# What is wrong with the following case against determinism?

I am thinking of determinism in the following way: if we knew all the laws of nature and the complete state of the universe at a given time, we could predict everything that would happen in the future. This seems to be a common understanding of determinism.

Determinism implies existence of a function/mapping which specifies for an agent a set of actions and a probability function defined on the action space, given a state space and laws. In other words, there exists a system of laws and states that can fully describe the behaviour of the agent.

Consider an agent with the capacity to learn the function and/or its outcomes (use these as input arguments). Furthermore, the agent’s objective function maximises reward if the agent chooses actions which violate the predictions of any such function.

If such a function exists and such an agent doesn’t exist, then we have determinism. It seems very complicated to prove the existence of such a function, beyond ascribing to faith. I think humans can be such types of agents. Simplest example is that of a binary action, and whenever the function predicts 1, the said human will do 0. It doesn't even have to be a human but just another function that can play the role of the agent.

If such an agent exists, then such a function cannot exist, and hence, we cannot have determinism (barring the example below). This is because no function will be able to accurately predict the actions of the agent. (There seems to be an infinite loop here which leads to inconclusiveness if one chooses to take that direction. For example, a function that accounts for agent's adjustment but then the agent can also adjust again and we loop again).

Assume such an agent exists (agent i). Determinism can still be true if either the agent never learns the function and/or its predictions. This reflects a limit to knowledge that believers in determinism must ascribe to. This would then imply that no agent inside the system would ever be able to prove determinism exists for to do so any agent would have to specify such a function, and agent i would falsify that function.

• This seems more like a qualitative way of motivating the halting problem; but there the implication is that no program can solve the halting problem, whose analog in this thought would be that the agent cannot learn the exact function.
– Dave
Commented Jan 8 at 15:15
• "I am thinking of determinism in the following way: if we knew all the laws of nature and the complete state of the universe at a given time..." so far so good, but then "given time" can (logically) be only "infinity", and "there" is neither a "predict" neither a "future" and barely an "I".. "given time" or "time point" or "now" is an unreal(istic)/blurry/only theoretic "idea", we can only (truely/falsely) approximate Commented Jan 8 at 15:20
• `if we knew all the laws of nature and the complete state of the universe at a given time` -- it should be noted that, even if determinism is true, THIS is in principle impossible for someone within the universe to do. And even if they did have all that information, they couldn't calculate the future faster than the future actually happens, in principle. This forumulation of determinism only works if you're talking from the perspective of someone OUTSIDE the universe.
– TKoL
Commented Jan 9 at 10:10
• Which means no agent, ever, within our universe, regardless of if it's deterministic or not, can ever know what the future simulation will be exactly, and then somehow choose to do contrary to it - they can never get tot he point of knowing the future perfectly in the first instance. The scenario has no actual bearing on reality, given that it's not only practically impossible, but in-principle impossible as well.
– TKoL
Commented Jan 9 at 10:12
• @user52932 not even those people presuppose that we would be in principle capable of knowing enough information about the state of the universe to actually calculate the future. They might believe we would know in principle enough to calculate a few seconds into the future for a tiny cube of space - that's about it. Certainly not the whole universe, or even a large enough fraction of the universe to say what a person is going to be doing an hour from now, not even a minute from now.
– TKoL
Commented Jan 9 at 11:59

A simpler form of your argument is:

• Knowledge of the future would inevitably change that future
• Therefore if the future is set, it cannot be known

It's a version of the "time-traveler paradox"--if someone could go back in time, they might be able to change things to the point that they wouldn't exist, or at least to the point that they would never go back in time. The difference is here there is no actual time-travel, just a perfect knowledge of future events.

Whether or not this is a cogent argument depends on if the premise is correct or not. Would perfect knowledge of the future inevitably change that future? It seems like an intuitive certainty, but is it provable? Your argument seems to make sense, but you would need to be able to express it formally, with rigor and exactitude, in order to know if it holds up. You might compare Gödel's Incompleteness Theorem, which is based on a similarly intuitive idea, but which was extremely difficult and complex to actually demonstrate in a rigorous manner.

