Philosophy of science: Determinism and indeterminism in statistical methods of science

Question

A variable is modeled as a random variable in a statistical model, often without reference to the question of whether it is random in reality. For example, when the outcome of a coin flip is modeled as a random variable, no one asks the question whether the process of coin flipping is "really random". A "really random" process is indeterministic. A latent or hidden variable is actually deterministic; however, due to a lack of knowledge (or convenience) it is treated as a random one.)

My question is if there is any stage in the scientific process that the question of whether the random component of the model represents "true randomness" becomes relevant?

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I have asked the question also on a statistics forum. However, I am interested in answers from a philosophical point of view.

Answer 1

The statistical concept of random (lack of pattern, unpredictability) does not make any distinction between truly random (unintentional) and pseudo-random (intentional).

The philosophical concept of random refers to the source of the value. A truly random value comes from a stochastic process that no-one controls. A pseudo-random value is deliberately selected to give the impression of randomness.

Answer 2

As with every part of mathematics applied in natural sciences one can embrace the point of view of instrumentalism. When investigating some natural phenomena (which I call the target system and denote it by T) scientist constructs a mathematical model M together with some sort of interpretation of that model I:M->T such that the pair (M,I) adequately describes T in the sense that it achieves some practical purposes of the scientist. From this perspective there is no serious difference between mathematical applications in natural sciences regardless if they are ordinary differential equations or probabilistic spaces in the sense of Kolmogorov. For the matter of applications of probabilistic spaces statisticians developed (and still are developing) a large arsenal of methods to measure accuracy of their models. This is all what natural and social sciences need.

Now let me be more philosophical. The reality is that we don't know the reality. From the point of view of ontology we don't know if there are any truly indeterministic processes and (not surprisingly) we also don't know if there are truly deterministic ones. For instance it is perfectly consistent with the structure of mathematics that some structures which in reality (ontologically speaking) are indeterministic can be to enormous degree of accuracy described by systems of ordinary differential equations satisfying the usual Lipschitz condition (which is the deterministic structure par excellence). Conversely there are truly deterministic processes which are to large degree of accuracy described by stochastic processes. There are no decisive criteria known in mathematics to demarcate between the two. Maybe we will find out some day, but as for today I haven't heard about such a criterion. Since we don't know what is the ontological structure of the world the question "what it truly is?" seems to be hopeless, but the good news are that it is completely irrelevant to science.

Answer 3

Short Answer

First, note that science is not a monolithic entity. Second, technically speaking, the role of statistical certainty in using models to determine what constitutes reality is the heart of a primary metaphysical debate in the philosophy of science: realism vs. instrumentalism. The most prominent example of this in practical science is in quantum physics and controversy around the acceptance of the Copenhagen interpretation.

Long Answer

Your question goes to a very important metaphysical debate in the philosophy of science, that of the underdetermination of scientific theory (SEP). When one starts throwing around the adverb 'really', what one is doing is presuming dualism: that is to say, that there are physical and mental "worlds" and they do not relate. Cartesian duality is the most famous dualistic theory, and many philosophers reject it outright, like material eliminativists such as Daniel Dennett.

From SEP above:

So a high correlation between cartoon viewing and violent playground behavior is evidence that (by itself) simply underdetermines what we should believe about the causal relationship between the two. But it turns out that this simple and familiar predicament only scratches the surface of the various ways in which problems of underdetermination can arise in the course of scientific investigation.

So, instead of determinism and indeterminism in the context of bivalued logics-- something is either deterministic or indeterministic-- statistical models often attempt to determine to what degree something is deterministic, like in the notion of correlation. If you presume that a statistical model is mental and is not absolutely a certain measure of the physical, then you wind up with ideas like the classic phrase: correlation does not imply causation. And if statistical measures are, given a degree of unpredictability or randomness inherent in their nature, not causal strictly speaking, then it actually begs the question, is there a reality at all or is our thought nothing but models, and relatedly, can we really know a thing-in-itself?