Scientia sub specie illuminatatis

Friday 17 May 2024

Nick Nielsen
9 min readMay 19, 2024
Antoine-Laurent de Lavoisier (26 August 1743–08 May 1794) was the perfect picture of Enlightenment science, and he was ultimately guillotined by the French revolutionary government.

In the past several newsletters I have discussed the lack of a science of science, and some of the ramifications of this absence. Another consequence of the absence of a science of science is the selective way in which science develops, and this in turn leads to Danilevsky’s philosophy of science, which acknowledges that science can be different in different social milieux. In other words, science is relative to the scientific community that practices science. Kuhn comes to an analogous conclusion, though for Kuhn it is the diachronic relativity of science that emerges from a history of scientific revolutions triggered by model crises and paradigm shifts. Kuhn’s work continues to be debated, are there are significant differences of interpretation that keep alive the controversy as to whether paradigm shifts are rational or irrational. (Why not both by turns?)

Danilevsky presents us with the prospect of the synchronic relativity of science, in which paradigms differ not down through historical time, but across ethnic communities. This strikes at the heart of Enlightenment universalism, but, as I have tried to argue in these newsletters, Enlightenment ideology is not intrinsically scientific, but for a time Enlightenment thinkers made common cause with the sciences as a way both to advance their interests and to fight the common enemy of traditionalism. But scientists themselves have so completely internalized Enlightenment ideology that, even if the Enlightenment can abandon science, scientists cannot abandon the Enlightenment. That science is the same, that it must be the same, for all who practice it, seems to be an unspoken presupposition of science practised sub specie illuminatatis.

Nikolay Yakovlevich Danilevsky (Николай Яковлевич Данилевский; 10 December [O.S. 28 November] 1822–19 November [O.S. 07 November] 1885)

I don’t know of any analytical philosophers who have taken up Danilevsky’s argument, even if only to refute it. Nor do I know of any analogous arguments, though my knowledge of contemporary philosophy of science is far from exhaustive. The closest we come to Danilevsky in the mainstream of Anglo-American analytical philosophy of science is the debate over Kuhn’s philosophy of science, which evades some of the most troubling aspects of Danilevsky’s account. But in the absence of a science of science, we cannot definitively exclude Danilevsky’s account, just as we cannot exclude the role of personalities in the development of science (the focus of last week’s newsletter), nor can we exclude the possibility of alternative sciences that explain as much of the world as our familiar sciences, but which are largely disjoint from the familiar sciences. This latter possibility is related as an anecdote in Eugene Wigner’s “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” which I have quoted many times (though, strangely, apparently not in these newsletters, as I searched back several years just now and didn’t find this quoted, though I could have sworn that I have referenced this so many times my readers may be tired to hearing of it).

Another problem potentially soluble by a science of science: every special science undergoes its own crisis in its turn as it is forced to recognize that it cannot define either the object of its research or the fundamental theoretical terms it employs. There was the crisis in the foundations of mathematics, the crisis in physics, the crisis in psychology, the replication crisis (which falls hardest on social psychology, but which leaves few disciplines unscathed), the crisis in cosmology, and no doubt further crises yet to come. Some of these crises resemble each other, suggesting analogous structural problems within the sciences, while other crises seem to be highly specific to a particular subject matter (as with the crisis in cosmology generated by diverging measures of the Hubble constant). Further research into crises may reveal a deeper commonality, or may reveal each crisis to uniquely supervene on the objects of knowledge distinctive to each science.

Eugene Wigner’s anecdote about counterfactual science in “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” has had a significant influence on my thinking.

The above assumes that a science of science would foreclose upon these troubling scenarios we would prefer not to contemplate. I think we can safely say that we have excluded some unwelcome scenarios for science, and this implies some rudimentary foundations of a science of science, and I think that if the project of a science of science ever came about, i.e., if it ever became a scientific research program on its own — or perhaps a meta-scientific research program — it would gradually foreclose upon the paradoxes of science, excluding them one by one, first taking care of the relatively simple problems, and then moving on to the more difficult ones. We don’t yet even know what the hardest problems are, or what they will be, when we earnestly turn toward formulating a science of science. It is all terra incognita to us.

In the absence of a science of science, however, we do have something to go on, and that is the record of the most successful special sciences, which, through their utility and fruitfulness, have provided a model for the other sciences to follow. And follow they do. A successful scientific discipline spurs imitation in the other special sciences, with the methods and the research program and theoretical structures copied. Science, then, has recourse to analogy. Later sciences are constructed along the lines of earlier successful sciences, and with good reason. The successful sciences have resolved many or most of their problems, and their methods have proved to be a successful way to derive knowledge from the empirical world.

How far can we push the analogies we use in science? In the absence of a formal theory of analogy, we are attempted to appeal to the intuitive power of analogies, but we can get ourselves in trouble this way.

