Description
In his 1900 Prolegomena, Husserl analyzes the two roles of mathematical symbols: the semantical role of referring to the corresponding number concepts and the syntactical role of “operational signs” (Hua XVIII, 202). Due to this ambiguity, mathematical symbols enable us to perform computations simply through symbol manipulation. For instance, by exploiting the structure of our decimal, positional number system, we can perform the calculation “times 10” by appending a zero. This can be done without conceptual insight into the meaning of the symbols or operations. Numeral systems are designed precisely to have such features, to render calculations as simple and quick as possible, despite our contingent psychological limits. We require a suitable numeral system to do mathematics with as little thought as possible, performing computations according to “blind psychological rules” (Hua XII, 357). Mathematics itself is “the most amazing mental machine” (Hua XII, 350), furthermore this psychological symbol system can be outsourced to a physical symbol system: an actual machine (Hua XII, 364). Just like we do, the machine exploits the syntactic characteristics of the symbols and symbol system, with no regard to the semantics: “we perform additions, multiplications, etc., with decimal numbers purely mechanically, if we don’t even use machines to infer the results.” (Hua Mat I, 247). Our own blind, uninsightful calculations and those done with computing machinery have the same epistemic status, since both implement the same algorithm. That is why Husserl can make the broader claim that “Science also has a subjective side. [...] Here belong the modern methods of calculation with calculating machines, logarithmic tables, etc.” (Hua Mat II, 294). Implementing an algorithm in a machine does not make it more objective or less psychological, since it was designed by humans for humans and therefore still follows the same psychological rules of human thought economy.This leads to a normative concern: the ethical consequences of outsourcing our thinking to machines. According to Husserl, I should ultimately be able to justify my actions in a self- sufficient manner, “from autonomous insight”, but he also cautions that “If I were to apply this principle with full rigor, then I would not be allowed to use any logarithmic table, any calculating machine, without having knowledge in all seriousness of the theory.” (Hua XLII, 272). Ethically, I should only accept the outcomes of computations which I could have performed myself insightfully, i.e. with full awareness of the semantics involved in the symbols and operations. Yet, Husserl acknowledges that this is impossible in practice: we cannot know and do all that is needed to satisfy this rigorous principle. The world, both natural and cultural, is far too complex for that. Hence, we cannot avoid relying on tools for thought. Husserl’s theory of symbolic computation leads to a very timely conclusion: in order to understand the world and act ethically in it, we need to understand the tools to which we have outsourced our thinking and the theories on which this very possibility is based.
| Period | 3 Dec 2021 |
|---|---|
| Event title | OZSW |
| Event type | Conference |
| Location | Tilburg, NetherlandsShow on map |
| Degree of Recognition | National |