• I guess I am arguing one can always define a function to which if you input how it should behave as per any other function, it by definition deviates. Such a function can exist in simple systems. For example, if you were to claim that you have a function that can perfectly predict a binary output of any other function, I can always define a function which does the opposite of what your function claims (similar to the halting problem as a user pointed out in the comments above). So does this mean that the premise is correct? Commented Jan 8 at 16:18
• It seems to me that there are unproven assumptions here, but it's a bit hard to tell since you've built your argument in informal language. It might be possible to build a rigorous, formal version of this argument, but short of that, it's impossible to know if this gloss is providing a real and fundamental insight, or if there would be some place along the way where it falls short. Commented Jan 8 at 16:23
• I see. Is there a way to learn how to write this more formally for philosophy? I am comfortable with mathematical syntax but not so much the syntax specific to philosophy (or would mathematical statements suffice)? Commented Jan 8 at 16:29
• You'd want to start on a foundation of "formal logic"( which you probably already have some background in, since it's used extensively in mathematical proofs). But I imagine you'd end up needing to innovate some notation in order to fully specify your meaning. Commented Jan 8 at 16:41
• I edited my answer to add some more context. You might look to Gödel for inspiration. Commented Jan 8 at 16:49

All you've shown is that knowing what you'd do would undermine that knowledge.

But this isn't a "case against determinism". It's a very constrained limit on our knowledge, and it's one that non-determinists must accept too (it's not a problem for them... but it's not a problem for determinists either).

Let's say we can't know that. So what?

I'm not aware of any respectable person that's ever said we're able to know everything. If anything, educated people may instead say we're definitely not able to know everything. So presenting one thing we're not able to know doesn't really say anything, unless how we concluded that we can't know that is itself significant, or that's a core part of what you're talking about, but that doesn't seem to be the case.

The case for determinism is made independent of whether we're able to make a prediction of our actions that is able to take that prediction into account, and not being able to make such a prediction does not undermine that case.

Determinism could be described as whether some hypothetical external observer would be able to exactly and perfectly predict what would happen. It does not say that some agent within the deterministic world should be able to perfectly predict this.

Under determinism, we are deterministic agents, so how we'd act in response to gaining knowledge about how we'd act if we didn't have that knowledge would be deterministic, and how we'd act in response to gaining knowledge about how we'd act in response to gaining knowledge about how we'd act if we didn't have that knowledge would also be deterministic, and so on.

Now it may be that someone would act differently from any prediction they learn of about how they'd act. But this could potentially be quite predictable, i.e. deterministic, for those other than that person - you could know how they'd act if you tell them they'd act in a certain way. If we act against a prediction of our actions, that mostly stems from a desire to be unpredictable, which can itself make our actions predictable.

On the subject of decisions, if you've ever decided to not have snacks in your house, because you know your future self wouldn't be able to exercise restraint (which is something many people decide), this is arguably acceptance that your actions would be deterministic in that future context. This suggests that people tend to accept some level of determinism. If you bought snacks and you're about to eat them, and someone tells you that you're about to eat them, you'd probably still eat them.

• Hi. Thank you for commenting. I think I agree with your first sentence as being a core concept behind the argument. I do disagree with the para "I am not aware...". I think several physicists and neurobiologists do believe in perfect prediction of all behaviour depending on laws governing particles, building on their argument that everything is composed of particles. I have interacted with them at universities, and you can look for this online as well. Commented Jan 9 at 7:35
• I do agree with the para starting "Determinism could be described as...". That is what I argue in the last para of my post. I have mixed feelings on what you wrote in the musings part. I do touch on the infinite loop in my original post. But I am not sure I am fully convinced "they'll do opposite of what they're told" is predictable in a complex system with mixed strategies and/or non-binary outcomes i.e. epsilon deviations to probability distributions and actions exist. You certainly predict that agent i wont adhere to the function but that doesn't mean you fully characterised his actions. Commented Jan 9 at 7:39
• @user52932 "you know they'll do the opposite of what they're told" - I made that part less definitive in my answer. Commented Jan 9 at 8:09

