door.
H2: She is there because of my charm and good looks.

Let's say the Pr(E|H1) is .4. Seeing as Pr(E|H2) is somewhere near 0:

Pr(E|H1) > Pr(E|H2) and therefore H1 is the better of the two hypotheses.

However, this explanation is problematic. For any E, is it possible to construe a hypotheses such that the probability of E given that hypotheses is 1; moreover, since there are an infinite number of such hypotheses, choosing between them would be impossible.

Example: The world exists in some fashion (E):

H1: It came to be this way via a series of natural events.
H2: There is a very powerful god whose only desire is create the world as it is.

If Pr(E|H2) = 1 (and it does), and Pr(E|H1) < 1, then H2 is the better of the two explanations! Moreover, there are an infinite number of similar explanations. For instance:

H3: There is a very powerful god whose only desire is create the world as it is AND he is fond of yellow hats.
H4: There is a very powerful god whose only desire is create the world as it is AND he thinks yellow hats are bad taste.

Ad infinitum.

Now, is this disingenuous on the part of the theorist? One philosopher, Eliot Sober, thinks so. He writes:

"This problem is not solved by simply inventing assumptions about the putative designer(s) goals and abilities; what is needed is information about the putative designer(s) that is independently attested."

Isn't this a silly!? Sober is asking the theorist to prove, independently, what he is already proving VIA an argument. Imagine that someone asked Einstein to "independently prove" relativity before he used it to explain the bending of light near the sun! The demand doesn't make any sense, does it?

Clearly, the objection that these hypotheses are unfalsifiable will not work, because the falsifiability criterion is flawed.

This framework for judging the relative strengths of hypotheses is unfortunately very popular. It has been used by a number of apologetics as a means to demonstrate the fitness of the god-hypothesis. Consider the probabilistic argument to design:

Where:

L = Life
I = Intelligent Design
N = Naturalism

1.Pr(L|I) > Pr(L|N)
2.Pr(I|L) > Pr(N|L) [conclusion]

In English:

1.The probability of life (given ID) is greater than the probability of life (given naturalism).

2.Therefore, the probability of ID (given that there's life in the universe) is greater than the probability of naturalism (given that there's life in the universe). [conclusion]

Now this argument is flawed regardless of the fitness of the god-hypotheses (I); but given this evidential framework, the hypotheses is acceptable – which is absurd.

---------------------

So, I hope I've shown that things aren't as clear as they seem!
Exponent
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Posted Oct 17, 2006 - 9:39 PM:

I think we need to keep in mind multiple criteria, rather than focus on just one. If a hypothesis is unfalsifiable, it is not scientific; if it is falsifiable, then it might be scientific. We still have to cover more criteria to be sure, though.

One big one that I think often gets forgotten or turned around inappropriately is the ability of a hypothesis to make predictions. This is generally the most important part of testing a hypothesis. And the hypothesis should only contain as much content as will lead to testable predictions. In your example "Water boils at 100 degrees Celsius and Thor likes jelly doughnuts", we could make a few predictions. One, if we heat water, measuring its temperature the whole time, we would predict, based on the hypothesis, that it would begin to boil at (but no sooner than) 100 degrees Celsius (within a margin of error, of course). We could also predict that if Thor is in the presence of a jelly doughnut and is otherwise unoccupied, he'll eat it. Now the first prediction is obviously testable/falsifiable, and the second is obviously not. So I would say that if any component of a hypothesis cannot produce a falsiable prediction, then that component should be removed from the hypothesis. Sort of like Ockham's Razor applied to hypotheses. If for some reason such a component cannot coherently be removed from a hypothesis without rendering the rest of the hypothesis broken (can't think of an example offhand), then I would say that the whole hypothesis is unfalsifiable.

An example of how hypothesis->prediction->testing is often misunderstood is with evolution and the fossil record. People arguing against evolution will claim that we can't actually go back in time and observe what happened, so we can't experimentally verify evolution. But the hypothesis of evolution, once considered in depth, provides all sorts of predictions, predictions that can be tested today. For example, evolution (when combined with specific studies of geology, taxonomy, and so forth) predicted that fossils of species in the evolutionary tree between fish and tetrapods would be found in geological formations of a certain age and indicating a certain environment/climate. Scientists used that prediction to figure out where to look, and they found Tiktaalik, thus providing a confirmation of a prediction.

Similarly, evolution, once combined with our knowledge of genetics, predicts a unique nested hierarchy, and as we sequence more and more genomes, we find that the genomes do indeed fit exceptionally well. (Note that there are some exceptions, and the awareness of these exceptions lead to the hypothesis of, and subsequent testing/confirming of the process of horizontal gene transfer.)

