No and no. That’s what I mean above when I say that the notions of ‘logical inference’ and ‘determinism’ part ways, even though they seem intuitively to be the same: the state U(d) is not (uniquely) determined by prior data, but if you actually ‘turn on’ the evolution, there is no freedom regarding what will happen. As I said above, the information is ‘implicit’ in {U(t[sub]B[/sub]), L}, but has to be ‘actualized’—by the process of evolving the state forward step by step, which involves the agent’s deliberations by necessity.
It’s as with the halting problem: a given TM will halt (or not), but there’s no way in general to decide whether it will halt (or not); you’d have to run it (and possibly wait infinitely long). Similarly, the Gödel sentence is true (or not), but there is no way to derive it (or its negation) from the axioms. So an agent will choose A (or B), but there is no way to derive this from {U(t[sub]B[/sub]), L}; the data doesn’t suffice to fix that choice, just as it doesn’t suffice for the TM, and just as the axioms don’t decide the Gödel sentence.
The idea that given a start state U(t[sub]B[/sub]), and given no freedom regarding what will happen (that is, given no randomity), that you’ll eventually end up at a fixed and inevitable U(d) could be given as the definition of determinism.
I’m not concerned with pretending that there is a generic way to convert U(t[sub]B[/sub]) to U(d) via application of L other than, well, applying the laws of physics to the universe for the specified amount of time. That’s not a requirement of my argument, or any argument I’ve ever heard of. As far as I’m concerned the {X, L} operator means “apply the laws of physics to universe X” (for the specified amount of time - we’re sort of missing a parameter here).
So I guess you can say that logical inference and determinism part ways - and neither of us is talking about logical inference. You are saying that under your model the universe is deterministic, because given U(t[sub]B[/sub]) and L you inevitably get to U(d); I am saying that under determinism the universe is deterministic because given U(t[sub]B[/sub]) and L you inevitably get to U(d). We’re talking about the same thing.
And given that we are talking about exactly the same model of the universe, mechanically speaking, and given that you are saying that under your model of the universe free will exists, it appears you’re a compatiblist too! Like me! Yay, we agree!
I am, though. The point is that under your model, only {U(t[sub]b[/sub],L,A} is logically consistent—and hence, a possible world (as in its complete history up to the point where A is chosen—and actually beyond)—while on my model, both {U(t[sub]b[/sub],L,A} and {U(t[sub]b[/sub],L,B} are logically consistent, and hence, possible worlds in this sense. It’s the process of choosing that decides between both worlds; thus, this process has a role to play that’s absent on your model.
Again, consider the analogy to Gödel’s theorem: in the absence of incompleteness, for every (syntactically valid) formula f, and a given formal system F, only either {F,f} or {F,~f} would be consistent. Given incompleteness, for the Gödel sentence G, both {F,G} and {F,~G} are consistent—indeed, lead to consistent formal systems, mathematical ‘possible worlds’. If we add, however, the consistency of the axioms of F, then we can deduce that G must be true.
Choice always exists. Miller postulated whether Jeffrey Dahmer had choice in being a serial killer; this is an excellent question and unanswerable. Are killers those who are unable to control the impulses coming from their amygdala?
But…but…if it might be true for impulse killers, there is no possibility ofvthid for contract killers whose every action is planned and wilful.
The larger question is unknowable given the limits of our knowledge and our senses. But its fun to debate.
Well, the only dispute is with those compatibilists who caricature the position of the determinists, in saying that the determinists deny choices are made.
I disagree. Your model explicitly includes the fact that the nonrandom laws of physics will be operating on the universe, and that because that is the case the inevitable outcome is inevitable. That alone is the full and complete definition of a deterministic universe. There is literally nothing else we need to know about your model - your model includes a deterministic universe, and you are a compatiblist.
And I don’t know why you dislike this fact.
Note: I did see your paragraph about Gödel; I just don’t consider your ‘analogies’ to be valid. And I can justify it - the universe in your model is mechanically identical to the one in mine in every way. Any ‘analogy’ that argues that their functional properties are different thus must be invalid. And that’s all I need to say about that.
There’s a huge difference between deterministic and computable. If the causes of human will are utterly untraceable, you might as well say “Because God made me that way”.
I actually acknowledged that one might view it like that way back:
On the other hand, some might not call it compatibilist, because that logical possibility of alternatives exists. In the end, it’s just nomenclature, and if semantics is all you’re arguing at this point, we might as well pack up.
That’s a strange sort of view. The universe after the discovery of quantum mechanics, or relativity, was mechanically the same as before—it’s just that we’d learned something more about it, which went on to shape our image of it, informing us that certain things are impossible which we previously thought possible—such as knowing the exact position and momentum of a particle—and opening up possibilities for certain other things that we thought were impossible—such as time moving differently for different observers.
