Paradox of Predictability

NotAristotle

The Paradox of Predictability concerns determinism. In particular, it concerns the idea that if determinism is true, then true predictions should be possible about the future state of the world (or people or subsystems therein).

The Paradox is roughly this: information or knowledge of the initial conditions and laws of nature should allow a true prediction of the action of some person or subsystem with those initial conditions and that is governed by those laws of nature. Such a prediction must be true. However, if the person or subsystem in question acts in a way that falsifies the prediction, then the prediction is not true. In brief, the prediction must be true, however it is not true when the prediction is falsified by the action of the person or subsystem considered.

Here are two papers I have read on the subject if you would like to reference them: https://link.springer.com/article/10.1007/s10670-009-9199-1
https://link.springer.com/article/10.1007/s10670-020-00369-3

Additionally, a similar thread has been posted on this forum, I will include it here in case the reader would like to refer to it: https://thephilosophyforum.com/discussion/6478/determinism-vs-predictability/p1

Here is a thought experiment concerning the paradox of predictability:

Ned is a neuroscientist. Ned believes causal determinism is true as it pertains to human action. One day, Ned decides to put his philosophical determinist convictions to the test. So, he hooks himself up to an EEG, an MRI, and some other futuristic measurement devices. He does this in order to measure and analyze his brain patterns in a way that will accurately predict his future actions. After the procedure, Ned waits for the results to print. “Ah, here they are,” he says with the printout in hand. “Here’s the part where I am waiting on the printout, yes, yes, okay, skip a bit…ah yes, I will go for a walk in 5 minutes” or so the printout says. But Ned decides he does not want to go for a walk in 5 minutes, instead he goes for a run.

Issue 1: What do you make of this thought experiment? Does it disprove determinism?

I think it does. If determinism were true, the printout should accurately predict Ned’s actions; however, because it could potentially not predict accurately, determinism must be false.

Anticipated objections to the thought experiment:

1. Self-referentiality/infinite regress: I may not say this very well, but here it goes.. if Ned is reading the entire chart, then his reading will be predicted by the computer; if his reading the chart is predicted, then it must be in the printout. Then the printout will include not just the initial printout, but also the part where Ned is reading the entire printout. But if the computer includes as part of a prediction the initial printout and the part where Ned is reading, then the computer would have to printout the initial printout, the part where Ned is reading about the initial printout, and the part where Ned is reading about the part where Ned is reading about the initial printout. Etc. (I may not have said that very well.. I hope I am making sense).

This objection is not a problem if Ned only reads part of the printout, and the part he reads is not a part of the printout that he has already read about (if that makes sense).

2. Objection 2: Ned’s measurements may affect the experiment, such that the measurements actually change the result (from “decision to walk” to “decision to run”).

It seems that this objection does not have a lot of traction; after all, it seems that the affect of the measurement on the experiment could be factored in to the analysis, or that procedures or applications could be used that minimize affection.

View Answer

wonderer1

1. Determinism doesn't propose that what detemines human behavior is purely a function of physical states internal to an individual. Inputs from the external world play a role in determining people's actions as well, and since your scanner isn't measuring the state of everything in the universe, you don't have sufficient information to make the prediction. Ned may walk out the door, smell the scents from a nearby bakery, and go get a donut. Furthermore, your scenario itself points out stimuli that seems likely to be relevant to Neds future actions, "After the procedure, Ned waits for the results to print..."

2. The Heisenberg Uncertainty Principle points towards it being impossible to gather complete information on Ned's internal state. Though perhaps a 'close enough' superscan is still worth considering.

3. There are issues with being able to do the fantastically complex computations needed to predict what Ned will do. At best, you would get a list of probabilities for future actions.

NotAristotle

↪wonderer1

I suppose we could stipulate that Ned has enough information about his immediate environment to make an accurate prediction about how he will act. It doesn't really concern us whether this sort of information can, as a matter of practicality, be acquired; the concern is whether in principle, if this information were acquired, could Ned act in opposition to it. And the answer to that seems to be yes.

wonderer1

I suppose we could stipulate that Ned has enough information about his immediate environment to make an accurate prediction about how he will act. It doesn't really concern us whether this sort of information can, as a matter of practicality, be acquired; the concern is whether in principle, if this information were acquired, could Ned act in opposition to it. And the answer to that seems to be yes. — NotAristotle

I'd like to see your reasoning for that layed out. It appears to me that you must be begging the question.

