Is the Subjective Interpretation of Probability Falsifiable?

[Fra]

A frequently seen opinion, for example expressed by Popper in reflecting over what he calls the "the fundamental problem of chance in his classic "The logic of scientific discovery", is to reject the subjective interpretation of probability because he thinks it is not falsifiable.

This really seems to be a key point. I am curious on how other people reflect on this.

Popper IMO seems obsessed with requiring falsifiable strategies. But he seems far less fundamentally concerned with the problem of what do to when a theory is falsified. In an evolutionary perspective, this means that Popper requires lifeforms to be mortal, but is less concerned with evolution of life as a whole when a particular lifeform dies.

In the quest of trying to find a new evolutionary logic for fundamental physics, I think Poppers scientific philosophy of falsification is very crude. He doesn't provide a satisfactory model for the progressive evolution of life. He seems to always relate back to a fixed selection by corroboration, but doesn't consider the effiency of hypothesis generation. If I am not mistaken I think Popper said somewhere that he doesn't consider this latter problem a scientific problem, except possibly of psychology.

If you instead of falsification focus on correctability, then the subjective interpretation is not concerned with asking wether it is wrong, it is more focus on how to make a revision in case it's wrong. So the focus is on learning, rather than trying to kill false statements. If we are wrong, the interesting part isn't to go anal about concluding that we are wrong, it's how to recover a consistent opinion mixing the prior opinion with the new evidence.

I have acquired a disliking to much of Popper's reasoning here. He is much concerned with mortality/falsifiability but gives insufficient attention to the issue of flexibility/evolution/adaptive power.

I think we need a new logic also for science, that is more fit to face the moderns of modern fundamental physics.

I simply want to fire a simple question here, and probe how many the think the standard falsification/corroboration model is "up to date", or who think the new problems of fundamental physics and the quest for new logic that some people ask for (Smolin for example) does propagate down to the scientific method, and thus touches the philosophy of science (by definition)?

/Fredrik

 

[granpa]

the subjective interpretation of probability is in my opinion just the probable probability and has the same relation to probability as probability has to certainty. If I don't know whether something will happen or not I may still be able to say what the probability is that it will happen. If I can't say what the probability is then I can still say what the probable probability is that it will happen.

 

[oldman]

...how many .. think the standard falsification/corroboration model is "up to date", or who think the new problems of fundamental physics and the quest for new logic that some people ask for (Smolin for example) does propagate down to the scientific method, and thus touches the philosophy of science (by definition)?

/Fredrik

When trying to answer this question it's useful to appreciate what physicists should be trying to do: this is simply to describe as best they can, quantitatively and predictively, with the help of mathematics if needed, "the world of day and night, earthquakes and eclipses" that we know as physical reality.

When the domain of enquiry can't be experimented with, or even observed: why then, being human --- like inventers of sea serpents and galactic empires --- they resort to exercising the imagination, in most cases bolstered by esoteric mathematical ratiocination. Alas, this leads to the invention of stuff like string theory, the anthropic principle and multiverses. Overworked Popperian principles go by the board, or labelled old-fashioned, but the speculators keep their jobs!

Take Smolin's "quest for new logic" with a pinch of salt. It's special pleading.

 

[Fra]

Hello granpa, I'm not sure I share that view.

The subjective or bayesian (ignoring for a second that there are different version of this) interpretation of probability usually is a conditional probability that is evaluated relative the condition. It acknowledges that the "probability is relative". This could be largely expanded indeed, but it wasn't my main focus. Perhaps I was confusing in my post.

So the subjective probability is also similar to relative probability. And this probability represents our expectations based on our premises. This can thus be justified even if future relative frequences doesn't comply to this. Thus the probability can be seen as a basis for our actions, and thus the question of wether the "probability" at t, was "right", in the light of the information at t + dt, is not that interesting. Popper objects that this is not falsifiable, and that's partly right. But then the process of falsification has an extension in time, so the question is what do we falsify and when? I don't like Poppers abstraction here.

But though this triggered my poll, my main question was really with regards to the falsification vs evolution focus. Do you have an opinion on that? You didn't vote :)

/Fredrik

 

[Fra]

Alas, this leads to the invention of stuff like string theory, the anthropic principle and multiverses. Overworked Popperian principles go by the board, or labelled old-fashioned, but the speculators keep their jobs!

I just want to add quickly that note that in case someone though so, nothing of what I wrote has some hidden purpose of defending string theory. I am not a fan of string theory.