Likewise, the discovery that there are undecidable questions about our universe, going back all the way to Turing, while it doesn’t change anything about the universe, changes what sorts of things we know can happen, and how—such that, while one might have to be resigned to your brand of compatibilism before, afterwards, new possibilities have arisen.
I’m quite certain that there is no logical possibility of alternatives, because that flies in the face of the deterministic model by definition.
To me, what you’re saying is something like:
“In the HMHW model the universe is deterministic, meaning that given a start state at time b, the state at later time d is inevitably determined by the prior state and physics. The outcome is inevitable.
However, logical alternatives exist, meaning that given a start state at time b, the state at later time d is NOT logically determined by the prior state and physics. The outcome is not logically inevitable.”
To me that reads like “A ∧ ¬A”. It reads this way to me because when you’re talking about logical possibilities, you’re talking about things that can be true. And if an outcome is inevitable due to deterministic physical processes, it is the only outcome that can be true.
Now, I get that you could be arbitrarily choosing to do your prediction using a symbolic logical system that operates dissimilarly to the way physics do, and that once you’d finished laboriously converting the position and state of all the matter in the fledgling universe into symbols, and after you’d mathed out on your statement set and found out what it said about possible outcomes, it might fail to reduce the set of possible outcomes it reports to you down to one single predicted outcome.
But that wouldn’t mean that the universe is logically indeterminate. It means that the symbolic logic system you chose to use is a poor model of reality and/or that your initial statement set failed to account for all existent starting data. It means that an error has been made in your calculations. And that’s all it means; it certainly doesn’t mean that there’s some sort of loophole in causality.
And lest you suggest that it’s impossible to create logical predictions of physical reality due to Gödel’s argument, I would point out that Gödel’s argument says within a given logical system there are certain specific coherently formed statements/states can’t be proven within the system, and all the ones it speaks about are wholly self-referential and deliberately self-contradictory. The universe as it proceeds will never be wholly self-referential and deliberately self-contradictory, so there’s no reason that a formal logical description of it will run afoul of those certain specific Gödelish states.
In my studies of such undecidable questions, I’ve noticed something. They’re undecidable about abstract things. Infinite sets, symbolic logical statements and so forth. They’re not undecidable about instantiated reality, because instantiated reality is not abstract. There are no instantiated infinities, for example.
And this goes double for mental processes, which operate in the physical world at the macro level and must necessarily correct for vague states to be able to result in coherent behavior.
Which is why I’ve been trying to hammer home that logical inference and determinism part ways: given the data, which option is realized is not logically implied.
Yes, that’s certainly what our intuition would tell us; but as sometimes happens, our intuition turns out to be wrong. Both the propositions ‘A occurs’ and ‘B occurs’ are consistent with the data; both can be true in that regard. Yet, only one of them actually does occur. This isn’t inherently more difficult than the fact that I had pizza yesterday, but it’s logically possible that I might not have had it.
To aid you in your studies, I’ve several times now pointed to a concrete physical system which has an undecidable property, so this is false by example.
Furthermore, undecidability is incredibly generic: in a formal system, almost all statements are undecidable; almost all real numbers are uncomputable, as are almost all functions over the natural numbers; and indeed, every nontrivial property of computer programs (such as whether it computes the sum of its inputs) is undecidable.
If quantum field theory is right, then this is also false: there are infinitely many degrees of freedom associated with every region of spacetime.
Ahem, how is it logically possible that you might not have had pizza, if you did? Unless you’re excluding a gross amount of obviously relevant data from your axioms, “Half Man Half Wit had pizza yesterday” should be among them, and any argument that attempts to show the opposite will very rapidly encounter disproof by contradiction.
Also, let’s just get this on the table now: presuming that “A occurs” and “B occurs” are mutually exclusive, then it’s absolutely impossible that they can both be true in any logical system that is both logically correct and supplied with enough data to speak at all on the subject. Like, literally: if “B occurs” ⇒ ¬"A occurs", then if your system allows you to prove them both true then all you’ve proven is that your axioms are jacked. As you well should know.
To NOT grossly misrepresent logic (and chronology), what your argument should have been is that the truth of both “A will occur” and “B will occur” are both unknowable based on the information available: the prior universal state and the laws of physics. Unfortunately for you this is of course not true - logically speaking the fact that the universe is deterministic grants you the ability to logically deduce truths about a later state from a prior state. The axiom set required to do so would be mightily complicated, of course, having to encode the prior universal state and how the laws of physics operate, but determinism by definition means that if you somehow managed to encode all the data, truths about the future would be provable. It’s inherent in the definition of the term.
Might as well stop here - your continuing attempts to pretend that physical reality operates like an abstract mathematical proof or whatever will do nothing for you if you don’t manage to do something about the fact you have this deterministic universe sitting right in the middle of your model like the elephant in the room.
I’m guessing the distinction is between computable in the future sense (e.g. halting problem) vs computed in the past tense (the universe computed it and the system is now in state X).
