Infinitisitic Epistemic Expansion

Knowledge in a World of Indefinite Extent

Nick Nielsen
8 min readMar 14, 2021


An interesting twentieth century perspective on the expansion of scientific knowledge was provided by Harlow Shapley:

“After seven years of work with large instruments on questions concerning the globular star clusters — their structure, relationships, stellar content — I realized that we were relatively more ignorant about them than when I had started my investigation. I had added more to the unknown than to the known.” (Harlow Shapley, The View from a Distant Star, p. 17)

This is clearly a tendentious way to characterize the results of scientific research. Shapley noted that, “…we were relatively more ignorant about [globular star clusters] than when I had started my investigation,” with relatively being the key term. He did not note that, in absolute terms, his investigations had significantly increased our body of knowledge regarding globular clusters.

Indeed, it was Shapley’s work on globular clusters — specifically, their distribution in relation to the Milky Way — that implied that we are not located in the center of the Milky Way, which became in its turn another Copernican demotion of human centrality in the universe. Mapping globular clusters showed them to be arranged in a roughly spherical shell, from the center of which sphere our observing location of the Milky Way is significantly offset: the study of globular clusters not only yielded knowledge of globular clusters, but also knowledge about Earth and the solar system.

One can regard Shapley’s claim as a humorous way of retaining his epistemic humility; this is the most charitable reading of his claim. A less charitable reading would infer that he regarded his lifework as a failure for having added more to the unknown than to the known, but Shapley would certainly have known that one cannot very well engage in scientific research without expanding the scope of potential objects of knowledge. Indeed, one might even characterize a scientific research program in the Lakatosian sense in terms of the ontology it implies and which it aims to bring to light, so that a proposed expansion of scientific ontology is intrinsic to all research.

Science must pioneer novel objects of knowledge to expand (it must expand the ontology of science), but philosophy can expand parasitically by schematizing the expansion of scientific knowledge, since philosophy can always continue to expand by formulating “the philosophy of x” where the variable x is to be given a value that might be any topic whatever, including topics pioneered by the expansion of science. Quine said that philosophy of science is philosophy enough, and insofar as science continues to expand and produce ever new forms of knowledge, philosophy can also expand as the criticism and elucidation of ever new forms of knowledge. Thus the cipher of “the philosophy of x” can be substituted by any of the special sciences of increasing narrowness.

Earlier in Reticulate Science I mentioned lichenology, mycotoxicology, and paleomycology as scientific specializations, and the possibility someday of a paleolichenology. There could also be a philosophy of lichenology, a philosophy of mycotoxicology, and a philosophy of paleomycology, so that the expansion of science implies the expansion of philosophy.

It may seem a bit ridiculous to speculate on a possible philosophy of paleolichenology, and indeed I can remember an exchange of letters with a friend many years ago — back in the day when people wrote letters on paper and sent them through the mail — in which my correspondent maintained the unlikelihood of philosophy having anything interesting to say about cell biology (or, contrariwise, the unlikelihood of cell biology having any philosophical implications). This probably was my point of view for many years, but having seen the growing sophistication of philosophy of science, and of philosophical inquiries into scientific specializations, I am ready again to argue for the relevance of philosophy even of the most minute and detailed research.

Also earlier in Reticulate Science I asked above the fate of disciplines tied to science, like big history, and whether they share the fate of science as science evolves over the longue durée, and perhaps over cosmological scales of time, if there is any being capable of doing science that can endure over cosmological scales of time. We can clearly see the possibility of philosophy following the development of reticulated history of science, with philosophies not only of the increasingly narrow specializations, but also philosophies of the interdisciplinary studies that attempt to converge on the big picture. Even philosophy merely as philosophy of science in the Quinean mould can continue to expand and diversify as science expands and diversifies.

As we saw with the concept of the reticulate structure of science, the development of science not only involves new and narrower specializations, but also new and broader interdisciplinary approaches to knowledge, which not only present philosophy with novel objects of knowledge, but also the interesting methodological problems of previously independent sciences each approaching empirical evidence in their own way, now working together in an interdisciplinary context and attempting to converge upon one and the same object of knowledge.

And when philosophy is applied to those disciplines with only a problematic relationship to the paradigm of empirical science — the examples I previously gave were mathematics and history — philosophy as philosophy of science passes imperceptibly beyond the strict bounds of science, but in doing so its development is consistent with its past as philosophy of science. In this way, philosophy can again grow back into its ancient role as the science of science.

