How to solve this paradox about determinism?

Question

I am thinking about this problem :

suppose the world is deterministic and there exist an entity "D" able to predict the future based on the knowledge of the state of the world at a given time T (like Laplace deamon).

then suppose we engineer an object "A" to shine some light or no light based on some input, and the experiment would go that way :

At time T, we ask D to predict "the state of the world at time T+2" and to present its prediction to A at time T+1, and we engineer A such that it shines a light at time T+2 if the prediction presented by D at time T+1 was "no light" and reversely, no light if the prediction was light. Then by construction D was wrong in its prediction.

It seems completely paradoxical to me and I don't know what to conclude or what to do with that. Has it been already solved somewhere ?

thanks

Answer 1

The problem arises already with the question of how the predicting of the future works. In order to compute the next time step D likely has to use as much time or more than the time elapsing to do that. Like gathering all the information takes more time crushing the numbers takes more time aso.

So he either needs to dumb down the problem and run a simplified simulation of the universe, where the result is no longer deterministic certainty but just an approximation.

Or D would need to "step outside of the system". In that he makes use of computing power and gathering tools that exceed the limits of the universe and doesn't himself interact with that universe.

The latter part is important because if he is part of the equation of the universe this will likely throw him into an infinite loop.

Which is precisely what you describe. Because if he tells the people within the universe his prediction, he becomes a factor in that universe, alters the equation and therefore the entire calculation was moot, because the initial conditions have changed. So he needs to recalculate the results and faces the same problem over and over again.

So ironically to predict the future he must himself "be free" and not interact with the system, hence never telling anyone his prediction. Or he could cheat write down his result place it in an envelop into a safe and then just tell people what he predicted so that his actual prediction turns out to be true.

Might also want to look at the halting problem which seems quite similar

Answer 2

This is known as Scrivens paradox (as the OP found himself in their self-comment), see also my answer in https://philosophy.stackexchange.com/a/90420/30526

In general, it is not logically possible to build a machine that both correctly predicts it's own behavior and is built to do the opposite of it's prediction.

It's the same as if I ask you to:

• pick "heads" or "tails" in a minute from now
• Before that, write down which one you will pick
• Then pick the other one than the one written on paper

You cannot both correctly predict the choice on paper and do the opposite of what you predicted.

But an outsider might (without telling you) correctly predict what you are going to to (choose one and pick it, choose one and pick the other, just walk away without doing either, ...).

This also happens in any common model of fully deterministic systems, which are fully predictable from the outside.

One way to interpret this is that systems or agents, even when fully deterministic parts of fully deterministic systems (like computer programs), can act in an opposite way of any prediction presented to it. In other words, determinism does not imply fatalism or predeterminism.

However, such agents could be fully controlled from the outside via predictions. E.g. an outsider might use "reverse psychology" telling you that you will take "heads", while knowing you will choose the opposite "tails", and thus make you take "tails" as they predicted without telling you. An outsider can fully predict what a system will do, and what a system would do given additional inputs from the outside.

Answer 3

Entity D, object A, any predictions or "we" cannot exist within that deterministic system. We all must be outside in normal indeterministic conditions, where predictions can be made, objects can be engineered, input can be accepted, results can be observed and possible paradoxes can be considered.

If object A is within the deterministic system, it will behave exactly as caused, exactly as predicted. No paradox. Like the whole system, object A cannot accept any "runtime" input to change its behaviour. All the input required to run a deterministic system must be present at the initial setup.

If object A is outside the deterministic system, it is outside the scope of the prediction. There will be no light at T2.