*The Physical Signature of Computation *is an impressive book. Anderson and Piccinini have given us one of the most thoroughly articulated account of physical computation to date. At the center of their discussion is pancomputationalism, and in particular an especially strong version—known as unlimited pancomputationalism—which holds that every physical system implements every computation simultaneously.

According to Anderson and Piccinini, unlimited pancomputationalism is trouble. They liken it to ‘pansculpturalism,’ the view that “a block of marble is every sculpture that could be chiseled from it” (p. 267). They worry that such a view would deny “any real distinction between an imagined surface within the block of marble and a real physical surface rendered from the chiseling of the block to expose it” (p. 267-8). Similarly, they contend, under unlimited pancomputationalism “the claim that a physical system performs a computation becomes almost trivial and vacuous; there is no real distinction between a physical computing system and anything else” (p. 145). And this matters, at least to a large extent, because it is hard to see how computation can play its expected explanatory role absent such a distinction.

The pansculpturalist analogy is powerful. But it not the only analogy that might help us assess unlimited pancomputationalism. An alternative starts by treating attempts to describe physical systems computationally as an instance of the more general practice of describing physical systems mathematically. Matthews and Dresner (2017) develop this idea with reference to the representational theory of measurement. Here, I’ll develop it with reference to a simpler case, involving applications of finite cardinals to physical stuff (Curtis-Trudel 2024).

Numerical descriptions of physical stuff are characteristically offered as responses to numerosity questions, which have the form “How many Xs are there?” And it is fairly widely recognized that one and the same hunk of stuff can fall under different finite cardinals. Frege (1884), for instance, makes much of this, noting that under one ‘way of regarding’ some physical stuff it falls under the number fifty-two (e.g., fifty-two cards), while under another way it falls under the number one (e.g., one deck).

Frege’s observation bears more than a passing resemblance to the pancomputationalist’s suggestion that one and the same physical system falls under multiple distinct *computational* descriptions. And, it turns out, with just a little bit of work, it is possible to use it to gin up an analogous argument for *pancardinalism*, the view that many (perhaps every) finite cardinal applies to every (sufficiently large) hunk of physical stuff. Given pancardinalism, should we therefore conclude ascriptions of finite cardinals are trivial as well?

I don’t think so. Numerical ascriptions, as Frege points out, proceed under an antecedently specified ‘way of regarding’ the stuff in question. For Frege, these ways of regarding are concepts. Under the concept CARD, the stuff is fifty-two. Under DECK, it’s one. Under more recondite concepts, we can arguably assign any count we like to them. Crucially, however, each of these counts is offered in light of a salient numerosity question. It’s of course true that, if we use a different concept, we might arrive at a different count. But it’s hard to see why this would trivialize anything. For these alternative counts are, as it were, answering questions that weren’t being asked.

A little more carefully, the point is just that the inference from pancardinalism to the claim that applications of finite cardinals are ‘trivial’ fails. That’s because there can be principled reasons for choosing to describe some stuff in terms of a specific concept *even when* multiple distinct concepts apply to that same very stuff. Transposing this to the computational case takes some work, since it requires, among other things, spelling out the computational analogue of a concept—a ‘way of regarding’ a physical system computationally. But the basic point is the same: the inference from unlimited pancomputationalism to the claim that computational descriptions are trivial fails, because there can be principled reasons for choosing to work with specific kinds of computational descriptions when we wish to characterize systems computationally, *even when* other computational descriptions truly apply to that very same system.

There’s much more that would need to be said to make all of this precise. I won’t try to do that here. Instead, I’ll just sketch out how things look from this perspective, focusing on perhaps the main way I think it departs from Anderson and Piccinini’s approach.

If we think about computation in the way I am suggesting, then it’s less clear that we need to specify a global, context-independent criterion for computation (what one might call a signature) which vindicates computational explanations of physical systems. Spelling out such a criterion is, of course, the usual strategy for blocking unlimited pancomputationalism. But I think it’s clear that in the *numerical* case such a criterion would be unnecessary. What matters is that we can indicate which counts, under which concepts, best serve our ends. And often enough we can. It is not clear what an additional, context-independent characterization that purports to draw a line between legitimate and illegitimate counts would add.