(Sorry for just evolution examples; I've been studying it a lot lately, so it's on my mind.)

So I would tentatively suggest this procedure for determining if a hypothesis is scientific: First, is it falsifiable as a whole? If not, then reject it as scientific. If so, then try to use it to make as many predictions as you can think of (or let those who advocate the hypothesis do all the thinking). Then, consider the falsifiability of each prediction, and for every component of the hypothesis that does not contribute to a falsifiable prediction, reject that component and all other components that logically depend on it. What you have left would likely be a decent scientific hypothesis, with one or more avenues available for testing.

Depending on what your purposes are for scrutinizing a hypothesis, you might be lenient with the falsifiability criterion. In some cases, a hypothesis might not be immediately falsifiable, but it could hypothetically and conceivably become so in the future. In that case, it might be worthwhile to not outright reject, but just keep in the back of your mind. Or in some cases, you might want to try to adjust, expand, or explore the hypothesis in order to find some predictions that can be tested presently. Such is the current situation with superstring theory/hypothesis. It has made trivial predictions that have been verified (it can account for a particle that would potentially end up producing the effect of gravity). It has made some predictions that aren't currently testable, but might be if/when we build better particle accelerators or other fancy devices. And the scientists researching it are continually trying to improve it to weed out other clever predictions that it makes that might actually be testable today.

As for choosing between two hypotheses, if you determine they both are scientific and have predictions that are testable today (but aren't yet tested), then I suppose it is up to your subjective whim regarding which one you'd be interested in testing yourself (or watching to see the results of others who do test it). At this stage, though, I wouldn't think you should choose which one to agree with, since that shouldn't be done until after at least some amount of testing.

If they both have already been tested, then I suppose there are a whole lot of different criteria involved. How many predictions did each make? How unique were each of the predictions? (It's obviously not as significant if two predictions that are nearly identical are both confirmed, rather than if two totally different predictions are both confirmed.) How accurate were each of the predictions when compared to the results of the experiments? How well does each hypothesis integrate with other hypotheses that are well tested and generally accepted as reasonably accurate models of reality? And so forth.

If one has been tested and the other hasn't, then I suppose the question is whether one should just stick with the tested and reasonably verified hypothesis, or spend time testing the new hypothesis. If there are any glaring gaps or exceptions in the tested hypothesis, or if the untested hypothesis makes some predictions that wouldn't be overly hard to test (no reason to spend billions of dollars testing a hypothesis that competes with a well accepted hypothesis that doesn't have any significant flaws), then you might go ahead and test it. If verified, and then verified even better than the former hypothesis, you'd probably get the advantage of money/recognition, so that's always a nice incentive to persue new hypotheses even when we have a reasonable one already in place.

With all that in mind, you'd never really choose between two hypotheses merely using the criterion of how possible observed events are given each hypothesis. You might do that after all the other criteria were used, if you still wound up with a tie. If both hypotheses are falsifiable, both produce similar numbers and types of predictions, and the predictions of both have both been equally verified, and they both fit with existing theories equally well, then you might be able to choose on this probability criterion, or other criteria that might be rather subjective in nature. But I personally would keep both in mind, looking for clever predictions that were overlooked originally, or looking for adjustments to either one that would produce more predictions that the other doesn't.

Either that, or I would consider the possibility that the two hypotheses are actually logical equivalents that will ultimately always end up producing the same predictions, just worded differently or viewed from a different perspetive. If this could be shown, then the need to choose should evaporate. For example, there are five different "flavors" of 10-dimensional string theory, each with its own formulas and predictions and such. However, it was eventually realized that by adding an 11th dimension appropriately, all five forms could be translated into each other, and thus the mathematicians realized that this was really just one single system, and it could be morphed into whichever form was most convenient for whatever task needed to be done at the moment, and also that all the predictions resulting from one form applied to the whole system and all forms, but would be very difficult to discover in different forms.

Summary: No criterion by itself is going to determine if a hypothesis is scientific or not, and no criterion by itself is going to allow you to choose between two competing hypotheses. Thus we shouldn't expect that there would be such a single criterion and shouldn't criticize science for not providing one single criterion. An appropriately chosen set of criteria will do just fine.
Unisonus
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Posted Oct 18, 2006 - 12:13 AM:

Thank you, Exponent. That was a very insightful post.

I've picked up on at least three criteria for a "good scientific hypothesis" from your post. A good theory is:

(1) Falsifiable. Do you think you could come up for a good conditional such as: "If a proposition is falsifiable, then.....". This would help us better understand falsifiability. The reason I ask for this is because you seem to be rather lenient in your interpretation of this criterion (allowing for future falsifiability and so forth). I think this might cause some problems unless the criterion is well-defined.

