You’re missing something. One key aspect of Popper’s theory on falsification is the argument it acts as a criterion for science. Most people fixate on this as being a way to distinguish between science and non-science, however there is another way to view it. To return to your example of bowling balls in space, when said bowling ball falls at the same speed as feathers, you are not proving Newton’s Second Law, you are failing to disprove it. However, what that means is that insofar as you are in the business of dropping bowling balls, your failure to disprove the law means that it does not matter if Newton’s Second Law is accurate or not, only that the difference between it and the truth is such that it does not impact on life. Insofar as a theory in a given environment is unfalsifiable, it means you do not need to care about whether it is true or not. This observation I’d argue is far more valuable that the argument of repeated falsification.

Ah, but there will be an infinite number of laws that agree with all of human experimentation. Out of these, why should we prefer any one over any other?

From an epistemological perspective you don’t have to - from a practical perspective you just go with whatever happens to be most useful to the situation. Even if on a logical level both are permissible, most people tend to find that Newton’s Second Law is a more useful way of framing things than appealing to magical invisible elves that do functionally the same thing.

Need there be one? The distinction between various mutually unfalsifiable theories is essentially just one of communicative convention, rather than substantive content. Insofar as you are debating the ‘correct’ one to use, this is arguably wasting time from the actually valuable practice of dealing with the relevant concepts themselves. Just pick one you like and go with it.

That my whole point - insofar as you are debating between two mutually unfalsifiable theories, you aren’t actually discussing anything about how reality works, only how you wish to refer to the way it works

I.e whether or not you go with Newton's theory, or Newton+invisible elves theory, may not matter from a practical perspective, but it sure as heck matters from a "we want to figure out how the universe actually works" perspective

Looking forward to more in this series. But in the reconstructed version I first learned, the logical positivists believed in affirming the consequent ( the possibility of generating confirmatory hypotheses was their criterion for a meaningful statement). Popper then improved on them by replacing verification with falsification, and by making it a criterion for a scientific statement rather than for a meaningful one (as mentioned by CW III below).

Then Lakatos fixed up a lot of the problems with Popper, avoiding the difficulty of the critical test etc. And Bayesian reasoning helped a bit more.

As I said, a reconstructed version, but seems reasonably close to the mark.

It's going to take a long time to work through the whole story here, but I you'll see that Meehl (and I) don't quite agree with this reconstruction. In particular, I'm still not convinced Lakatos fixed anything nor do I think Bayesian confirmation theory brings anything particularly actionable to the table. But I promise to discuss both in depth as I work through these video lectures. Please call me out when you disagree!

I've always had a hard time with the notion of Popperian Falsification [that many scientists seem to take way too seriously. I definitely agree about "scientists' favorite philosopher" title...].

Besides the obvious and important "social" aspects of it [waiting for your next post about that] here's another argument against it from logical grounds. It somehow elaborates the predicate-calculus analysis you provided.

[I've discussed this in the past with few friends from philosophy, but I or them haven't seen this particular argument written out anywhere. I'm happy to hear if anyone knows any writing about/resembling it.]

We can think about (at least) two distinct types of claims about the world:

1. Claims of the form ∀x. P(x) ("for all x, P(x) holds")

2. Claims of the form ∃x. P(x) ("there exists an x such that P(x) holds")

False claims of type (1) can be _refuted_ in finite time, because in order to refute them you simply need to come up with one counter-example. In fancy words, they belong to the complexity class co-RE, or to the Pi_1 class in the arithmetic hierarchy.

However the general process of proving a true claim of this type might never terminate because it could always be the case that the very next example you haven't checked yet will fail (compare to the problem of induction).

Completely dual to that, true claims of type (2) can be proven in finite time because you'll eventually find a satisfying x. (They belong to the class RE, or equivalently to the Sigma_1 class of arithmetic hierarchy). But refuting a false claim might never terminate, because it could always be that the very next x you haven't checked yet is satisfying.

The Popperian falsification principle seems to implicitly suggest that scientists are only allowed to be interested in sentences of the first type. While it is true that many "natural laws" are formulated as universal quantification, it seems like a very unfair judgement that existential statements be deemed "unscientific" just because they "aren't refutable" (Indeed it's not too hard to think about famous "existensial" claims from history of science.)

Very interesting. Let me ask about an example to see if I'm following. Consider the statement "For the Standard Model of particle physics to be true, there must exist a Higgs Boson with mass between 100 and 200 GeV." Is this a sentence of type 2 in your mind?