I know Smolin writes a lot of stuff, and some of his quest for new logic is more I think a reflection, he didn't in the book where I read it present a concrete suggestion. I figure he wants to stir up reflections and encourage new thinking of the readers and I appreciate this.

/Fredrik

 

[granpa]

http://business.clayton.edu/arjomand/business/l4.html

Relative probability is based on cumulated historical data. The following equation is used to assign this type of probability:

P(X) = Number of times an event occurred in the past/ Total number of opportunities for the event to occur

Note that relative probability is not based on rules or laws but on what has happened in the past. For example, your company wants to decide on the probability that its inspectors are going to reject the next batch of raw materials from a supplier. Data collected from your company record books show that the supplier had sent your company 80 batches in the past, and inspectors had rejected 15 of them. By the method of relative probability, the probability of the inspectors rejecting the next batch is 15/80, or 0.19. If the next batch is rejected, the relative probability for the subsequent shipment would change to 16/81 = 0.20.but this won't work until you have historical data. bayesian probability takes historical data into account but also works without any such data. simply knowing how many outcomes are possible is sufficient to determine a bayesian probability.relative to what condition? not sure what you're saying here.

 

[granpa]

So the subjective probability is also similar to relative probability. And this probability represents our expectations based on our premises. This can thus be justified even if future relative frequences doesn't comply to this. Thus the probability can be seen as a basis for our actions, and thus the question of wether the "probability" at t, was "right", in the light of the information at t + dt, is not that interesting. Popper objects that this is not falsifiable,
/Fredrik

It wasnt wrong because it didnt claim to know the probability, only the probable probability.

 

[granpa]

If I flip a 2 headed coin then you know the outcome. If it is a regular coin then you know the probability. but what if you don't know whether it is a regular coin, a 2 headed coin, or a coin with 2 tails? then you don't know the probability but if you live long enough and encounter this situation often enough then you would expect to see heads half the time. that would be the probable probability. (maybe 'probable probability' isn't the best choice of words but it makes it intuitive to me)

 

[Fra]

The terminology got confused here I think. The link you refer to mentions relative frequencies, this is not what I meant with "relative probability". I refer to the conditional version, setwise defined as

"P(a|b) = P(a or b)/P(b)"

See http://en.wikipedia.org/wiki/Conditional_probability

It can be seen as a probability of a "relative to b". Or given that we know b, what's the "chance" of "a" beeing true.

Probable probability to me sounds like you are considering the probability of a probability. Ie. a "probability of a distribution". That is an interesting concept too but something different and I think of that as belonging to higher order constructs.

So the conditional probability is not in my view the same as an "uncertain probability". It is certain, it's just that it's relative to it's second argument. If it is uncertain it means the second argument is uncertain.

Just like relative velocity in SR. It doesn't mean the velocity is uncertain (unless of course, you are uncertain of who is the observer), it just means it's relative (to the observer).

Anyway my original poll didn't concern the basic definitions. It aims to ask if we think anything in the challanges that we face in fundamental physics, suggest that we would benefit from a deeper analysis of the scientific method itself?

/Fredrik

 

[granpa]

http://en.wikipedia.org/wiki/Bayes'_Theorem

Bayes' theorem relates the conditional and MARGINAL probabilities of events A and B, where B has a non-vanishing probability:
P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.Each term in Bayes' theorem has a conventional name:
P(A) is the PRIOR PROBABILITY or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
P(B|A) is the conditional probability of B given A.
P(B) is the prior or marginal probability of B, and acts as a normalizing constant.

conditional probabilities arent themselves bayesian in nature. it is the marginal probabilities that make bayesian probabilities bayesian. marginal probabilities are what I am calling probable probability.

 

[granpa]

So the conditional probability is not in my view the same as an "uncertain probability". It is certain, it's just that it's relative to it's second argument.
/Fredrik

thats more or less what I said in post 7

 

[granpa]

personally I don't expect the scientific establishment to be perfect any more than I expect democracy to be perfect. democracy isn't perfect but its better than any alternative.

IMHO, the main troubles with the establishment are political more than scientific in nature.nonobservables like intuition are unfortunately unfalsifiable and I don't see any practical way of working them into the scientific method/establishment. I don't think bayesian probability falls into this category though.

 

[Fra]

nonobservables like intuition are unfortunately unfalsifiable and I don't see any practical way of working them into the scientific method/establishment.