(2) Able to make predictions. I would ask for another conditional here. It seems to me that there are a variety of hypotheses which entail future states of affairs - and many of these are unscientific.

(3) Passes Occam's Razor. I think that this is also problematic. Let me give this interpretation of the maxim:

"In the context of science, posit the least number of necessary entities."

Now take two accounts of why the planets move:

H1: God moves them about.

H2: Inertia and gravity and so forth....

Is there a difference in the number of entities posited by either theory? Each entity within each of these theories seems in some way essential to the theory as a whole.


fredrick
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Posted Oct 18, 2006 - 7:01 AM:

i've only read this last post, i'm sorry but the above is quite long and i don't have much time, however...

Able to make predictions. I would ask for another conditional here. It seems to me that there are a variety of hypotheses which entail future states of affairs - and many of these are unscientific.


that should be narrowed down a little... many things make predictions, but in order to be scientifically useful those predictions should have a degree of uniqueness.

There are many hypothesis' which predict, for example, the motion of the planets. But we already have a theory which predicts the motion of the planets, so these other hypothesis' need to make a unique prediction regarding their motions.

If the hypothesis says exactly the same thing will happen as the already established theory, then it is useless. But if the theory makes the unique prediction, using a historic example, of a funny little wobble in the orbit of Mercury, then this hypothesis is far more useful; and we say it is strongly confirmable.

Still, doesn't this come under falsifiability? by making unique predictions, it is made more falsifiable. I'd argue for only the criterion of falsifiability, as predictiveness and testability all come under the same heading. Other common sense rules of thumb, like Ockham's should be recognised provisionally, but i don't think they should be necessary to scientific hypothesis... and i wonder if many string theorists would agree...
Kwalish Kid
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Posted Oct 18, 2006 - 8:06 AM:

Unisonus wrote:
(2) H1 is better than H2 if the probability of E given H1 is greater than the probability of E given H2:

Pr(E|H1) > Pr(E|H2)

Suppose for instance, an incredibly hot chick knocks on my door (E). There are two rival hypotheses:

H1: She is at the wrong door.
H2: She is there because of my charm and good looks.

Let's say the Pr(E|H1) is .4. Seeing as Pr(E|H2) is somewhere near 0:

Pr(E|H1) > Pr(E|H2) and therefore H1 is the better of the two hypotheses.

This is not exactly the right way to go about things. We want to come to come sort of conclusion about the hypothesis given the available evidence. We might ask which hypothesis makes a particular body of evidence more likely, but in the end we should use this in an attempt to justify an hypothesis from evidence.

The actual use of statistical reasoning in science is far different from the way that it is used in these examples.
Example: The world exists in some fashion (E):

H1: It came to be this way via a series of natural events.
H2: There is a very powerful god whose only desire is create the world as it is.

If Pr(E|H2) = 1 (and it does), and Pr(E|H1) < 1, then H2 is the better of the two explanations! Moreover, there are an infinite number of similar explanations.

It cannot be, in this example, the case that we would, upon adopting H1, revise our beliefs to believe that Pr(E) < 1, can it? It might be that Pr(H1) < Pr(H2), outside of the available evidence, but that doesn't necessarily bear on the probability of E given the assumption of H1 or H2. Simply that the world exists does not have any bearing as evidence on theories about the existence of the world (unless those theories claim that the world does not exist).
H3: There is a very powerful god whose only desire is create the world as it is AND he is fond of yellow hats.
H4: There is a very powerful god whose only desire is create the world as it is AND he thinks yellow hats are bad taste.

Interestingly, hypotheses like these are part of every serious design argument. And they are the reason that the design argument a) can be taken seriously, and b) historically failed in the face of the data.
Now, is this disingenuous on the part of the theorist? One philosopher, Eliot Sober, thinks so. He writes:

"This problem is not solved by simply inventing assumptions about the putative designer(s) goals and abilities; what is needed is information about the putative designer(s) that is independently attested."

Isn't this a silly!? Sober is asking the theorist to prove, independently, what he is already proving VIA an argument. Imagine that someone asked Einstein to "independently prove" relativity before he used it to explain the bending of light near the sun! The demand doesn't make any sense, does it?

No, it makes sense. It's what Einstein actually did and what science is all about. Einstein addressed a host of independent methods of measuring parameters of his theory. The bending of light around the sun, and the Eddington eclipse test, is merely one such means of testing these parameters. At the beginning of General Relativity, there was also the measurement of the perihelion precession of Mercury. The relativistic effect is fairly subtle in the solar system, but many other tests have been devised. (Clifford Will's book, Was Einstein Right?, is excellent and quite readable. You can hear a lecture by Will at this WGBF Lecture page.)