Pierre-Normand

I suppose we could stipulate that Ned has enough information about his immediate environment to make an accurate prediction about how he will act. It doesn't really concern us whether this sort of information can, as a matter of practicality, be acquired; the concern is whether in principle, if this information were acquired, could Ned act in opposition to it. And the answer to that seems to be yes. — NotAristotle

I concur that we must accept, in principle, that this information can be acquired by Ned in order for his contrarian behavior to make any sense. Would Ned's decision to act contrary to his prediction be an arbitrary or unexplainable one? No, we cannot attribute his behavior to the occurrence of miracles and then use it as evidence against determinism.

But, if we consider that it is Ned's reaction to the acquired information (provided by a computer, for example) that prompts him to act differently, the computer's prediction must also account for the possibility that Ned will read and respond to its output. In other words, the computer's predicted output becomes a component of its own predictive behavior loop, transforming Ned into a sort of "contrarian cog" within the deterministic system.

This issue can be reduced to the challenge of programming a computer capable of modeling its own deterministic algorithmic process in such a way that it will output "yes" if it predicts it will output "no" and vice versa. This is a conundrum that can't be resolved in principle, yet this doesn't impact the deterministic nature of the computer's behavior. It rather highlights the impossibility of creating a self-referential prediction system within the boundaries of determinism.

NotAristotle

↪wonderer1

1. With sufficient information about Ned’s internal states and sufficient information about the surrounding environment, Ned’s immediate actions could be predicted.
2. There is sufficient information about Ned’s internal states and sufficient information about the surrounding environment.
3. Therefore, Ned’s immediate actions can be predicted.

NotAristotle

↪Pierre-Normand

One of the papers I included in my original post does go into what is known as the "Halting Problem" - a problem in computer science proposed by Alan Turing. This is what I take to be your objection to the thought experiment. And, I agree that the situation can be formulated such that a self-referential issue arises. However, all I need for the thought experiment to be effective as an argument against determinism, is a situation where there is no self-referential issue, but a paradox remains anyways.

In the original scenario as I have described it, Ned reads the printout, but he only reads a part of it. And, importantly, he does not read a part of it where he is reading the printout -- that would be self-referentially problematic. Because there is no self-referentially in the parts of the printout that Ned does read, there is nothing necessarily theoretically vicious about Ned reading some parts of the printout.

wonderer1

1. With sufficient information about Ned’s internal states and sufficient information about the surrounding environment, Ned’s immediate actions could be predicted.
2. There is sufficient information about Ned’s internal states and sufficient information about the surrounding environment.
3. Therefore, Ned’s immediate actions can be predicted. — NotAristotle

I probably should have been more explicit as to what I saw as question begging. Earlier you said:

the concern is whether in principle, if this information were acquired, could Ned act in opposition to it. And the answer to that seems to be yes. — NotAristotle

On the other hand the conclusion of your argument at the top of this post contradicts your earlier claim that Ned could act in opposition to the prediction. So I am unclear about what you are arguing.

NotAristotle

↪wonderer1

Right, the contradiction is the paradox that the thought experiment expresses. Ned's immediate actions can be predicted.. if determinism is true, they should correctly predict how he should act. However, there seems to be no reason Ned could choose not to follow the prediction, and were he to act otherwise, he would falsify the prediction. Because determinism leads to this paradoxical conclusion, it must be false. That is what I am arguing.

wonderer1

However, there seems to be no reason Ned could choose not to follow the prediction... — NotAristotle

But if determinism is true, then Ned will not act contrary to the prediction. Furthermore understanding the details of how the prediction was made should demonstrate that Ned will not act contrary to the prediction, and therefore if you fully understood how the prediction was made you would have a reason to think Ned could not act contrary to the prediction. The fact that you lack a reason to believe the prediction, when you don't know the details that went into making the prediction suggests you are relying on your ignorance of the determinitive factors as your basis for your conclusion. IOW, you are making an argument from ignorance.