I meant it was possible beforehand, although what decision occurred is now a fixed fact. So say I based my decision on whether a radium atom decayed within a given time-span (thereby bringing an actually indeterministic element into things): then, I suppose, even you would agree that beforehand, it was logically possible that I will have either pizza, or something else (let’s say a burger). (And I probably should point out here that this doesn’t mean my model is indeterministic; I’m just drawing a comparison.)
So. Yesterday, whether I will have pizza was indeterminate. Today, it’s determined; I couldn’t not have pizza yesterday, seeing how I indeed did have pizza. Hence, what was ‘undecidable’ at one point in time has become fixed. But that’s as with my proposal: it’s logically undecidable, using data from before the decision, which option is taken; and only after a choice is being made does this become definite.
Furthermore, we could envision a block universe, i.e. one in which past, present, and future all exist ‘side by side’, so to speak. Still, then, using all the data up to before I ordered my pizza, it’s logically possible—in the sense that this data does not suffice to tell whether the radium atom decays—that I will not have pizza; but of course, as the whole universe is concerned, that decision is fixed. The point is that this is not in conflict.
I could even go and erase all the information about whether a given event occurred. For instance, quantum measurement is in principle reversible; and before such a measurement, which outcome occurs is unknowable (and hence, likewise after the reversal). So, I could make a dichotomic (i.e. two-valued) measurement, and then reverse it. Naturally, I would not have any knowledge about the outcome of that measurement, and neither would anything else within the present state of the universe. It’s thus logically possible that either outcome occurred, yet still, only one presumably did.
You say that as if it’s in conflict with anything I’ve said so far; it’s not, and if you think it is, you should really re-read this exchange. All I’ve said is that both A and B occurring is consistent with the data; that neither one can be shown true is just what ‘undecidability’ means, which is what I’ve been harping on and on about in this thread.
And again I’m somewhat flabbergasted as to how you could have paid even minimal attention to the debate so far and still honestly hold this position. I’ve now almost a dozen times pointed you to a case where exactly this occurs: for certain quantum many-body systems, it is undecidable, in the formal sense of being impossible to logically deduce, whether there is a spectral gap. Yet, these systems do, or don’t, have one: it’s not an instance of indeterminism. It’s OK if you don’t understand this—you can always ask—, but just ignoring it and sticking to your preconceived notions doesn’t really make for good debate.
I saw an article a couple of days ago about this subject, and I don’t know if I want to yell at the writer or the person who did the research. Here’s the article:
They’re asking whether people feel if they’re in control of their lives, finding the obvious correlation to job satisfaction, and then equivocating by calling that sense of control a “belief in free will.”
For people interested in the spectral gap undecidability problem, here is Scott Aaronson’s take on it: “Ask an unbounded question, get an uncomputable answer”
This is not in my field of expertise, but it strikes me that this explanation does not mesh well with how this has been presented, repeatedly, in this thread where the result has been held up as a chief piece of evidence in favor of “free will”, idiosyncratically defined. I don’t have much more to say on that particular topic. I made a long post earlier before my out-of-town family issues and trip. However, the main point of my post was quite comprehensively ignored. No substance was offered against my main idea.
Instead, my comments were taken out of context and misrepresented. Again. That doesn’t strike me as “truth seeking” behavior, but I suppose opinions on this must differ. There is no purpose to long posts when they just provide more content for willful distortion. I’ll try to keep things short now. Shorter, at least. Slightly less long. A smidge briefer.
Aaronson is perfectly right, of course: no theoretical result ever implies that there is some physical system that must fit it. Nature always simply might not work that way. However, the model systems studied by Cubitt et al. are not terribly far removed from real-world physical systems. So while this isn’t a proof that real-world systems exist that show this kind of behavior, it opens up that possibility—there’s nothing that prohibits their existence, although happenstance might have it that none are actually found in the world. (Incidentally, regarding the point made about finiteness, one should note that quantum field theories are not finite systems—they contain an infinite number of degrees of freedom, and are indeed often thought of as the limit of just the kind of lattice systems discussed in the article.)
You argued against a kind of ‘free will’ that introduces ‘something more’ than what goes on in the brain; but that’s not what I’m arguing for. Hence, I left the defense of this thesis to others that actually hold it.
In fact, the notion of complexity you’re describing—Kolmogorov- or algorithmic complexity—is very closely related to the phenomena I’m talking about: for an object of maximal complexity (in the sense that there is no program significantly shorter than said object that produces it, formalized in some appropriate way), it’s generally the case that it will include undecidable propositions—the paradigm case here being Chaitin’s halting probability, whose digits (past a certain, finite index) form undecidable propositions.
I have reacted to your comments in the way that I understood them. It may be that I’m completely wrong in my understanding, but in my experience, a failure in communication is rarely located at one end exclusively; but your presumption that this must be so, that indeed I acted purposely here to ‘misrepresent’ your words, does little to convince me that the fault lies only with me.