For the part "There exists a Higgs Boson with mass between 100 and 200 GeV" -- I would say yes, this is precisely an example for a sentence of type 2. So as "a theory" about the world, it is in some sense "non-refutable" [somewhat similar to the famous Russel's teapot]

If you add to that the "For the standard model of particle physics to be true, then", I assume it depends on how we interpret this part of the sentence (it might itself entails complicated structures within?)

> Typical reasoning in science goes something like this: “If my theory is true, then I’ll observe this outcome of my experiment. I observe exactly this outcome. Therefore, my theory is true.”

I think this is incorrect. Typically it's

> “If my theory is true, then I’ll observe this outcome of my experiment. I observe exactly this outcome. ~~Therefore, my theory is true.~~ I will tentatively assume my theory is true until more information comes in”

Isn't it? I don't know of any practicing scientist who would conclude their theory is true after a single positive result.

Yes, I agree. I am guilty---and will continue to be guilty---of glib oversimplification. And this is what the Meehl quote is referring to. Something like this would also be an approximation of practice:

“If my theory is true, then I’ll observe this outcome of my experiment. I observe exactly this outcome. Therefore, my credence in the theory goes up."

Regardless, all three versions are *logically* invalid.

But any reasoning you add there is ampliative reasoning. Some philosophers in the 1920s and 1930s thought they'd be able to purge all ampliative reasoning from the philosophy of science. They were wrong, but it's helpful to work through they were wrong.

Yup definitely ampliative reasoning - but why is that bad? I'm a big fan of ampliative reasoning - not possible to derive everything from first principles

Actually this might be a better link re. credences - rewrite of poppers formal disprove of the idea of probabilistic induction: https://arxiv.org/abs/2107.00749

Damn, so many scientists, even mathematicians, can not present facts accurately but we expect there is a purely logical machine for them. Science is messy. Many of us are just using available mathematical/logical tool.(like null hypothesis). We can still get something useful. And we can even prove the existence by engineering

You’re missing something. One key aspect of Popper’s theory on falsification is the argument it acts as a criterion for science. Most people fixate on this as being a way to distinguish between science and non-science, however there is another way to view it. To return to your example of bowling balls in space, when said bowling ball falls at the same speed as feathers, you are not proving Newton’s Second Law, you are failing to disprove it. However, what that means is that insofar as you are in the business of dropping bowling balls, your failure to disprove the law means that it does not matter if Newton’s Second Law is accurate or not, only that the difference between it and the truth is such that it does not impact on life. Insofar as a theory in a given environment is unfalsifiable, it means you do not need to care about whether it is true or not. This observation I’d argue is far more valuable that the argument of repeated falsification.

Ah, but there will be an infinite number of laws that agree with all of human experimentation. Out of these, why should we prefer any one over any other?

From an epistemological perspective you don’t have to - from a practical perspective you just go with whatever happens to be most useful to the situation. Even if on a logical level both are permissible, most people tend to find that Newton’s Second Law is a more useful way of framing things than appealing to magical invisible elves that do functionally the same thing.

But then what is the logical reconstruction of use value?

Need there be one? The distinction between various mutually unfalsifiable theories is essentially just one of communicative convention, rather than substantive content. Insofar as you are debating the ‘correct’ one to use, this is arguably wasting time from the actually valuable practice of dealing with the relevant concepts themselves. Just pick one you like and go with it.

There does if you're interested in figuring out how reality actually works - i.e if you're interested in usefulness _and_ truth, not just usefulness.

That my whole point - insofar as you are debating between two mutually unfalsifiable theories, you aren’t actually discussing anything about how reality works, only how you wish to refer to the way it works

I.e whether or not you go with Newton's theory, or Newton+invisible elves theory, may not matter from a practical perspective, but it sure as heck matters from a "we want to figure out how the universe actually works" perspective

Looking forward to more in this series. But in the reconstructed version I first learned, the logical positivists believed in affirming the consequent ( the possibility of generating confirmatory hypotheses was their criterion for a meaningful statement). Popper then improved on them by replacing verification with falsification, and by making it a criterion for a scientific statement rather than for a meaningful one (as mentioned by CW III below).

Then Lakatos fixed up a lot of the problems with Popper, avoiding the difficulty of the critical test etc. And Bayesian reasoning helped a bit more.

As I said, a reconstructed version, but seems reasonably close to the mark.

It's going to take a long time to work through the whole story here, but I you'll see that Meehl (and I) don't quite agree with this reconstruction. In particular, I'm still not convinced Lakatos fixed anything nor do I think Bayesian confirmation theory brings anything particularly actionable to the table. But I promise to discuss both in depth as I work through these video lectures. Please call me out when you disagree!