I think the concept of what is an observable is also at heart of these issues. I see what you are saying here, but one might ask what the reference is for characterizing observables? I do not think it's a priori obvious that different observers see the same observables.

Therefore, observables could possibly be hidden to other observers. Then the question is, which observer is to be considered the one beeing right about what is observable?

My take on this, is that we need no a priori answer to this. This very uncertainty is I think part of what gives rise to interactions between observers. There disagreement are the basis for interaction.

It's common for people that argue against "subjective theories" to raise points such as "mental" or "pshycological". But the subjective notions exist also in the inanimate objects. But there we usually call it relative rather than subjective. I think it's ultimately of the same nature, where objectivity is emergent. This is however as I read Popper in contradiction with his choice of reasoning.

/Fredrik

 

[vanesch]

I think there are different issues here (which, btw, also show up in other areas, such as the interpretation of physical theories, especially quantum theory). I think that what Popper tries to point out is that the "hard backbone" of science is falsifiability, that is, in order for you to make a "hard claim", it needs to make predictions that can be tested (falsified) by experiment/observation.
However, that shouldn't refrain us from "dressing up" that backbone with non-falsifiable clothes, in order to make a smoother, more complete "story". Usually this dressing-up goes under the name of "interpretations" or "pictures" or whatever. I think these things ARE useful for us, as human beings, in order to help us get a "mental picture" or a "view on the mechanics" or how would you call it from the bare hardcore theory. We should however keep in mind that there is a distinction between the backbone which is falsifiable, and the "story" which is just the packaging for human minds. It serves no big purpose to go into conflict over the packaging, because the main technique we normally use to settle disagreements, namely observation/experiment, won't help us out. So it is subjective. We CAN go into disagreement over the falsifiable backbone, because that IS something that can be settled by experiment - at least in principle. However, it is not because we won't be able to settle the dispute in a "scientific way" that the subjective part, the dressing up, is useless. It isn't useless. It gives us a picture, it can inspire us, it can give us some "feeling" for what goes on etc...

 

[Fra]

Vanesch, I see what you say and the backbone view vs interpretations that's useful. I don't directly disagree with anything but I think that I an more hopeful than you about the emergent objectivity from subjectivity so to speak.

I think for various reasons that poppers illusion of "hard claims" are somewhat illusionary, in particular when you analyze the PROCESS of falsification, in particular when it comes to random phenomena, then falsification becomes degrees of falsification, and then. I think popper looses effiency by trying to hold on to his "deductive mode", rather than some inductive mode.

Popper makes great sense for most purposes, so don't get my suggestions wrong. I just think that an analysis of the actual meaning of falsification and measurement, in particular when the observer itself is part of the equation, this deductive thinking isn't satisfactory.

When we consider degrees of falsification, even the poppian idea boils down to statistics, and probability. And there we go again.

I don't think we should toss falsfiability for random opinion, I think we should replace falsfiability by relative confidence and falsfication by a automatic self-correction that not only kills a statement, but instead deforms the statement, so we are having an evolution.

If actions of a system, is determined by it's subjective view, then it seems to me that could indeed ultimately lead to predictions on the interactive properties of such system.

/Fredrik

 

[statdad]

This

the subjective interpretation of probability is in my opinion just the probable probability and has the same relation to probability as probability has to certainty. If I don't know whether something will happen or not I may still be able to say what the probability is that it will happen. If I can't say what the probability is then I can still say what the probable probability is that it will happen.

makes absolutely no sense.

 

[granpa]

This


makes absolutely no sense.

read posts 8 and 10.

 

[statdad]

Regarding

read posts 8 and 10.

I did before I posted, and just re-read them. Perhaps my response was knee-jerk, if it seems that way I apologize. However, I still don't see the point. If it is simply this:
''marginal probabilities are what I am calling probable probability''
why go through the work of inventing new names for old.

The comment referencing life experience and developing a feel for the probability of an event seems to be what we refer to as the empirical approach to probability. again, why the need for new language?

 

[granpa]

I didnt make it up myself. I read it on wikipedia. I tried to look it up but it appears that they have completely changed it.

 

[statdad]

I'm not surprised about the second part of your statement:

I read it on wikipedia. I tried to look it up but it appears that they have completely changed it.

I must hasten to say that my comments were not meant to be taken as an attack on you: they were a simple, if poorly worded, statement of my opinion. Nowhere in my graduate programs did I see discussions of probability with those terms.

If I offended you I apologize; that was not my intent.