Models models everywhere
“Do not mistake the map for the territory.” This critique is meant to be a generic criticism of drawing conclusions about the real world from one's scientific model. The map is the model and the territory is the target of the modeling endeavor.
This instrumentalist view is consistent with the Bayesian view, which holds that models serve only to represent or summarize statistical regularities present in observations. A model is never correct or true, it is simply more likely than other models under consideration. Finite data and failure to consider all possible models render metaphysical (a priori true) conclusions unavailable. Paraphrasing Laplace and Maxwell, all knowledge is conditional. Bayesians have priors and likelihoods with relative truth values that are conditioned on the data. Mathematicians have axioms (priors) and tools for generating additional truths conditioned on those axioms (likelihoods with logical structure). Philosophers specify relationships between and properties of intuitive “concepts” (likelihoods) and then prune and organize them to fit into axiomatic logical decision trees (priors). For example, Russell's paradox arises from the intuition that sets can be defined solely by a list of properties. His theory of types resolves this by introducing a hierarchal generative model for sets and sets of sets (Russell, Reference Russell and Russell1903). Zermelo's solution was to say that elements of a set can have properties that further divide them into subsets. This corresponds to generative models for subsets that have the philosophically preferred logical tree structure (Zermelo, Reference Zermelo1908).
Regardless, all we have are models. This is as true for the philosopher as it is for the mathematician and scientist. The above criticism reduces to the true but irrelevant statement that metaphysical (a priori) conclusions cannot be drawn. Ultimately, I believe the problem here is that “reality” is an evocative but poorly defined term that should be avoided. Territory, on the other hand, may be a sensible notion and Markov blankets can play a role in its identification. In the Bayesian framework, models, hypotheses, parameters, latents all receive the same treatment. There is only one quantity that has a special role: the observations or data (D). A Bayesian doesn't care about which model is correct or what values the parameters and latents take. This is explicit in posterior predictive modeling, which marginalizes out these details to generate a summary of previously observed data in the form of a prediction about future or unobserved data given the set of models under consideration, that is, p(D′|D,{M}). If observations are the territory, then this posterior predictive object has the appealing property that it is conditioned on the territory and its domain is the territory. Alternatively, it takes in something that can be called “facts” and generates predictions about future or unobserved “facts.” Model details simply provide a language to talk about relationships between observations. For example, suppose some observations of d 1 and d 2 are linearly correlated. A model with independent latent z that linearly drives d 1 and d 2 provides a compact language that describes the observed correlation. The posterior predictive formulation also demonstrates that science is ultimately concerned with prediction and data compression and nothing else. Models simply provide a language for talking about relationships between observations.
Markov blankets define objects
Markov blankets have two domains of application: latent variables of a model or observations. Historically, Pearl blankets are applied to latent variabes in a model. This allows us to define macroscopic objects (collections of latents) within a model and establish a taxonomy of objects defined by the statistics of their boundaries. It also has the potential to establish a language for discussing similarities between models in the same way we discuss motifs of connections between latents. When applied directly to observations, as in “The Markov blankets of life” (Kirchhoff, Parr, Palacios, Friston, & Kiverstein, Reference Kirchhoff, Parr, Palacios, Friston and Kiverstein2018), Markov blankets identify macroscopic objects in the territory.
By virtue of the epistemic seal, the blanket also defines the territory of the macroscopic object. As with Pearl blankets, this can lead to a taxonomy of objects defined by the statistics of their boundaries. The presence of a Markov blanket in our observations also tells us that we can ignore the territory within the boundary without consequence to our ability to predict what is going on outside the boundary, so long as the boundary persists and is observed. This is why it is generally irrelevant that protons are made up of a zoo of more fundamental things. Regardless, this line of reasoning establishes the link between Markov blankets and “thingness” and defines a thing by the relationship between the statistics of its boundary and the statistics of its environment. It also suggests that if there is any philosophical distinction to be made between Friston and Pearl blankets, that distinction is derived or inherited from the domain of application.
Regarding the notion of “inference with a model.” I do not view this as a categorically unique thing. The free-energy principle offers up a normative description of the behavior of objects (defined by their Markov blankets) in the language of agent–environment interaction. That is, objects (1) form beliefs about the external world, (2) use that information to predict changes in the boundary, and (3) act to affect the boundary (and indirectly the external world) in a way that drives boundary statistics to a desired stationary distribution. This is necessary because boundary maintenance and object identity are inexorably linked.
However, from the complete class theorem, we know that the language of agent–environment interaction is uniformly applicable to coupled systems. Thus, the relatively innocuous statement that objects are defined by the statistics of the interactions between their boundary and their environment is equivalent to the statement that objects perform inference with a generative model and “act” to enforce a particular statistical relationship between boundary and environment. That said, the moral of this story seems to be that the simple language of object–environment interactions should be preferred over the language of agent–environment interactions because the latter tends to generate confusion and unnecessary philosophical reaction. Still, it is just two ways of saying the same thing (Ramstead, Friston, & Hipólito, Reference Ramstead, Friston and Hipólito2020).