That's really great.

I've always had a hard time with the notion of Popperian Falsification [that many scientists seem to take way too seriously. I definitely agree about "scientists' favorite philosopher" title...].

Besides the obvious and important "social" aspects of it [waiting for your next post about that] here's another argument against it from logical grounds. It somehow elaborates the predicate-calculus analysis you provided.

[I've discussed this in the past with few friends from philosophy, but I or them haven't seen this particular argument written out anywhere. I'm happy to hear if anyone knows any writing about/resembling it.]

We can think about (at least) two distinct types of claims about the world:

1. Claims of the form ∀x. P(x) ("for all x, P(x) holds")

2. Claims of the form ∃x. P(x) ("there exists an x such that P(x) holds")

False claims of type (1) can be _refuted_ in finite time, because in order to refute them you simply need to come up with one counter-example. In fancy words, they belong to the complexity class co-RE, or to the Pi_1 class in the arithmetic hierarchy.

However the general process of proving a true claim of this type might never terminate because it could always be the case that the very next example you haven't checked yet will fail (compare to the problem of induction).

Completely dual to that, true claims of type (2) can be proven in finite time because you'll eventually find a satisfying x. (They belong to the class RE, or equivalently to the Sigma_1 class of arithmetic hierarchy). But refuting a false claim might never terminate, because it could always be that the very next x you haven't checked yet is satisfying.

The Popperian falsification principle seems to implicitly suggest that scientists are only allowed to be interested in sentences of the first type. While it is true that many "natural laws" are formulated as universal quantification, it seems like a very unfair judgement that existential statements be deemed "unscientific" just because they "aren't refutable" (Indeed it's not too hard to think about famous "existensial" claims from history of science.)

Very interesting. Let me ask about an example to see if I'm following. Consider the statement "For the Standard Model of particle physics to be true, there must exist a Higgs Boson with mass between 100 and 200 GeV." Is this a sentence of type 2 in your mind?

For the part "There exists a Higgs Boson with mass between 100 and 200 GeV" -- I would say yes, this is precisely an example for a sentence of type 2. So as "a theory" about the world, it is in some sense "non-refutable" [somewhat similar to the famous Russel's teapot]

If you add to that the "For the standard model of particle physics to be true, then", I assume it depends on how we interpret this part of the sentence (it might itself entails complicated structures within?)

> Typical reasoning in science goes something like this: “If my theory is true, then I’ll observe this outcome of my experiment. I observe exactly this outcome. Therefore, my theory is true.”

I think this is incorrect. Typically it's

> “If my theory is true, then I’ll observe this outcome of my experiment. I observe exactly this outcome. ~~Therefore, my theory is true.~~ I will tentatively assume my theory is true until more information comes in”

Isn't it? I don't know of any practicing scientist who would conclude their theory is true after a single positive result.

Yes, I agree. I am guilty---and will continue to be guilty---of glib oversimplification. And this is what the Meehl quote is referring to. Something like this would also be an approximation of practice:

“If my theory is true, then I’ll observe this outcome of my experiment. I observe exactly this outcome. Therefore, my credence in the theory goes up."

Regardless, all three versions are *logically* invalid.

Ooph no all the credence stuff doesn't work at all... leads immediately to piles and piles of paradoxes... https://vmasrani.github.io/blog/2021/the_credence_assumption/

Also it's * not * logically invalid to say:

> "I will tentatively assume my theory is true until more information comes in"

Because it's not logic at all (there's no "... and therefore, X! ") - it's just reasoning.

Besides these small quibbles though, loving the series so far!

But any reasoning you add there is ampliative reasoning. Some philosophers in the 1920s and 1930s thought they'd be able to purge all ampliative reasoning from the philosophy of science. They were wrong, but it's helpful to work through they were wrong.

Yup definitely ampliative reasoning - but why is that bad? I'm a big fan of ampliative reasoning - not possible to derive everything from first principles

Actually this might be a better link re. credences - rewrite of poppers formal disprove of the idea of probabilistic induction: https://arxiv.org/abs/2107.00749

Damn, so many scientists, even mathematicians, can not present facts accurately but we expect there is a purely logical machine for them. Science is messy. Many of us are just using available mathematical/logical tool.(like null hypothesis). We can still get something useful. And we can even prove the existence by engineering

edited Apr 24This reminds me of the Nietzsche quote "What are man's truths ultimately? Merely his irrefutable errors."