Notes on “Programs as Causal Models: Speculations on Mental Programs and Mental Representations”

I just read the paper from Nick Chater and Mike Oaksford.

I found this paper from reading “Creativity, Compositionality, and Common Sense in Human Goal Generation”.

Very cool paper:

They follow Judea Pearl’s thinking that counterfactuals and causality are central to intelligence, both natural and artificial intelligence.
I know of Judea Pearl’s work and influence, but have not done a deep dive into his work yet, I’ll have to do that soon. Causality is the scientific term for cause and effect. I recommend you read more here.

Counterfactuals are how we explain the causal claims.

X causes Y if and only if, without X, Y would not exist. Or written out longer:

An event E causally depends on C if, and only if, (i) if C had occurred, then E would have occurred, and (ii) if C had not occurred, then E would not have occurred.

Some specific examples of counterfactuals:

  • “If Peter believed in ghosts, he would be afraid to be here.”
  • “If it is raining right now, then Sally is inside.”
  • “If it was raining right now, then Sally would be inside.”

They argue that programs, which consist of algorithms and data structures, have a casual/counterfactual structure. Their definition of a program, simply restated is “Algorithms + Data Structure = Programs”, which is from a a paper, Wirth 1975. And such programs can provide a casual model of the world.

They state in cognitive science, the main view is that thought processes are programs (algorithms + data structures). And so that means we are able to define and test counterfactuals by changing the contents of the data structure while holding the algorithm constant.

Another way they state their argument, is that programs generate counterfactuals. Another way they say this: Algorithms capture putative “laws of nature” and data structures describe the state of the world. So modifying those data structures and tracing their consequences generate counterfactuals.

One more way they restate their argument: “Counterfactuals and causation are fundamental to computation and cognition. A program is a causal system: the algorithm determines counterfactuals over potential interventions on the data structures over which it operates.

In the paper, they also discuss how we still have no idea on the underlying neural representation, is it symbols, code, images, 3D, 2D, etc.

It seems like it is 3D, but it is inconclusive. The ideas in this paper excite me as it fits closely with my idea that the human mind is a model building engine of the world. Models are small simulations that be modified and run in real time to simulate phenomenon. I have been contemplating on what that data structure would look like and how to implement this in a computer. It has been increasing clear that there is some form of probabilistic computation involved. So I will be investigating this direction more. Fun stuff!


  • read paper one more time
  • share example of

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