NotAristotle

↪wonderer1

I am supposing that the details that went into making the prediction are known. Ned has every reason to believe the prediction, there is no reason to doubt it. It is simply the case that Ned chooses contrary to the prediction. It would be strange, would it not, if some magical events transpired to guarantee that Ned's choice was always consistent with the prediction? And that's the point, if we bar these magical occurrences, Ned can choose to act contrary to the deterministic prediction. But that should not be possible if determinism is true.

And if you are talking about me specifically, I do not lack a reason to believe the prediction, I concede that the prediction should be correct if determinism is true. However, given that the prediction cannot be correct if Ned acts contrary to it, I conclude that determinism is false. I do not see how that is an "argument from ignorance." Unless you are saying that I do not have all the information that is contained in such a prediction, and in that case you are correct, I do not, but I do not see what impact that has on the thought experiment. The fact remains that, in consideration of the prediction, Ned can always choose to act in opposition to it.

wonderer1

↪NotAristotle

It is an argument from ignorance because you are basing your belief that determinism is false on your ignorance of what determines Ned's behavior. You haven't observed Ned behaving contradictory to the predictor's output. You are just sticking with your unjustified assumption that Ned could act contrary, despite having never observed such a situation.

Pierre-Normand

In the original scenario as I have described it, Ned reads the printout, but he only reads a part of it. And, importantly, he does not read a part of it where he is reading the printout -- that would be self-referentially problematic. Because there is no self-referentially in the parts of the printout that Ned does read, there is nothing necessarily theoretically vicious about Ned reading some parts of the printout. — NotAristotle

If Ned only reads a part of the printout that doesn't mention him reading it, his actions wouldn't contradict the thesis of determinism. For instance, suppose determinism entails that, given some initial conditions at time t1 (along with the laws of nature), Ned will drink a glass of water at time t2. The printout Ned reads must inform him of this prediction. In response, Ned decides to drink a glass of orange juice instead, fulfilling his intention to act contrary to the prediction.

We must consider when Ned's reading of the printout occurs. Does it occur before or after time t2 in the scenario you're envisioning?

If it takes place after t2, then Ned's actions wouldn't actually contravene the prediction. Indeed, by then, he would have already drunk the glass of water, hence aligning with the prediction. However, if he reads the printout prior to t2 to pre-empt the predicted outcome, we run into the self-referential issue. In this case, the computer would need to forecast what occurs as a consequence of Ned reading the printout. This would invariably involve predicting Ned's reaction to the prediction, triggering the problematic self-reference loop I had mentioned.

andrewk

Issue 1: What do you make of this thought experiment? Does it disprove determinism? — NotAristotle

As formulated, I don't think it proves anything, because it doesn't tell us WHY Ned decided to not go for a walk. Typically, interest zeroes in on the case where Ned makes that choice specifically in order to contradict the machine's prediction. Assuming that to be the case, the thought experiment only demonstrates that, while determinism might still be true, a Laplacian daemon that can predict the future of our universe must be causally isolated from it. That is, the daemon cannot do anything that affects the universe - she can look but not touch.

An intuitive but non-rigorous demonstration of this is that, for the daemon to predict the future, it must have complete detail about the initial state of everything causally related to the future of the universe. If not causally isolated, that includes information about the state of the daemon itself, which includes all the information about the universe. So the daemon must have more information than it has, since it needs to have information about the information it has (like a description of contents of its RAM, hard drive), plus information about things outside itself. No information store can hold more information than it holds, so such a store must be impossible. Hence it must be causally isolated.

That's a bit hand-wavy because it doesn't define information, amongst other limitations. But hopefully it gives the general idea.

On the other hand, if we assume that Ned wasn't influenced by the readout at all (impossible in practice, as he touched it, even if he didn't read it - butterfly effect etc), then all the experiment demonstrates is that the prediction machine must have been faulty.

