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