The Intentional Agency Experiment

Dear Vaniver, thank you for sharing your thoughts. You bring up some important points.

The Intentional Agency Experiment is an idealisation, a model that tries to capture what 'intention' is supposed to be. How to translate this to the real world is often ambiguous and sometimes difficult. Similar issues crop up all over applications of pure science&mathematics. 'Real' applications usually involve implicitly and explicitly many different theoretical frameworks and highly simplified models as well as practical knowledge, various mechanical tricks, approximation schemes, etc.

When I ask that R has a set of actions, this only makes sense within a certain framework. A rock does not have 'actions', and neither does a human within a suitably deterministic framework. So we have to be careful; the setup only works when we have a model of the world that is suitably coarse-grained and allows for actions & counterfactuals. Like causality, intention & agency seems to me intensely tied up with an incomplete and coarse-grained model of the world.

To clear any misunderstandings; if we have a physical object that at our level of coarse-graining may indeterministically evolve, for example a rock balancing on a mountain peak, we would not say it has possible actions. One could be under the impression that the actions that are considered are actually instantiated; but of course that is not what is meant. In the Intentional Agency Experiment $R$ is only asked to give an action given a counterfactual (hypothetical) world. If you'd like you can read 'potential action' everywhere where I write 'action'. Actions are defined when we have an agent that we can ask to consider hypothetical scenarios and outputs a certain 'potential action' given this counterfactual world.

We cannot ask a rock to consider hypothetical scenarios. Neither can we ask an ant to do so. Only a human or sophisticated robot can. Even a human or sophisticated robot will usually not consider just the 'clean' counterfactual $P\left(G|A\right)=0$ but will also implicitly assume many other facts about the world. When we ask the $R$ to consider $P\left(G|A\right)=0$ we don't want it to assume other facts about $W$. So one should consider a world where the action $A$ is instantiated but an omnipotent being keeps $G$ from happening at the last possible moment.

In practice, it is frequently difficult to ask agents to consider hypothetical counterfactuals and impossible to have them consider 'clean' counterfactuals (where all else is held fixed). Nevertheless, just like in Economics we assume Ceteris Paribus, considering highly idealised models&situations often turns out to be a useful tool.

Moreover, we may try to approximate/instantiate the Intentional Agency Experiment in the real world. However, sometimes those approximations may not be the 'right' implementation. As mentioned, an ant cannot be asked to consider hypothetical scenarios directly. Yet, we may try to 'approximate' the piece of information $P\left(G|A\right)=0$ by putting an obstacle in its way. If the ant tries and succeeds to overcome the obstacle the conclusion shouldn't be that 'it chose a different action'; rather the correct conclusion was that putting this obstacle in its way was not a sufficient implementation of the mathematical act of asking $R$ to consider $P\left(G|A\right)=0$ .

Yes, in practice situations arise where the implementation of a model can be ambiguous, very hard to implement etc. These are exactly the problems engineers and experimental physicists deal with; and these are interesting and important problems. But it should not prevent us from constructing highly simplified models.

Dear gworley,

Thank you for the link, it seems like an interesting result. The kind of proof that you'd like, purporting to show that a mathematical model is 'always' applicable to a real world situation, is surely nigh-impossible. If I try to summarise your main objection: the paper you linked to is a form of a 'partial' no go theorem for IRL; and you think it might be likely that there are very general No Go Theorems which would apply to any possible implementation of theoretical models of agency. This is of course possible, but I find it unlikely; in the real world humans are able to discern agency. No doubt there are many hidden assumptions and subtleties but I think it shouldn't stop us from trying to understand intention&agency in highly simplified situations.

In the model this is simply stated as given; we are trying to define intention; it might be that this definition does not accord to your intuitions about intention, but inside the model one cannot reject the conclusion. Of course, someone might come along and might come up with a more sophisticated model that has even more subtle distinctions. I look forward to such a model.

In danger of repeating myself, I cannot 'prove' that I can do what I can do. There is simply a model, which might be accurate in some respects and inaccurate in others; in the model one can do whatever one likes (following the rules of the model); applying it to the real world is trickier. As stated earlier there are many situations where the exact implementation is ambiguous or needs extra-theoretic assumptions. This is normal and occurs all over science. Galileo's results can be objected to in individual situations by referring to all kinds of contingencies like air resistance etc. Indeed, I have heard it said -but cannot confirm- that one Jesuit scholar refused to look through the telescope when Galileo founds the moons of Jupiter, objecting to possible smudges on the telescope. I think you will agree that Galileo's perspective was more productive then that of the Jesuit scholar, even though of course Galileo couldn't prove that his model was applicable [the fact that the moons weren't smudges on the telescope is one of those extra-theoretical assumptions].

It is clear that explications are somehow bouncing off, as (it seems) you are the second person to object in this manner. Perhaps the nomenclature 'experiment' was ill-begotten.

EDIT: The story about Galileo is almost certainly false; see Gignoramus