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

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?

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

• While it seems to bother people ethically and conceptually, the difference between "true" and seeming randomness has no direct empirical consequences. There is no sure way to know whether we do not know because there is nothing to know or because we will never know. So, if it matters at all, it is only at the highly refined theoretical stage where epistemic values like coherence, simplicity, unification, etc., contribute to choosing the overall "best" theory among those that fit empirical facts. Currently, the majority choice is in favor of true randomness in quantum mechanics. Nov 1, 2020 at 3:01

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.

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.