You have
Access
Models models everywhere
“Do not mistake the map for the territory.” This critique is meant to be a generic criticism of drawing conclusions about the real world from one's scientific model. The map is the model and the territory is the target of the modeling endeavor.
This instrumentalist view is consistent with the Bayesian view, which holds that models serve only to represent or summarize statistical regularities present in observations. A model is never correct or true, it is simply more likely than other models under consideration. Finite data and failure to consider all possible models render metaphysical (a priori true) conclusions unavailable. Paraphrasing Laplace and Maxwell, all knowledge is conditional. Bayesians have priors and likelihoods with relative truth values that are conditioned on the data. Mathematicians have axioms (priors) and tools for generating additional truths conditioned on those axioms (likelihoods with logical structure). Philosophers specify relationships between and properties of intuitive “concepts” (likelihoods) and then prune and organize them to fit into axiomatic logical decision trees (priors). For example, Russell's paradox arises from the intuition that sets can be defined solely by a list of properties. His theory of types resolves this by introducing a hierarchal generative model for sets and sets of sets (Russell, Reference Russell and Russell1903). Zermelo's solution was to say that elements of a set can have properties that further divide them into subsets. This corresponds to generative models for subsets that have the philosophically preferred logical tree structure (Zermelo, Reference Zermelo1908).
Regardless, all we have are models. This is as true for the philosopher as it is for the mathematician and scientist. The above criticism reduces to the true but irrelevant statement that metaphysical (a priori) conclusions cannot be drawn. Ultimately, I believe the problem here is that “reality” is an evocative but poorly defined term that should be avoided. Territory, on the other hand, may be a sensible notion and Markov blankets can play a role in its identification. In the Bayesian framework, models, hypotheses, parameters, latents all receive the same treatment. There is only one quantity that has a special role: the observations or data (D). A Bayesian doesn't care about which model is correct or what values the parameters and latents take. This is explicit in posterior predictive modeling, which marginalizes out these details to generate a summary of previously observed data in the form of a prediction about future or unobserved data given the set of models under consideration, that is, p(D′|D,{M}). If observations are the territory, then this posterior predictive object has the appealing property that it is conditioned on the territory and its domain is the territory. Alternatively, it takes in something that can be called “facts” and generates predictions about future or unobserved “facts.” Model details simply provide a language to talk about relationships between observations. For example, suppose some observations of d 1 and d 2 are linearly correlated. A model with independent latent z that linearly drives d 1 and d 2 provides a compact language that describes the observed correlation. The posterior predictive formulation also demonstrates that science is ultimately concerned with prediction and data compression and nothing else. Models simply provide a language for talking about relationships between observations.
Markov blankets define objects
Markov blankets have two domains of application: latent variables of a model or observations. Historically, Pearl blankets are applied to latent variabes in a model. This allows us to define macroscopic objects (collections of latents) within a model and establish a taxonomy of objects defined by the statistics of their boundaries. It also has the potential to establish a language for discussing similarities between models in the same way we discuss motifs of connections between latents. When applied directly to observations, as in “The Markov blankets of life” (Kirchhoff, Parr, Palacios, Friston, & Kiverstein, Reference Kirchhoff, Parr, Palacios, Friston and Kiverstein2018), Markov blankets identify macroscopic objects in the territory.
By virtue of the epistemic seal, the blanket also defines the territory of the macroscopic object. As with Pearl blankets, this can lead to a taxonomy of objects defined by the statistics of their boundaries. The presence of a Markov blanket in our observations also tells us that we can ignore the territory within the boundary without consequence to our ability to predict what is going on outside the boundary, so long as the boundary persists and is observed. This is why it is generally irrelevant that protons are made up of a zoo of more fundamental things. Regardless, this line of reasoning establishes the link between Markov blankets and “thingness” and defines a thing by the relationship between the statistics of its boundary and the statistics of its environment. It also suggests that if there is any philosophical distinction to be made between Friston and Pearl blankets, that distinction is derived or inherited from the domain of application.
Regarding the notion of “inference with a model.” I do not view this as a categorically unique thing. The free-energy principle offers up a normative description of the behavior of objects (defined by their Markov blankets) in the language of agent–environment interaction. That is, objects (1) form beliefs about the external world, (2) use that information to predict changes in the boundary, and (3) act to affect the boundary (and indirectly the external world) in a way that drives boundary statistics to a desired stationary distribution. This is necessary because boundary maintenance and object identity are inexorably linked.
However, from the complete class theorem, we know that the language of agent–environment interaction is uniformly applicable to coupled systems. Thus, the relatively innocuous statement that objects are defined by the statistics of the interactions between their boundary and their environment is equivalent to the statement that objects perform inference with a generative model and “act” to enforce a particular statistical relationship between boundary and environment. That said, the moral of this story seems to be that the simple language of object–environment interactions should be preferred over the language of agent–environment interactions because the latter tends to generate confusion and unnecessary philosophical reaction. Still, it is just two ways of saying the same thing (Ramstead, Friston, & Hipólito, Reference Ramstead, Friston and Hipólito2020).
Financial support
I received no funding for this effort.
Conflict of interest
None.