by Sven Nilsen, 2023
Neither Naturalism or Scientism have been properly formalized in mathematics. In this blog post I suggest a weak overarching framework for natural science: Path Functorialism. I will discuss how Naturalism fits inside this framework and why there is some reason to criticize Naturalism as a philosophical position for Scientism.
When science uses experiments as the foundation for consensus, this naturally leads to Functorialism as a mathematical understanding of natural science. The reason is that experiments are local hubs of mathematical knowledge in space-time. The relations between these local islands of “knowledge sources” leans the language bias toward functors as means of transferring knowledge in repetitive experiments, where the form of knowledge is assumed similar to something like a category in Category Theory.
However, natural science has traditionally been more strongly biased than Functorialism.
This implies that one needs a perspective modifier X as in X Functorialism.
One argument is that X should stand for “Space” since natural scientific theories
often are grounded in some notion of mathematical spaces.
I argue that X should stand for “Path” since “Space” often implies some notion of symmetry
which is not necessary. The word “Path” both illustrates the modern intuitionistic understanding
of mathematical foundations and a weaker notion of space that allows some level of mathematical plurality.
This is how “Path Functorialism” became my recent position, taken at least temporarily, for a more formal understanding of Naturalism.
Most people are concerned about the supernatural in relation to Naturalism. However, I am not criticizing Naturalism from this point of view.
There are various notions of Naturalism, which implies that Naturalism is a set of subjective philosophical positions. Therefore, as scientific progress is taking place, one must consider the perspective of Naturalism as positions being relative to experiments.
Now, if I choose Path Functorialism as my position to understand science, one can see the Wittgensteinean problematic stance in this position:
From this one can recognize generating hypotheses and testing them by experiments to rule out theories, as the driving mechanism by the mathematical plurality of Path Functorialism.
The mechanism of generating hypotheses is independent of the mathematical plurality, a way to solve the Wittgensteinean conflicts between incompatible ontologies, hence also not depending on the notion of Naturalism that is preferred.
While Naturalism is a strong motivation for driving scientific progress, and it is a reasonable position to assume established theories by scientific consensus, this overall does not include the understanding of science from a bird perspective.
For example, when a new theory is established by consensus, it is easy to forget the past developments since the utility and interest of old theories might go down. This is both a good and a bad thing, so one should not take this as a point for one-sided critique.
The argument is whether Naturalism can claim authority on science as a discipline. If Path Functorialism is taken as position, then Naturalism seems more like an overall driving motivation for science, aka Ready-at-Hand, while Path Functorialism is more like Present-at-Hand (Ready-at-Hand and Present-at-Hand are concepts in philosophy developed by Heidegger).
The mathematical formalism is likely to lead to new developments of understanding science that are more Present-at-Hand in comparison to experimental science. Thus, by Wittgensteinean synthesis, there ought to be people present in such communities who are aware of the problematics of such developments.
Today, Path Semanticists are frequently exploring language biases that lean toward Avatar Extensions, such as religion and some variants of philosophy, e.g. Continental Philosophy. One can contrast these explorations with the emphasis on Functorialism in science. Since Path Semanticists might also explore language biases in science, this means that Path Semanticists do not find it easy to self-identify as a scientific discipline, when the approach is more about Wittgensteinean problematics.
At the same time, the toolbox of Path Semantics allows taking on problematics of language biases, which includes the possible development of Path Functoralism as a framework for science. This means that Path Semanticists might take more pluralistic approaches than usual, at least when compared to individual notions of Naturalism.
A Path Semanticist might be interested in ontological differences between various positions of Naturalism, which probably is not ruled out by scientific experiments and hence not an authentic position within Naturalism (in sense of Heidegger).
For example, in principle it is not a problem that some notion of Naturalism seek to claim authority over the understanding of science. However, since language biases often come to play in conflicts between different notions of Naturalism, it is a good idea to use frameworks developed by Path Semanticists to settle debates, in order to not risk stagmentation in pure language bias.
In the case that one notion of Naturalism wins, the past developments of scentific progress is “handed over” to Path Semanticists, as there is no reason for an established notion of Naturalism to claim fair Intellectual History over competing notions, something that is over and over confirmed by history, that a such stance is a bad idea.
The reason to do this, is like the difference between an athlete competing in Olympics for a gold medal and the people who arrange the Olympics itself with fair and formal rules. Here, the athlete striving toward the goal is like some notion of Naturalism, but the overall arrangement must be according to well developed frameworks of science that can give fair rules between different ontologies.
It is probably not necessary to have a correct notion of science in order to develop a framework for fair rules between different notions of ontology that relate to science. A Present-at-Hand approach to science does not mean we have a full understanding. Also, it is unclear whether a Ready-at-Hand approach can ever be finalized.
Since Naturalism usually self-portrays various notions as seeking dominance, this implies caution is adviced, as the lack of Wittgensteinean problematics does not provide success or solutions to real world problems (e.g. the historically naive philosophical approach to AI).
The problem here is that if no single notion of Naturalism can win, then Path Semanticists dominate simply in terms of synthesizing various language biases, but if a single notion of Naturalism can win, then it must be according to some framework, possibly synthesized by Path Semanticists, to provide fair competition between competing language biases. It looks like, in either case, Path Semanticists will be the overall winners of this game.
Another perspective is that Naturalism is by definition self-defeating and when its ultimate goal is reached, the remaining utility is in Path Semantics.
There is something strange about this, so I suggest that the language bias of science is Path Functorialism with some notion of internal skepticism.