>I cannot really engage with your question. First, because I am not an expert in philosophy
I feel the entire field of philosophy is mostly useless and full of categorization errors. I don't buy into it, I just use the word for speculative stuff. A lot of the things that the actual field of philosophy chooses to speculate on (Animism for example) is just random garbage. They also pair religion and logic together as two peered pillars of study, as if religion is just as fundamental as logic. I have little respect for the entire field from a formal perspective. In my reply, I was using the word informally.
>You see, in the pragmatist view of a statistician (and in the math that goes with it), randomness - for example in the form of statistical independence
No we're talking about randomness as a fundamental phenomena in a procedural and physical universe. Meaning that what is a definition of a pure stateless function that takes no input and will always output a completely random number? The probabilistic definition of a random variable does not actually produce such a function and sort of avoids the concept of randomness all together.
In physics, quantum physics specifically, such a function is not defined but is taken as an axiom. The actual location of a atom after decoherence is assumed to be axiomatically random.
>Instead, we need the "switch" variable to be uncorrelated with things we do not observe, or can not adequately model.
Arguably everything in the universe is correlated and shares a causal connection. A butterfly flapping it's wings in China causes a hurricane on the other side of the world. On a grander scale: A perturbation of an atom in one corner of the universe eventually changes the parameters of every atom in the universe.
According to certain theories in physics information can only travel as fast as the speed of light. Therefore according to this logic all things can be causally connected but only up to a point. If you imagine multitudes of infinite spheres continuously growing out of an atom at the speed of light, then everything outside of a sphere that started growing at t0 is guaranteed to not have a causal connection to any events that happened to the atom at t0 or after.
However in math we create our own playground devoid of all the messiness of the universe and it's atoms and limits to causal transmission across large distances. Within this world there seems to me, to be an issue with your notion of a switch to be "uncorrelated."
For something to share a causal connection with another thing, both have to be correlated. You cannot establish causality if the switch is uncorrelated with the observation. The result will always be a failure in establishing causation if you are selecting this type of switch.
There is a paradoxical problem with the definition here. I get your intuition and you understand mine as well but this definition seems to be incomplete or not an accurate illustration of both of our intuitions of this concept.
Using "randomness" as a concept and leaving "correlation" out of the definition seems to better fit our intuition of what's going on when *I* or another human flips the switch. After all, you cannot have a causal relationship without a correlative one.
>Statisticians know that the idea of causality is by default not a philosophically "true" concept.
I would say the just "don't go there." They stop at the definition of a random variable and don't dig any deeper. https://en.wikipedia.org/wiki/Random_variable <--- on wikipedia a random variable is defined informally in terms of "random phenomena." Additionally the formal definition is defined in terms of "possible outcomes" so they're really side stepping the problem here. But that's ok, it's not really needed to play the mathematical game of probability.
>Related to this, let me offer you the perspective of social scientists.
A social scientists opinion is not any more valid than an average persons opinion. A social scientists views human behavior as a black box. They don't just put one human brain in a black box, they actually put a population of human brains in a black box and they try to analyze everything from that perspective. It simplifies things but inevitably there's a lot of missing information. One piece of this information is whether the output of the black box is random. If you can't peer into the black box you can never know if it's random or not random. Thus the social scientists viewpoint doesn't mean any more than someone who isn't a social scientists because most people view the brain as a black box as well.
That being said if there was a field that could closest determine "free will" it would be neuroscience and quantum physics. When I am flicking that switch and attempting to randomize the timing of it all what neurons are firing and what chemical reactions are occurring in my brain? What is the exact mechanism producing this action? Does the randomness of the quantum world leak out of a chemical reaction to influence the macro output of my timing on flipping that switch?
>That is, they would reject the notion that free will is indeed (or at least always) random.
Again they can't reject anything or accept anything related to this. To them, this part of the universe is underneath a black box.
>Sorry again that I have to rely on the statistical view - it is the only one I know a little bit about.
Who says you have to restrict yourself to viewpoints from certain groups? When you restrict yourself to "the statisticians" viewpoint or "the social scientists" viewpoint you are also restricting your intelligence.
Not to talk past each other’s: The definition of causal statistical identification is a formal one, but builds on the axioms of probability theory. The philosophical and even physical underpinnings of these axioms are, as they have always been, part if a heated debate.