NotAristotle

In this case, the computer would need to forecast what occurs as a consequence of Ned reading the printout. This would invariably involve predicting Ned's reaction to the prediction, triggering the problematic self-reference loop I had mentioned. — Pierre-Normand

I think the self-reference objection you are describing is a good one, I am just not sure that it applies in every case that Ned reads the printout. It would be problematic if Ned read the entire printout. In that case, we have our prediction, then we have Ned reading the prediction, so our final prediction will have to be a prediction of Ned reading the prediction, but then Ned will read that, so our final prediction will have to be a prediction about Ned reading the prediction of himself reading the prediction...to infinity.

On the other hand, if Ned only reads part of the printout in a non-self-referential way.. suppose it says "Ned will go for a walk in 5 minutes," that seems unproblematic. In that case, the reading of part of the prediction will itself have to be part of the prediction, however I cannot see why that is an issue. If you still think it is, would you explain to me in greater detail why you think it is an issue? It seems to me that reading only a specific part of the printout is significantly different than reading the entire printout.

T Clark

Additionally, a similar thread has been posted on this forum, I will include it here in case the reader would like to refer to it: https://thephilosophyforum.com/discussion/6478/determinism-vs-predictability/p1 — NotAristotle

Thank you for resurrecting this old thread. One of my favorites. My position on the subject hasn't changed from that original discussion. As I noted:

It feels intuitively to me that in some, many, most? cases unraveling cause is not possible even in theory. It's not just a case of being ignorant. Part of that feeling is a conviction that sufficiently complex systems, even those that are theoretically "caused," could not be unraveled with the fastest supercomputer operating for the life of the universe. There is a point, isn't there, where "completely outside the scope of human possibility" turns into "not possible even in theory." Seems to me there is. — T Clark

If something is completely unpredictable, does it still make sense to say it is caused. Isn't cause inextricably tied up with prediction? It may be possible to model and predict a coin flip or build a machine that can flip a coin with near perfect uniformity, but how about 1,000 flips using 1,000 random coins flipped by 1,000 random people? — T Clark

My conclusion - most events in the world are completely unpredictable by the standards discussed above. Therefore, it doesn't make sense to consider the world deterministic.

If determinism were true, the printout should accurately predict Ned’s actions; however, because it could potentially not predict accurately, determinism must be false. — NotAristotle

I don't think your thought experiment proves anything. Just because you failed to predict something doesn't mean it can't be predicted. A predicting device that didn't take into account the effects of it's prediction on the future would be a pretty crappy device.

SophistiCat

The Paradox of Predictability concerns determinism. In particular, it concerns the idea that if determinism is true, then true predictions should be possible about the future state of the world (or people or subsystems therein). — NotAristotle

Predictability, in the sense that you employ in your thought experiment, is not usually part of the definition of determinism, nor does it follow as a necessary implication. The first paper that you cite gives a more conventional definition:

a universe U is deterministic when, for any arbitrarily chosen time t₀, there exists a law-like function f_L which maps the initial state of the universe U₀ at time t₀ in a unique manner onto the state of the universe U_t at any arbitrarily chosen later time t:

U_t = f_L(U₀) — Determinism and the Paradox of Predictability

Therefore, even if we accept the reasoning in your example, it does not logically follow that determinism is false. All that we can conclude is that not all of the assumptions can be true at the same time. Rather than determinism being false, it could be that predictability is not achievable under the specified conditions.

The first paper that you cited makes an important point about predictability right in the abstract, by drawing a distinction between external predictability and embedded predictability:

The inference from determinism to predictability, though intuitively plausible, needs to be qualified in an important respect. We need to distinguish between two different kinds of predictability. On the one hand, determinism implies external predictability, that is, the possibility for an external observer, not part of the universe, to predict, in principle, all future states of the universe. Yet, on the other hand, embedded predictability as the possibility for an embedded subsystem in the universe to make such predictions, does not obtain in a deterministic universe. — Determinism and the Paradox of Predictability

↪andrewk

also made this point: a Laplacian demon might have the knowledge of the state of the world at a different time, but the demon, being external to the world, does not have to know its own state.