Similarly, I suggest, we should ask which ‘ways of regarding’ systems computationally best serve our scientific ends. These ends may be best served by deploying computational descriptions which satisfy Anderson and Piccinini’s PCE principle, or which latch on to the counterfactual, causal, mechanistic, or semantic features of physical systems. But, *pace* Anderson and Piccinini’s attempt to unify these proposals under the robust mapping account, rather than regard these as competing accounts of the *signature* or *nature *of computation, we should instead regard them as competing proposals about how computational notions might best be deployed for certain scientific ends – just as we can regard certain kinds of concepts well or ill-suited to serve our (rather more straightforward) ends in describing systems numerically.

I have no better argument for this way of thinking than that it lets us avoid questions better left unasked. Rather than engage in potentially interminable attempts to draw a line between physical systems that compute and those that don’t, we should focus the role computational notions play in scientific practice: in virtue of what these notions apply, when they do, and the kinds of scientific achievements they support. Although nothing stops one from supplementing such an account with a story about which systems, in fact, compute and which do not, it is rather less clear what such efforts contribute to our understanding of computation and its role in science.

Curtis-Trudel, A. (2024). Computation in Context. *Erkenntnis*. https://doi.org/10.1007/s10670-024-00851-2

Frege, G. (1884). *The Foundations of Arithmetic* (J. L. Austin, Trans.). Northwestern University Press.

Matthews, R. J., & Dresner, E. (2017). Measurement and Computational Skepticism. *Nous*, *51*(4), 832–854.

Continued thanks to Andre Curtis-Trudel for his engagement with our work. His prior comments on a draft of the full manuscript led to many improvements in the presentation.

In his commentary here, Curtis-Trudel draws a contrast between, on one hand, drawing a line between systems that compute and systems that don’t, and on the other hand, figuring out “the role computational notions play in scientific practice: in virtue of what these notions apply, when they do, and the kinds of scientific achievements they support.” In our book, we pursued precisely such a project, and we take that to be compatible and complementary with drawing a meaningful and principled line between systems that compute and systems that don’t.

Perhaps the best-known role of computational notions in scientific practice is in computational modeling. Any physical system may be given any number of computational models at different levels of granularity, employing a vast array of techniques and formalisms. But the mere existence of computational models of a physical system need not entail that the system itself implements computations, let alone that some of its behavior can be explained by appealing to putative computations it performs. Historically, computational explanation and computational modeling were often kept insufficiently distinct, leading to inadequate accounts of physical computation and premature endorsements of pancomputationalism. One sign of progress in the philosophical literature is that nowadays fewer people confuse computational modeling and computational explanation. In the book, we are mostly concerned with scientific practices that involve attributions of computations to the physical systems themselves along with the possibility of explaining some behaviors of some systems in terms of the computations such systems perform. The existence and properties of ordinary computational modeling is largely orthogonal to our book’s concerns, although we do discuss the relation between modeling and explanation where needed.

To explain why figuring out the role that computational notions play in scientific practice complements drawing the line between systems that compute and systems that don’t, consider the example at the center of most of Curtis-Trudel’s commentary. He correctly points out that different cardinal numbers may describe accurately how many things there are within a portion of reality. One of us has contributed to a rigorous analysis of what such descriptions involve by means of a combination of mereology and measurement theory (Schumm, Rohloff, and Piccinini 2020). In that work, Schumm et al. show that the relevant “ways of regarding” a portion of reality are not “concepts” as Curtis-Trudel suggests, but partitions, where partitions are complete pluralities of parts of a portion of reality that cover the whole portion and leave none of it out. Concepts are not the relevant “ways of regarding” a portion of reality because one and the same concept is compatible with multiple numbers of objects (e.g., a thousand cat statues can be arranged in the shape of a cat, so that there is both one cat statue and a thousand cat statues within that portion of reality; this example is due to Achille Varzi) and some partitions may employ multiple concepts, or no concepts at all. But each partition comes with one and only one number of parts. More specifically, Schumm et al. prove representation and uniqueness theorems to the effect that cardinality descriptions are objective measurements of how many objects there are within a portion of reality relative to one of its partitions, in accordance with measurement theory. The details are complex but the gist is that, if we are careful, we can state precisely in what ways different cardinal numerical descriptions of a portion of reality are objective, compatible with each other, and even equivalent to one another in the technical sense of measurement theory. And this is why, as Curtis-Trudel correctly points out, the application of (multiple) cardinals to portions of reality is neither trivial nor vacuous.

