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Imagine an automata universe (an example of a universe in which all causation is defined as an operation on the current state of the object of change defined by a set of immutable rules/axioms, which are applied at discrete intervals).

To an observer, within the automata, with knowledge that the world is an automata, would all causation be viewed as formal causation (in the Aristotelian sense)?

My initial thought is that since change is determined by fixed rules, and all resultants of change are necessarily effected by the previous condition of the object of change, then an object that has been changed has been changed by virtue of the object's previous configuration.

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  • What do you mean by formal causation in the Aristotelian sense? – Jo Wehler Mar 7 '16 at 5:01
  • As in a formal cause is one of the four causes he identifies: material, formal, efficient, and final. – socrates Mar 7 '16 at 5:33
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Mathematician David Woplert proved in 2008 that no intelligent agent can fully predict the evolution of a system that it is part of. In the context of your question, an observer within the automata can never completely predict the future state of the automata.The only way to do that would be from outside the automata. This means that there would be limits on the ability of the observer to provide formal causal explanations/models of their automata universe, and some parts of it would have to appear non-causal/non-deterministic (even if the automata is completely determined when observed from the outside).

His result is analogous in a way to Godel's "No theory can prove it's own consistency", in that he shows that no universe can be completely predicted from the inside, hence no universe can predict itself. The universe is inherently unpredictable from the inside, showing that formal causal explanations are bound to be incomplete.

Here's the original article and a general explanation of the idea.

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Cellular automata are examples of the automata you describe. In particular they are deterministic automata. Causa efficiens according to Aristotle is just what we today name causality.

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  • I am aware of cellular automata, I just wasn't going to explicitly reference it in case some were unfamiliar. My question was aiming at whether objects determined by an automata can be said to be changed by virtue of what they are (objects in the automata so produced such that their subsequent state is determined by their current state, so their current state is the cause of their subsequent state; a formal cause of sorts). – socrates Mar 7 '16 at 7:58
  • @socrates I do not understand your question. Every clock is an object where its subsequent state is determined by its previous state according to a deterministic rule . – Jo Wehler Mar 7 '16 at 8:12

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