that might be a part of determinism but it is not necessarily what it is. Generally, for determinism to be proven true, you dont have to prove that knowledge of all things is possible or that knowledge of all future things is possible, knowledge is trivial here. What one seeks to demonstrate is that all events that occur or have occured could not have not occured, and all events who will occur must occur, and this necessity has been the case since forever. The hypothesis of an agent who knows the future does not necessarily entail that the agent will be able to change the future he seems, though that might be intuitive. On the hypothesis that i know that i will think X in the future, it doesnt seem the case that i cannot not think of X in that future, but really this may just be a gut feeling, specially because, if there is actual knowledge of the future, by definition the agent ought to think X. Perhaps the pre-assumed fact that X can choose to oppose any future presented to him is the problematic point.

• Hi. Thanks for comment. I guess I am confused how your definition of determinism relates to mine, where I claim its the same as existence of a function/mapping which specifies for an agent a set of actions and a probability function defined on the action space, given a state space and laws. I am not entirely sure - I don't have a philosophy background and so was trying to think this through as a math problem. Commented Jan 9 at 11:48
• I do think the existence of such an agent X is an assumption. I don't have a formal proof of that. But I think that believing in existence of such a function is certainly intuitively more unappealing than arguing for existence of an agent that just to spite the "meta" does something different. I think hardcore determinism people argue using the choice of cereal. It seems to me that its easy to imagine a human/function which whenever told as per a function his choice of cereal, will do something different. Commented Jan 9 at 11:51
• Well, i was trying to firstly talk about the general definition of determinism, which would not be reduced to merely predictive capacity but also infallible predictive capacity. That's why i commented on the impossibility of an agent knowing the future and being able to do something differently, because if that is the case then the agent doesnt actually know the future. The function does, thus, provide a non-certain prediction of the future, which is no problem if that is possible for you, except that would be some sort of weak determinism. Ur argument could hold in this case. Commented Jan 9 at 12:09
• I think I agree with this "That's why i commented on the impossibility of an agent knowing the future and being able to do something differently, because if that is the case then the agent doesnt actually know the future.". But I am using this to conclude that no such function or future exists or can be made known to the agent for determinism to be true - because its intuitively easy to see how an agent that violates any such thing exists Commented Jan 9 at 12:29

Indeed, it might be impossible to prove that the Universe is deterministic. However, the alternative would be a Universe where things spawn into existence at random, and we have no reason to believe that this happens in our world. We might just as well assume that, paraphrasing John’s Gospel, all things were made by their causes; and without a cause was not any thing made that was made.1

At the same time, it’s easy to see that even though the future might be already set, there is no way for an agent to know it. And it’s exactly because we can’t know the future we have free will.

1 In fact, I am positive that this is what John 1:3 actually describes -- a Universe that is deterministic and, as such, understandable. Or here's Spinoza echoing the same sentiment: "Even if these things are inconvenient, they are nevertheless necessary and have determinate causes through which we seek to understand their nature." Or here's Hegel: "All that is real is rational." (Quotes are from Athens & Jerusalem by Lev Shestov)

• Thanks for comment. I do agree that this view of determinism is compatible with notion of God being the entity who fully knows the function. Commented Jan 9 at 11:52
• Thank for your reply! I wouldn't go this far though. Personally, I don't believe that even God knows everything. Commented Jan 9 at 19:35

Your definition of determinism is correct, but you have made some wrong conclusions from it. A deterministic system is predictable only for an imaginary being, the Laplacian Demon, who is an outside observer of the system.

Within a deterministic system every event is completely determined by the previous event. There is no possibility for any predictions. There are no agents, probability functions or action spaces.

There is no "case" against or for determinism. Determinism is only an idea of an imaginary system with certain properties.

• Thank you for commenting. I think I agree with your first para and support that in the last para of my post. I am slightly unsure of your second and third paras because when I have seen discourse on the matter, people tend to apply these concepts to systems with agents solving optimal control theory problems (for example, humans in the universe). In fact there are even books on this matter. So perhaps my argument works only against how determinism is described in the mainstream (outside of strict philosophy) and hence the premise of my question is wrong. Commented Jan 9 at 7:46