As we show in our book, nothing of the sort applies to the sort of descriptions cooked up by unlimited pancomputationalists, because those descriptions are based on arbitrary and unprincipled assignments of computational state transitions to physical state transitions that capture nothing about the physical structure and dynamics of a system. They are not even legitimate computational models, let alone explanations. While we are unsure how far Curtis-Trudel’s analogy between cardinal numerical descriptions and unlimited pancomputationalism is meant to be taken, it seems to allude to the partitioning of a physical system’s state space into subspaces and the association of some or all of these subspaces with computational states. Since unlimited pancomputationalism is enabled by the unconstrained freedom to do so arbitrarily, and is blocked by constraints imposed by our independently motivated physical-computational equivalence condition (PCE), it seems worth clarifying our intentions here.

We are not claiming, as Curtis-Trudel seems to imply, that lack of a subspace partitioning constraint like PCE trivializes computation because we are ignoring the fact that other partitions are possible. We recognize that alternative partitions are indeed possible and might be useful “other ways of regarding” the physical system. Rather, we are claiming that physical computation is trivialized if it relies upon computational descriptions constructed from state-space partitions that are incompletely or insufficiently justified for the purpose of regarding a system computationally. Specifically, we are claiming that only selected state-space partitions pass muster for that purpose and we further identify such partitions: those that support groups of physical states that satisfy PCE and the other conditions for robust implementations of computations (which go beyond state-space partitioning).

So, yes, context matters. But the context of interest here is physical computation, and our book is about what is appropriate in that context. We consider what is relevant to that context, which is in no way undermined by acknowledgement of other contexts. If the robust computational descriptions of physical systems defined in our book do indeed identify the physical signature of computation, as we argue, then that is scientifically meaningful in contexts where computations are ascribed to physical systems and used to explain some of their behaviors. Additionally, we pointed out in the book that there are other classes of computational descriptions that are either weaker or stronger than robust descriptions, and we characterized all such descriptions precisely so that anyone who wants to use and analyze the scientific achievements that they support may see what roles they may or may not play and where they draw the line between systems that compute and systems that don’t. Thus, drawing that line and appreciating scientific achievements complement one another. Efforts to draw such a line—themselves part of scientific practice—contribute to our understanding of computation and its role in science. Curtis-Trudel’s commentary leaves us wondering what scientific context he feels is better served by not asking — and not trying to answer — the question of what it takes for a physical system to have computational capacities.

We argue in our book that there is no scientific value in the sort of arbitrary labeling of physical state transitions as computational that unlimited pancomputationalism countenances, and that is one reason that the sort of conclusions drawn by unlimited pancomputationalists do not follow. Let’s remember that unlimited pancomputationalism was concocted primarily to undermine the Computational Theory of Mind (CTM). For, if computational descriptions are as trivial and vacuous as unlimited pancomputationalism entails that they are, then asserting that mental processes involve computation says something utterly trivial and vacuous as well. To be fair, those who defended unlimited pancomputationalism were operating with rather simplistic and inadequate accounts of how computational descriptions apply to physical systems. Thus, developing a more adequate account, as we do in our book, allows us to show what goes wrong with unlimited pancomputationalism. In turn, this is an important aspect of showing that CTM, and the scientific research programs that come with it, are viable and nontrivial.

We finally emphasize that none of this is to say that physical systems have unique computational descriptions. As our book also discusses in detail, the same physical system may be given different kinds of computational descriptions, which in this context are descriptions that attribute computations to physical systems. We catalog and characterize precisely three main classes of computational descriptions (weak, robust, and strong) and explain what they do and do not capture about physical systems. We also explain that within each category of computational descriptions, many distinct descriptions of the same system may be given that capture a smaller or larger proportion of the physical dynamics of the system, and there is nothing trivial about that.

As Curtis-Trudel says, to appreciate the scientific achievements supported by computational descriptions requires figuring out the role they play in science. But it also requires studying such descriptions and their properties rigorously, as we do in our book, and working out and comparing the possibilities and implications of various descriptive strategies. For example, we show in our book how a robust implementation of a given computation may embed robust implementations of simpler computations, providing a principled explanation for how multiple robustly-implemented computations may be attributed to a given physical system without the interpretive excesses of pancomputationalism.

— Neal Anderson and Gualtiero Piccinini

Reference:

Schumm, A., Rohloff, W., and Piccinini, G. (2020). “Composition as Trans-Scalar Identity.” https://philsci-archive.pitt.edu/18253/

Pingback: The Brains Blog