If determinism cannot be proven to be true or false is it rational to believe it is true on the grounds it is likely to be true and I am reasonably justified to do so? Or would the rational position be to withold believe one way or the other until stronger evidence is presented. Is it even possible to have evidence in favor of determinism?

Interesting question! On the first question, many of us think that, yes, even if some philosophical thesis cannot be proven or is not proven at the time to be true of false, it can be reasonable to justifiably believe the thesis is true. I suggest that this is true in most matters of substantial philosophical concerns. For example, belief that some form of naturalism or idealism or theism is true might well be justified even if this is a matter that is very far from (if ever) justified, as are competing philosophical accounts of space and time, values, externalism or internalism in epistemology, and so on. Although the book is now 7 years old, I still highly recommend Gary Cuttings's What Philosophers Know (published in 2009 by Cambridge University Press) which recounts multiple cases of when philosophers in the 20th century claimed to *know* with certainty that theory X is true, but yet it only too often becomes apparent on further reflection that the arguments are far, far less than decisive.

So, in many cases, I suggest you would be warranted in believing that determinism (or indeterminism or libertarian freedom) is justified, even if you (we) lack proof on this matter. When you refer to what is "likely to be true," many (but not all) philosophers might have in mind a general, not precisely quantified use of the idea of likelihood or probability. So, if a philosopher is debating the merits of physicalism versus non-physicalism, the debate is not often put in statistical terms (e.g. it is only 51% certain that X is true...), though Bayesian theorems are available to explore (see the Stanford Encyclopedia of Philosophy).

Your second and third questions are especially fascinating.

Sometimes a belief X can be more reasonable to believe than not-X but the (perhaps) better or more fitting response would be to be agnostic / uncommitted. To use an unoriginal example, if I was asked right this moment to answer the question "Is the Pope in Rome right now?" I would probably (rightly?) answer "yes." I am in a position of not knowing the Pope is somewhere else, and because (or so I believe) the Pope is often in Rome, I think I would be warranted to "bet" the Pope is in Rome, but (all things considered) it seems I should be agnostic and not to claim that I know one way or the other. So, about determinism, if you do not believe you have compelling reasons to believe determinism is true, you may find it fitting either to be an (intuitively?) reasonable position to accept ( or believe or assume) even if you do not claim to know it is true.

About evidence about determinism: this is absolutely fascinating. I take it that determinism is the view that every event that occurs, occurs necessarily given the laws of nature and all antecedent and contemporary events. This would entail that there is only one possible future, given all these conditions. Can there be good or even excellent evidence that determinism is true? If there are compelling reasons to think that indeterminism is incoherent it is hard to imagine that there would be a "proof" that determinism is true. All that would be needed to "refute" or "disprove" determinism would be a single case of (irrefutable) indeterminism. But, if it turns out, that all and every case of events that we humans investigate are not just explainable (in theory) but actually explained (in which we have good reason to believe that the event was necessary and not random, contingent or the outcome of libertarian agency), then that would (I suggest) be good reason to believe that determinism is true. It would be another matter, however, to conclude that determinism is necessarily true.

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