What Sober is demanding is that a design theory be something that can gather evidence. Historical design arguments are actually this kind of theory. So are some intelligent design arguments, just not the slippery political things offered in popular media.

At one time, the argument for design rested on the evidence that organisms were suited for their environment. There are reasons, when considering the concept of a designer, to propose certain characteristics for organisms. The argument for design fails because of the evidence that organisms are not suited for their environment and the evidence that organisms are related in many other different ways to their environment. No design argument has been able to predict these other relationships of organism to environment without simply adding in specific predictions. That is, no design argument has been able to produce a reason why organisms should be the way they are. The slippry political thing in the popular media makes the claim, organisms are the way they are because that's the way they are.

This is not an independent process. It would be like Einstein adding a new parameter to his theory that was only about Mercury and nothing else.

Full Clifford Will lecture url, just in case: www.forum-network.org/wgbh/.../forum.php?lecture_id=3176
rabeldin
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Posted Oct 18, 2006 - 9:27 AM:

The effort one is willing to put into finding the evidence that a hypothesis is false is interesting. For example, some scientists spend their entire careers inventing/developing more sensitive methods of observation, even to the point of never having a chance to use them.

On the other hand, some scientists refuse to spend a full minute on something that reeks of supernaturalism or fundamental misunderstanding of the basics of thermodynamics.

In a sense, the effort that one is willing to exert is a measure of one's subjective evaluation of the hypothesis. If it seems promising, in that it will answer current questions, we will work at it.
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Posted Oct 18, 2006 - 10:11 AM:

Exponent wrote:
I think we need to keep in mind multiple criteria, rather than focus on just one. If a hypothesis is unfalsifiable, it is not scientific; if it is falsifiable, then it might be scientific. We still have to cover more criteria to be sure, though.

I agree with the idea of looking to multiple criteria, but plenty of unfalsifiable things are scientific.

The basic ideas of natural selection are unfalsifiable. What matters is the extent to which they apply to organisms in the world.

f=ma is unfalsifiable, as it appears in Newtonian mechanics (though the extent to which it appears in Newton's work is somewhat debatable). It is part of the basic by which we identify forces.What matters is the extent to which this description of forces is applicable to the world.
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Posted Oct 18, 2006 - 12:31 PM:


fredrick wrote:
There are many hypothesis' which predict, for example, the motion of the planets. But we already have a theory which predicts the motion of the planets, so these other hypothesis' need to make a unique prediction regarding their motions.


When you write, "we already have" - what does that mean? There is one theory which explains the motions of the planets, and there are others. Which of these theories is "unique" - as you say - and what does that mean?

kwalish kid wrote:
Einstein addressed a host of independent methods of measuring parameters of his theory. The bending of light around the sun, and the Eddington eclipse test, is merely one such means of testing these parameters. At the beginning of General Relativity, there was also the measurement of the perihelion precession of Mercury.


Let me make my interpretation of Sober's objection clearer:

If the probability that relativity is true given that light bends around the sun is .9 - and this is proof of the theory's superiority - then Sober's objection would be akin to: "One needs an independent verification of relativity; it is not enough merely to posit the most probable theory given the data." But this objection is as absurd here as it is in the case of the god-hypothesis; every theory verified when it is seen as likely given the data - it makes no sense to beg for an independent verification.


I do not mean that Einstein ignored the data when he construed his theory; I do not mean that the data was inessential to its verfication. Sober is objecting to the practice of holding a theory merely because it is probable given the data. At least, that was my impression.

Here are a bunch of links (I can't access them right now, for some reason) to Sober's writing on this very question.

This doesn't so much reveal a flaw in Sober's reasoning as it does in Bayesian evidential schemes (which Sober rejects, it seems to me, in his more recent work).




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Posted Oct 18, 2006 - 12:57 PM:

I'm not sure that I understand your interpretation of Sober's point.

The problem with designing ad hoc theory is that the probability of any evidence given the theory is going to be 1. This means that we are not going to do any Bayesian reasoning, because we are not going to update our proability. So we are not really doing evidence-based theory justification.

Evidence-based theory justification does not stop with particular experiments. It might be that the Eddington experiments justify us in revising our estimation of relativity upwards, but this doesn't mean that we put absolute faith in either relativity or the experiments. They must play some part in a host of other investigations, including those of our everyday lives.
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Posted Oct 19, 2006 - 1:06 PM:


Kwalish Kid wrote:
The problem with designing ad hoc theory is that the probability of any evidence given the theory is going to be 1.


But all theories are formulated after the fact. Scientists do not explain observations which haven't been made, data that haven't been collected, or phenomena that haven't occured.

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