Preface

This was written as https://www.quora.com/How-can-free-will-or-determinism-be-scientifically-mathematically-deduced-or-proved/answer/Anil-Mitra-2.

Here, I will be improving the foregoing answer.

Answer

“Is it at all possible to demonstrate free will from physics and perhaps biology? Now some people hold that physics is deterministic and therefore disproves the possibility of free will. However, there is no consensus on determinism in physics (e.g. concerning quantum theory and less commonly noted concerning the finality of such theory). Other people argue from causality in physics that since mind is not causal, free will cannot be proven. But I do not think that mind is acausal. There is another argument from the closure of physical systems that intervention from mind is impossible; this argument is similar to the causality argument. However, there are two problems with it: since our physics is not necessarily complete (and most probably is not complete), the closure of our physical theories is by no means given. The second problem is that even if physics is closed it is not necessarily the case that mind is non physical. In fact if physics is (when) complete and closed, mind or experience must be physics from the ‘inside’. The point to this introductory paragraph is that mind, free will in particular, is not inconsistent with what know from physics.

But can we use physics, either in principle, or with mathematical modeling to show that we have free will? We would have to have a sufficiently complete neurological map of the brain, perhaps with endocrinal and other input into the model. I don’t think there are any such sufficiently sophisticated models and I suspect the theoretical or computational power required is beyond our present capacity (proof is quite different and far more difficult than showing consistency as above which is trivial).

How about biology? Evolutionary biology suggests a paradigm of process that may be regarded as new to science. The variation and selection model is a paradigm that addresses two common fundamental objections to free will. The first objection is that determinism rules out free will; the variation part of evolution is indeterministic. On the other hand, randomness alone is essentially chaos, the argument goes, and hardly makes for free will. The point to the evolutionary paradigm is that structural novelty occurs at the intersection of structure which is mostly deterministic and indeterministic process (and is therefore neither merely determined nor merely random). And then analogy suggests that something similar might happen in the brain. But of course, the analogy is far from proof. But the question is whether we can use the analogy to develop a model and then a proof (see below).

So, certainly at the present time, even if physics and biology provide what we think should be essential ingredients to freedom of will, there is no proof from physics and/or biology.

For proof, then, we would have to turn to psychology—especially the study of experience—and philosophy (a) to carefully define free will (some definitions are inadequate and there are straw man arguments that overstate the capability of free will and so argue against it) and (b) to supplement the analysis of concepts which is a necessary prerequisite to the analysis from psychology.

There are experiments that suggest that in ‘decision making’ decisions are made before the apparent conscious decision. However, (a) this is but one possible interpretation of those experiments and (b) the experiments involve trivially simple situations. These experiments have naively been interpreted by anti-free willists to support their case.

Is there will? Will is the presence of mind in the causal course of events. There is no reason from science to rule it out; and we experience internally and externally the effect of will everyday. Yes, this can be doubted. But philosophically it may be counter-argued that will is simply the name of the phenomenon under which there is human agency.

What about the free part of free will? Here it is important to note that some people seem to think that ‘free will’ is unimpeded will (see Free will - Wikipedia) and others seem to think free will means that we can do anything we want. Neither of these is inherent in the meaning of free will.

The idea of the free part of free will is that we (a) employ will toward one of a number—more than one—of possible outcomes (i.e. the future is not determined) and (b) that we may even conceive such outcomes (over and above just being presented with them). Here, biology reminds us of the indeterminist with structure of the universe; for proof see this.

So the crucial questions are (i) are there multiple outcomes in some situations from which we can choose and (ii) can we create such outcomes. If we can argue / show (ii) that would take care of (i).

That we can create such outcomes is apparent from the fact that—it is clear that—human intellectual achievement was not predetermined at the dawn of human history or earlier. That is a reasonable if not knock down argument that we are capable of conceiving / creating and so choosing alternatives. Again, see the above link.

The foregoing are (a) arguments against arguments against free will (b) reasonable arguments for free will. To improve the latter I suspect we must turn to philosophical analysis.

We would have to show that the universe is indeterministic. The very fact of showing this would also show that intellect is creative. The two points together would make for freedom of will. These arguments need to be refined.

Consequently I feel strongly and think that there is freedom of will; and its proof comes from science and philosophical analysis.

The science is observation of human behavior and thought; the philosophy concerns elucidation of the concepts and some necessities and justification of the observation as science.”