One of the most gratifyingly clear definitions of philosophy of which I know is that of R. G. Collingwood from his paper “Philosophy of History” (1930), which begins, “Philosophy is thinking about the world as a whole.” In the next section of the paper, Collingwood writes, “‘The philosophy of something’ is a legitimate phrase only when the ‘something’ in question is no mere fragment of the world, but is an aspect of the world as a whole — a universal and necessary characteristic of things.” Then in the third section, Collingwood turns to philosophy of history specifically, and argues for the universal and necessary human interest in history as the basis for the legitimacy of a philosophy of history, whereas, according to Collingwood, there can be no philosophy of horse-racing, which does not possess this universal and necessary human interest (I’m not sure that I agree with this, but leave that aside for the time being).

Collingwood’s definition of philosophy and what can legitimately serve as a philosophy of something has important implications for the parasitic expansion of philosophy as enabled by the expansion of science. I don’t think there is any question but that philosophy of science is a legitimate philosophical undertaking and possesses the same universal and necessary characteristics that Collingwood identified in the philosophy of history. Could a philosophy of paleolichenology also possess the same universal and necessary characteristics? Would paleolichenology be, “…pregnant with philosophical truths that [the philosopher] cannot learn from another source”?

Certainly science does not cease to be science as it focuses on a narrow specialization, but do narrower specializations involve any particular insight into the world not offered by science simpliciter? Suppose we take this question and apply it reflexively to history. There is history simpliciter, which is presumptively the object of the philosophy of history, but are there (or should there be), philosophies of specialized subdisciplines within history? Hegel divided history into original history, reflective history, and philosophic history. Nietzsche divided history into the monumental, the antiquarian, and the critical. As divisions in history drawn by philosophers, all of these strike me as being of philosophical interest. Hegel further subdivided reflective history into universal history, pragmatic history, critical history, and specialized history. With the latter we have arrived at the more familiar decompositions of history into domains like art history, political history, environmental history, and so on. Here we are presented with the same difficulty as we saw with the relationship of science simpliciter to its specialized subdisciplines: the relationship of history (and philosophy of history) to its specialized subdisciplines. History does not cease to be history when it is focused on a narrow subdivision, but do these reveal what cannot be learned from another source?

I would say that, both in the cases of science and history, there are instances when a narrow focus reveals insights not otherwise obtained, but this is not invariably the case. Thus whether a given subdivision of a discipline can reveal new insights can only be determined by studying the subdivision to determine its relative fruitfulness for philosophical investigation.

Just as we do not know if the subdivision of science into further specializations can be carried on indefinitely, or whether it must eventually come to a halt, so too we do not know if the expansion of scientific knowledge will continue indefinitely, or whether the expansion of knowledge will continue to drive the further expansion of the unknown that had distressed Shapley. Science could be exhausted when the empirical world has been studied to its limit, and in the finite cosmos defined by the consequences of the big bang, this is a very real possibility. But if our universe is part of a larger and more extensive cosmological system, and the big bang is but our big bang — one big bang among many — then there would seem to be no limit to the expansion of scientific knowledge because there would be no limit to the universe; there would always be further reaches of the empirical world not yet studied.

However, even contemplating the infinitude of the universe, science might still be exhausted if the uniformity of nature — a fundamental presupposition of science — holds at the largest scales. If studying a part of the universe reveals to us the nature of the whole, and the nature of reality is purely iterative, then even an infinitistic universe could be exhausted for scientific knowledge. However, it would not be exhausted for experience. If a conscious being could sustain and perpetuate itself in an infinite universe, it could travel infinitely in the cosmos without experiencing any perfect repetition of experience, and this in itself could be the datum of some science. I would hesitate to call this datum psychology, as we do not know if an infinitely old being would have anything like what we call a psychology, even if it constitutes a form of conscious cognition. Whatever this lived experience would be, if could be self-reflexively the source of unending scientific knowledge.

In so far as an infinitely old being continuing to have experiences constitutes a history, the possibility of ongoing scientific knowledge at this extreme, at this farthest edge of knowledge, would be historical knowledge. This is similar to my line of reasoning a few years ago when I wrote Who will read the Encyclopedia Galactica? In this essay I imagined Dyson’s eternal intelligence with nothing to work upon after the cessation of most physical processes other than the historical records of the earlier history of the universe. Thus Dyson’s eternal intelligence is essentially an historian. Now I see that the experience of the eternal intelligence itself could be an object of knowledge, meaning that the history that it could contemplate could include its own history, this being a further exemplification of infinitistic historiography. In this case, the known could increase exponentially even as the unknown continues to increase exponentially, and so on, world without end.

Harlow Shapley



Nick Nielsen