But analogy itself is a theoretical problem. It has no standing as a formal principle of reasoning, and empirically it forces us into the kind of metaphysical speculation that most scientists hate — reflections on the uniformity of nature and such like. If nature is uniform, then a scientific methodology for the investigation of nature can be uniform, and we can know that it is (or will be) as effective in one region of experience as in another region of experience. Proof of this, however, is a metaphysical proof, and not anything scientific in the usual sense.

I should not belabor this idea of the absence of a science of science without acknowledging that it was, of course, the traditional idea that philosophy was the science of science, or, more narrowly, philosophical logic as it was elaborated prior to the mathematization of logic, that was understood to be the science of science, or, as it was also commonly known, the theory of science. Many logical works were called the theory of science, as, for example, Bernard Bolzano’s four volume Theory of ScienceWissenschaftslehre — which was completed in 1837, but the first complete English translation of which did not appear until 2014. In the meantime, between 1837 and 2014, logic, philosophy, and science all underwent rapid growth, and even, we could say, directional growth, that took them in a developmental direction of elaboration that was not anticipated prior to this time.

Bernard Bolzano (born Bernardus Placidus Johann Nepomuk Bolzano; 05 October 1781–18 December 1848)

We can imagine a counterfactual history of logic (and of science) in which logic developed linearly, and did not experience a sudden growth along with a sudden realignment, gradually converging upon the ideal of a theory of science imagined by logicians like Bolzano. While mathematical logic transformed both logic and mathematics both, what was lost in the elaboration of mathematical logic was its connection to this traditional function of logic as the science of science. Moreover, the internal integration of logic was lost, though, it must be observed, other forms of integration appeared as logic was reconstructed analogously to mathematics.

Lately I have been thinking how, with the advent of mathematical logic and analytical philosophy, theory of meaning and theory of reference bifurcated, and with this bifurcation the inverse relationship between the two, explicitly recognized in traditional logic, was lost. Traditional logic asserts that as intension expands, extension narrows, and as extension expands, intension narrows. Intuitively it is easy to see that this is the case: a highly definite meaning applies only to a very few referents, while a generic meaning applies to a great many more referents. But with the development of mathematical logic and analytical philosophy, the theory of meaning and the theory of reference developed in different directions.

What happened? The whole of Western civilization was redirected and realigned by the industrial revolution. Some years ago I wrote about how the industrial revolution essentially hijacked other developments that were already taking place, and which therefore did not have the opportunity to come to a natural fruition because industrial change was so rapid and so catastrophic. I called this the preemption hypothesis (and gave it a further application in Late-Adopter Spacefaring Civilization: The Preemption that Didn’t Happen). We can understand preemption as a more generic historical process in which one historical process that is aggressively expansive overtakes another historical process that is slower and more gradual. An invasive weedy species of cognition expands universally and crowds out endemic species of cognition, driving them to extinction, and leaving us with a philosophical monoculture and its attendant disadvantages.

The kind of industrial civilization we might have gotten had the industrial revolution been an industrial evolution instead of a revolution, unfolding over millennia, as it is likely that the development of agriculture developed, would have been dramatically different. And the industrial revolution spawned revolutions in every adjacent sphere of life and thought. The preemption that was the industrial revolution can also be seen at work in intellectual history, and even in aesthetic and spiritual history. Science and philosophy began to transform early, more or less defining by themselves the advent of modernity when science and philosophy were modern but economics and industry were not. However, with the industrial revolution, science and philosophy were given a new and more violent spur to further growth and realignment.

These redirections and realignments of science, philosophy, and logic are vivid illustrations of the kind of selective development of science that Danilevsky imagined, though he thought of these selective developments in terms of their being embedded in cultural-historical traditions. Western science was embedded in the Western cultural-historical tradition (though Danilevsky called this the Romano-Germanic cultural-historical type), and when this tradition changed due to the industrial revolution, the science (and philosophy and logic) changed along with the tradition. Had the change been given an impetus in a different direction, or had the change not happened at all, science and its adjacent intellectual activities would look rather different today. I will not deny that change would have been much slower, but qualitatively different change might have had unprecedented impacts on history. Obviously, in the present context, what I am thinking of is a tradition like the logic of Bolzano being developed gradually, perhaps over hundreds of years, until it becomes the genuine science of science the want of which we feel at present.

It is ironically reflexive that we cannot exclude the possibility of a counterfactual science, based on a counterfactual logical tradition that grew into a mature theory of science, precisely because we lack this same theory of science. We also cannot prove that our rapid progress in science since the industrial revolution might stagnate for want of a proper theory of science, and due to the cognitive monoculture favored by rapid progress, nor that a counterfactual science, based on a counterfactual logic, might ultimately overtake and outstrip the rapid progress of science after an industrial revolution. It may be the case that, when a civilization experiences a rapid and violent industrial revolution, the accelerated rate of change cripples the other institutions of that civilization, and inevitably leads to both industrial and scientific progress eventually grinding to a halt, because the rate of progress was unsustainable. We could call the two implied scenarios of scientific and industrial development the tortoise scenario and the hare scenario, where slow and steady wins the race.

The industrial revolution not only drove economic and social change, it also drive scientific and intellectual change, and may have preempted other developments that were slower and less violent.