Jonathan Day

There are three distinct problems under discussion here. Problem 1: There exists a set of questions for whom the answers cannot be uniquely ascribed the value of true or false. (ie: They violate Aristotle's excluded middle.) There is no requirement that those answers to any given question of this type be both true and false, they can be neither. This cannot be generalized. Nor can it be used to prove that true is false. Problem 2: In order to assume that true is always false, we must have a universal set of questions such that each question maps to the universal set of answers, and a universal set of answers such that each answer maps to the universal set of questions. Because all results are equal, it also necessitates that the universal set is the empty set. If we were to argue that the set of all questions for which all possible answers to any possible question are both true and false answers to that question is the empty set, then this would at least make some sort of sense. Problem 3: The original proposition requires that, for all questions, the power set of all possible answers is a strict subset of itself. It isn't enough for there to be a special case where this would be true, it would need to be true for every question. It would be true for the empty question and the empty answer, if we allow the empty set to be a strict subset of itself, but it would not be true of any other.

There are a number of problems with this particular philosophical question, the most obvious one being that we don't have a single definition of free will. (We have many, some of which are contradictory, but what we don't have is a single agreed definition that we can then actually test against.) A second problem lies in the fact that science is based on observable phenomenon, falsifiability, measurement and invariance. You can't observe free will directly, so we'd need something we can observe that is a surrogate. That's fine, physicists do that a lot. Only, what do we observe or measure here? Without a working definition and model, we don't know what to look for or how to quantify it. Unless we can distinguish between random, hidden variables, undiscovered interactions and choice, free will is unfalsifiable. In principle they can be distinguished, since free will implies that a variable that is actually independent as far as the physics is concerned can affect the outcome. In practice, since we only know a variable is independent experimentally, you can't readily distinguish between free will and simply getting the physics wrong. We do have one possible path, Professor Conway's Strong Free Will Theorem. This is a dense mathematical argument that essentially states that free will can only exist within the universe if physics itself has a notion of free will. If something that is fundamental within the universe has the capacity to behave in non-random, non-deterministic ways, then this can potentially accumulate into free will in something as complex as a brain. If there is no such capacity, there is no free will. This part's fun, since physicists don't know if this would be fundamental particles, superstrings, M-branes, pure mathematics or something yet to be determined. So once we know what "fundamental" means and what the physics is at this level, we can presumably figure out how to do some experimental test that can rule out all of the alternatives. And, of course, it relies on both the theorem being correct in all the particulars AND of there being nothing that can be considered "outside" of physics/mathematics. Now, if we can get past all of that, then we can determine if there is free will. But at this point, any answer is essentially meaningless.

You have the canonical five (A, G, C, T and U), although I'm seeing articles where it's a little more complicated because there's also a non-standard base of I, although I'm a little fuzzy on when this one appears. There also seems to be a new base, discovered in viruses, dubbed Z. (Because viruses get involved, I'm looking at both RNA and DNA together.) https://www.wired.com/story/dna-has-four-bases-some-viruses-swap-in-a-fifth/ I seem to recall reading this one does appear in certain fungi and not just viruses, but can't find the article on that. Besides which, it's not always reliable to go with one-off pieces, especially outside of the scientific journals, which is why I'm not even feeling 100% confident that Z is real. Besides which, since (according to TFA) "during gene transcription, T-Z was still treated as though it were T-A", it's not even clear if it's reasonable to call Z a new base even if it does exist. That would seem to depend on whether a base is defined chemically or functionally. Although, as TFA suggests Z exists to fool immune systems, do we define function in terms of what it does or how it is seen? I'm excluding synthetic bases, since there can be an arbitrarily large number of these. I'm therefore curious as to what geneticists consider to be the bases that arise in nature, without regard to whether they're considered canonical.