However, the system is indeed consistent. And so, in this framework, neither true randomness (which is not a concept that has a definition here) nor independence is mathematically required for causal identification, instead, the switch variable needs to be uncorrelated to unobservables (and so on). That it needs to be correlated to the target variable is obvious, as you say. That is all tautological and simple to show.
I should also note that both independence and correlation are defined in terms of statistical properties that can hold irrespective of whether the world has true randomness. In a way, think if statistics as tying to the world that we see (the data) a consistent way of understanding and inferring. Now, whether the world actually works in terms of measures and moments, well, that is another question. And, I would propose, one that will be difficult to decide, in that it transcends our best ability to work with observational facts.
Note that there are other conceptions of causality and inference, distinct from statistics. I have worked with a group using models without any randomness, relying instead on the modeling of fully deterministic chaotic systems. They can indeed also fit the data, even if they are less practically useful.
As it turns out, a procedure of identifying causality, getting useful results, looks not too different.
So yeah, I think we agree in basic terms. In your view, causality as it is typically applied is fuzzy since its axiomatic framework does not arise from physical, philosophical or perhaps metaphysical facts as you believe or know them to be true. In my view, causality is fuzzy because any pragmatic definition, including one based on experiments, is based on assumptions without which causal identification is impossible. For instance, no matter what experiment you construct, we will need to assume that the operator switching randomly has not been paid money to choose a predetermined sequence by some James Bond villain. Of course, only one of us can be the operator, and so any pragmatic definition of causality (in being communicable) will eventually be fuzzy.
>switch variable needs to be uncorrelated to unobservables
What is an unobservable? Do you have a source for the formal definition of causal identification?
In wikipedia, they immediately skip logics and math and jump to science which indicates to me if a formal definition exists, it's controversial and likely not well known.
Unobservable is any factor that is correlated with outcome and switch, which you do not model or do not have data for.
To identify a causal effect of x on y, you need to exclude the possibility that x is correlated with z and z influences y. If it is so, you need to model z in some way (here, it depends on what we talk about). There are also other considerations, but that is perhaps the most pressing and obvious one. You can quickly convince yourself that the above must hold if a causal effect is to be identified. Under assumptions, for example induced by experimental conditions, the above is also sufficient to identify a causal effect.
The absence of any unmodeled z ( eg the Bond villain in our aforementioned randomness experiment) is essentially always an assumption and not a provable fact, which motivates my earlier discussion. Note also that measuring, modeling or otherwise taking into account any such Z depends on the Z and therefore the data generating process (aka the situation at hand )
Given that causal identification requires assumptions on the DGP, no general or non model based definition can exist.
That is, we CAN say what we mean by causality, however the task of identifying causality has to be stated in terms of a of the data generating process.
Perhaps herein lies the confusion.
Based on the DGP, mathematical definitions of causality do of course exist. For example, in the framework of switch and outcome, as defined, causality is semiparametrically identified if the switching is uncorrelated with other factors that are not modeled. In that case, we identify the qualitative direction of causality, or causal effect. For example, if the switching is true randomness, as per your definition, then the condition is fulfilled. However, randomness is only sufficient not necessary.
What a causal effect is, well, that means depends on the data and situation, for example what values outcome can take and what measures you apply: Expectations, Distributions, Order Statistics and so on.
If we see three people operating switches in terms of dials, we would for example be able to identify the average marginal effect of dialing on outcome. This would be an estimated expectation.
Formal definitions of these concepts can be found in, hopefully, any modern statistics textbook.
Otherwise, there are many formal treatments available. For the concept of statistical identification, Lewbells article „Identification Zoo“ is a good introduction. Formal definitions of identification and causal identification (albeit written for econometricians) are presented.
http://fmwww.bc.edu/EC-P/wp957.pdf
The first sections give a good understanding why it only makes sense to talk about causal effects and causal identification, if we have a model (restrictions on the DGP) in mind.
While the text is generally about statistical identification, you can do the following: Assume that based on your DGP/model, theta_0 (in the text) is the parameter telling you, whether X causes Y. Then, reading section 3 is probably sufficient to get an understanding of what causal identification is.
As it applies to causality and counterfactuals specifically, read Pearl as one framework, and research on Rubin for another. There are now, I think, good books on amazon treating both in more generality, especially outside of econometrics (which is or was for some time leading in non experimental causal analysis). Then, literature on experiments is also concerned with causal analysis, though since the distinction between correlation and causation is less of an issue, the literature has less focus on stating what exactly makes a procedure a causal analysis and what does not.