Another point concerns the possibility of prediction qua computation. It is one thing for the function f_L to exist in the abstract (and even for some hypothetical entity to have the knowledge of this function), but this is not the same as being able to compute this function given finite computational resources. Determinism, in its most general formulation, does not commit to computability. This, I think, is similar to the point made by

↪T Clark

NotAristotle

↪Pierre-Normand

I think I understand your objection now. You are saying that a prediction of a prediction is necessary for the computer to printout anything intelligible about what Ned will or will not do.

Maybe you can see where I am coming from too? It seems to me that with sufficient information about the state of the world at time t1, one should be able to make an accurate prediction about how the world would be at time t2. What seems to matter is mapping information about where each atom is, neural activity, electrical activity, etc., such that a prediction at time T2 is possible. If determinism is true, the subjective state of someone "I am a counterpredictor in such and such situation" should not matter. In other words, what someone reads on a printout should not affect their behavior if we have already a complete map of their behavior in terms of atoms etc. So I agree with you that a counterpredictor can always act otherwise, but that seems to pose a contradiction for determinism; namely, that the prediction and counterprediction must both obtain.

It feels intuitively to me that in some, many, most? cases unraveling cause is not possible even in theory. It's not just a case of being ignorant. Part of that feeling is a conviction that sufficiently complex systems, even those that are theoretically "caused," could not be unraveled with the fastest supercomputer operating for the life of the universe. There is a point, isn't there, where "completely outside the scope of human possibility" turns into "not possible even in theory." Seems to me there is. — T Clark

The problem of computability described by T Clark seems to me to be a salient one. If the prediction cannot be made because of instrumentation that is not precise enough, or because there is just too much information for a supercomputer to process, then the prediction just cannot be made.

it could be that predictability is not achievable under the specified conditions.

The first paper that you cited makes an important point about predictability right in the abstract, by drawing a distinction between external predictability and embedded predictability: — SophistiCat

At first glance, it appears that determinism should imply predictability, if not in an embedded way, at least in an external way. The paper cited says about as much, although I am unclear as to why an embedded predictor cannot make a true and accurate prediction in a deterministic universe. Or at least, it is unclear to me why an external predictor cannot be physical. Seems as though an external predictor could be physical, and yet still external to the situation (e.g. a computer that does not share its predictions with the system or person that it is predicting about).

thanks everyone for commenting

T Clark

Determinism, in its most general formulation, does not commit to computability. This, I think, is similar to the point made by ↪T Clark — SophistiCat

Yes. And my claim is that the idea of determinism is meaningless if prediction is not possible, even in theory.

wonderer1

Yes. And my claim is that the idea of determinism is meaningless if prediction is not possible, even in theory. — T Clark

I suspect that what people typically mean these days when saying the accept determinism is that they accept it as a corollary of accepting physical causal closure. So I don't see it as a meaningless idea inasmuch as it conveys such a perspective at the very least.

I would think a better objection might be that, in light of the predictive issues, a hypothesis of determinism might not be falsifiable. Does that maybe get more at your objection?

T Clark

I suspect that what people typically mean these days when saying the accept determinism is that they accept it as a corollary of accepting physical causal closure. So I don't see it as a meaningless idea inasmuch as it conveys such a perspective at the very least. — wonderer1

To take a step back, I see the whole issue of determinism as a metaphysical one, not subject to empirical verification or falsification. It's a matter of point of view, not fact. I don't see it as a very useful way of thinking - it's misleading.

For that matter, I think the idea of causation can be misleading except in the simplest cases.

T Clark

I would think a better objection might be that, in light of the predictive issues, a hypothesis of determinism might not be falsifiable. Does that maybe get more at your objection? — wonderer1

Left out my response to this.

I intended my objection to be stronger than what you've written. 1) Except for in the simplest situations, events are not predictable even in theory 2) Therefore the idea of determinism is not unfalsifiable, it's meaningless.

wonderer1

To take a step back, I see the whole issue of determinism as a metaphysical one, not subject to empirical verification or falsification. It's a matter of point of view, not fact. I don't see it as a very useful way of thinking - it's misleading. — T Clark

I don't see it as misleading, but I do recognize that people often jump to wrong conclusions about determinism and equate it to fatalism. I've described my view in the past as "interactive determinism", in an attempt to head people off from jumping to simplistic conclusions. In any case, I'd be interested in hearing more about what you see as misleading.

