Falsification

[Moonwood the Hare]

I think the whole issue of swans on other planets is a red herring if number of possible swans on earth is infinite.

But an infinite number of swans on the earth is not possible and so an infinite number of possible swans does not support your thesis. All that does is diminish the probability of any particular possibility.

If there are an infinite number of possible swans and a finite number of actual swans and an even smaller number of observed swans and the only swans we can know about directly are the observed ones and if we have no way of knowing which possible swans are actual the thesis stands. If there is another way of knowing about the actual but unobserved swans that must take the form of another theory about all swans which in turn will be subject to the same limitations.

While the nunber of actual swans is finite but immeasurable

But it is not immeasurable.

How would you measure it?

If the number of potential swans is massively larger than the number of observed swans then the probability of all swans sharing the properties of the ones we have observed approaches zero.

Incorrect. You cannot presume that all possibilities are equally likely, and howeverr large the number of potential swans may be, "all swans" is a finite number and so your conclusion does not follow.

Nor can you presume that all possibilities are not equally likely so any claim that they are not must take the form of another universal theory. If all swans is a finite and measurable number then the earth as a whole is a single exhaustively searchable location; a point in Popper's sense and that does change things.

By infinite universe, do you then actually mean an infinite earth (and thus an infinite number number of swans on the earth) or that by "all swans" you mean all the swans that ever exist assuming that they exist and reproduce forever? Then and only then does the nonzero probability of a non-white swan being produced become a certainty.

I would say as long as the potential number of swans is infinite we have the nonzero probability unless we can treat the earth as a single point.

I am not sure where we are going just now. My may point for a long time has been to get rid of the idea of universal theories being probably true in the formal sense. Do you think there is a way of measuring the truth of theories in terms of calculable probability?

[mitchellmckain]

I think the whole issue of swans on other planets is a red herring if number of possible swans on earth is infinite.

But an infinite number of swans on the earth is not possible and so an infinite number of possible swans does not support your thesis. All that does is diminish the probability of any particular possibility.

If there are an infinite number of possible swans and a finite number of actual swans and an even smaller number of observed swans and the only swans we can know about directly are the observed ones and if we have no way of knowing which possible swans are actual the thesis stands. If there is another way of knowing about the actual but unobserved swans that must take the form of another theory about all swans which in turn will be subject to the same limitations.

That is incorrect. The calculation of probability is never based suppositions of what is possible but only on what is observed to be possible (like in rolling dice). But in what we are talking about estimates of probability is based only on what has been observed and the actual (estimated) population.

While the nunber of actual swans is finite but immeasurable

But it is not immeasurable.

How would you measure it?

Measurements always have error bars. In this case we would calculate a mean based on observed frequencies and set error bars according 95% or 99% certainty according to what is consistent with observation. A simple 100% error bar can be always calculated based on various physical realities like physical living space or food availability. Science use such methods in every field all the time.

I would say as long as the potential number of swans is infinite we have the nonzero probability unless we can treat the earth as a single point.

potential in what sense? The number of molecules on the earth is finite so how could there be infinite swans?

Do you think there is a way of measuring the truth of theories in terms of calculable probability?

No. That isn't what theories are for and talking about them that way is just weird. We can estimate the probability of the truth of some propositions to be sure. But theories are a set of general principles which allow us to explain a whole range of phenomenon, and the only way in which their truth is measured is by their continuing success in explaining new observations.

[Moonwood the Hare]

Hi Mitch.
I realise that I said

I would say as long as the potential number of swans is infinite we have the nonzero probability unless we can treat the earth as a single point.

When I meant:

I would say as long as the number of potential swans is infinite we have the nonzero probability unless we can treat the earth as a single point

.
Anyway you say

That is incorrect. The calculation of probability is never based suppositions of what is possible but only on what is observed to be possible (like in rolling dice). But in what we are talking about estimates of probability is based only on what has been observed and the actual (estimated) population.

and

Measurements always have error bars. In this case we would calculate a mean based on observed frequencies and set error bars according 95% or 99% certainty according to what is consistent with observation. A simple 100% error bar can be always calculated based on various physical realities like physical living space or food availability. Science use such methods in every field all the time.

The question I take to be whether observation of less that all of something can be used to establish a claim that all of that thing share the properties of the less than all already observed. All scientific theories either contain 'all' claims or are inferred from 'all' claims (some people want to call these inferences from 'all' claims hypotheses) therefore in order to estimate a population you need to use existing theories and thus existing 'all' claims. To claim that using existing 'all' claims which are themselves induced from the observation of samples raises the probability of another all'' claim is to presuppose the validity of the prior 'all' claim. It's a lot like trying to defend induction by saying that it has always worked so far. Or as Skinner would put it you are presupposing what you need to prove. In the case of rolling a nice we can base our calculation on what is observed to be possible precisely because we know how many possible outcomes there are but we do not know how many possible swans there are so either we just say the probability of a universal claim is incalculable or we say as Popper does that it is zero.
But I do agree here:

That isn't what theories are for and talking about them that way is just weird. We can estimate the probability of the truth of some propositions to be sure. But theories are a set of general principles which allow us to explain a whole range of phenomenon, and the only way in which their truth is measured is by their continuing success in explaining new observations.