For that reason I actually recommend looking at the non experimental literature first, since the need for definition arises.
I feel the entire field of philosophy is mostly useless and full of categorization errors. I don't buy into it, I just use the word for speculative stuff. A lot of the things that the actual field of philosophy chooses to speculate on (Animism for example) is just random garbage. They also pair religion and logic together as two peered pillars of study, as if religion is just as fundamental as logic. I have little respect for the entire field from a formal perspective. In my reply, I was using the word informally.
>You see, in the pragmatist view of a statistician (and in the math that goes with it), randomness - for example in the form of statistical independence
No we're talking about randomness as a fundamental phenomena in a procedural and physical universe. Meaning that what is a definition of a pure stateless function that takes no input and will always output a completely random number? The probabilistic definition of a random variable does not actually produce such a function and sort of avoids the concept of randomness all together.
In physics, quantum physics specifically, such a function is not defined but is taken as an axiom. The actual location of a atom after decoherence is assumed to be axiomatically random.
>Instead, we need the "switch" variable to be uncorrelated with things we do not observe, or can not adequately model.
Arguably everything in the universe is correlated and shares a causal connection. A butterfly flapping it's wings in China causes a hurricane on the other side of the world. On a grander scale: A perturbation of an atom in one corner of the universe eventually changes the parameters of every atom in the universe.
According to certain theories in physics information can only travel as fast as the speed of light. Therefore according to this logic all things can be causally connected but only up to a point. If you imagine multitudes of infinite spheres continuously growing out of an atom at the speed of light, then everything outside of a sphere that started growing at t0 is guaranteed to not have a causal connection to any events that happened to the atom at t0 or after.
However in math we create our own playground devoid of all the messiness of the universe and it's atoms and limits to causal transmission across large distances. Within this world there seems to me, to be an issue with your notion of a switch to be "uncorrelated."
For something to share a causal connection with another thing, both have to be correlated. You cannot establish causality if the switch is uncorrelated with the observation. The result will always be a failure in establishing causation if you are selecting this type of switch.
There is a paradoxical problem with the definition here. I get your intuition and you understand mine as well but this definition seems to be incomplete or not an accurate illustration of both of our intuitions of this concept.
Using "randomness" as a concept and leaving "correlation" out of the definition seems to better fit our intuition of what's going on when *I* or another human flips the switch. After all, you cannot have a causal relationship without a correlative one.
>Statisticians know that the idea of causality is by default not a philosophically "true" concept.
I would say the just "don't go there." They stop at the definition of a random variable and don't dig any deeper. https://en.wikipedia.org/wiki/Random_variable <--- on wikipedia a random variable is defined informally in terms of "random phenomena." Additionally the formal definition is defined in terms of "possible outcomes" so they're really side stepping the problem here. But that's ok, it's not really needed to play the mathematical game of probability.
>Related to this, let me offer you the perspective of social scientists.
A social scientists opinion is not any more valid than an average persons opinion. A social scientists views human behavior as a black box. They don't just put one human brain in a black box, they actually put a population of human brains in a black box and they try to analyze everything from that perspective. It simplifies things but inevitably there's a lot of missing information. One piece of this information is whether the output of the black box is random. If you can't peer into the black box you can never know if it's random or not random. Thus the social scientists viewpoint doesn't mean any more than someone who isn't a social scientists because most people view the brain as a black box as well.
That being said if there was a field that could closest determine "free will" it would be neuroscience and quantum physics. When I am flicking that switch and attempting to randomize the timing of it all what neurons are firing and what chemical reactions are occurring in my brain? What is the exact mechanism producing this action? Does the randomness of the quantum world leak out of a chemical reaction to influence the macro output of my timing on flipping that switch?
>That is, they would reject the notion that free will is indeed (or at least always) random.
Again they can't reject anything or accept anything related to this. To them, this part of the universe is underneath a black box.
>Sorry again that I have to rely on the statistical view - it is the only one I know a little bit about.
Who says you have to restrict yourself to viewpoints from certain groups? When you restrict yourself to "the statisticians" viewpoint or "the social scientists" viewpoint you are also restricting your intelligence.