For that matter, I think the idea of causation can be misleading except in the simplest cases. — T Clark

I don't see the idea of causation as misleading. However, I do think humans are extremely susceptible to jumping to simplistic causal explanations, as a consequence of the fact that we can't grasp the full causal web, even if we recognize it exists and want to grasp it.

Janus

Yes. And my claim is that the idea of determinism is meaningless if prediction is not possible, even in theory. — T Clark

The Three Body Problem has been known about for more than 300 years. It establishes that it is impossible even in principle to predict the future of sufficiently complex systems. However, that the prediction of the future is impossible does not entail that determinism is false, much less meaningless. It is not meaningless simply by virtue of the fact that it can be imagined as a metaphysical possibility.

Perhaps you meant that it is meaningless in the sense that it is of no significance to us whether or not the Universe is deterministic, and I would agree with that.

wonderer1

Perhaps you meant that it is meaningless in the sense that it is of no significance to us whether or not the Universe is deterministic, and I would agree with that. — Janus

Perhaps it depends on your preferences. Few long term determinists, that I have observed, fail to recognize the monkeymindedness of retribution. I think humans recognizing their nature is a good thing.

Of course that's fallacious in all sorts of way. Not least, it's an appeal to consequences.

T Clark

I'd be interested in hearing more about what you see as misleading. — wonderer1

It's a simple pragmatic judgment. If a claim has no meaningful consequences in the real world, it is 1) metaphysics or 2) meaningless. As a metaphysical position, I don't see it as useful either ontologically or morally. Ontologically, I think it's misleading because it underpins the idea of causation, which I think leads people to look in the wrong places for the genesis of phenomena. Morally, I think it's misleading because it is used to justify a willingness not to hold people responsible for their actions.

I don't see the idea of causation as misleading. — wonderer1

We've had a few threads here on the forum where I've made the case that the idea of causality is unnecessary and misleading. Admittedly, most people have found my arguments unconvincing.

T Clark

Perhaps you meant that it is meaningless in the sense that it is of no significance to us whether or not the Universe is deterministic, and I would agree with that. — Janus

Yes. This is exactly what I mean. As I noted in my response to @wonderer1, above:

It's a simple pragmatic judgment. If a claim has no meaningful consequences in the real world, it is 1) metaphysics or 2) meaningless. As a metaphysical position, I don't see it as useful either ontologically or morally. Ontologically, I think it's misleading because it underpins the idea of causation, which I think leads people to look in the wrong places for the genesis of phenomena. Morally, I think it's misleading because it is used to justify a willingness not to hold people responsible for their actions. — T Clark

wonderer1

We've had a few threads here on the forum where I've made the case that the idea of causality is unnecessary and misleading. Admittedly, most people have found my arguments unconvincing. — T Clark

Did you happen to observe my recent demonstration, here on the forums, of how predictable people can be?

SophistiCat

To take a step back, I see the whole issue of determinism as a metaphysical one, not subject to empirical verification or falsification. It's a matter of point of view, not fact. I don't see it as a very useful way of thinking - it's misleading. — T Clark

I rather see it instrumentally, as a characteristic of specific theories or models that we adopt. And I mean not just scientific theories, but also our informal folk theories, including theories of mind. At the same time, I am not convinced that there is one true theory to rule them all at the bottom of creation. Which in turn makes it meaningless to ask whether the world is really deterministic or indeterministic.

T Clark

Did you happen to observe my recent demonstration, here on the forums, of how predictable people can be? — wonderer1

No. I'll take a look if you provide a link. I'm skeptical that the level of prediction you are talking about is as rigorous as what would be required to claim strict determinism. I don't doubt that events in the past have effects in the present and future. That's different.

T Clark

At the same time, I am not convinced that there is one true theory to rule them all at the bottom of creation. Which in turn makes it meaningless to ask whether the world is really deterministic or indeterministic. — SophistiCat

Agreed.

Paradox of Predictability

Welcome to The Philosophy Forum!

Categories

More Discussions