Frege and Logicism

Today’s Digital Culture reading was on Frege. After the historical process shaped by thinkers like Hobbes and Leibniz, and by the effects of capitalism, I thought reading Frege would provide a good foundation before moving on to Wittgenstein.

Gottlob Frege (1848-1925) was a German mathematician and logician. He spent most of his academic life at the University of Jena. Regarded as one of the founders of modern logic and analytic philosophy, Frege argued that the foundations of mathematics should be sought not in human intuition or psychology but in objective logical principles. With his approach known as Logicism, he aimed to “reduce” arithmetic to logic. He is known for his work on language, meaning, and the structure of thought. I became interested in him especially because of his influence on Wittgenstein. 

Frege’s approach had a Platonist orientation. Thoughts and logical truths exist independently of the human mind. In my view, his real aim, like that of some thinkers before him, was to understand a reality outside the “human condition.” Notice that the paradox has already appeared in this sentence: a human being trying to step outside the human condition. Russell’s Paradox exposed a crack in the foundations of Frege’s system. This is already the well-known popular history.

Graham Priest’s lecture on Frege is the most impressive one I have seen so far. In it, Priest discusses why Frege was understood so late, covering the English translation process and Russell’s influence. We can follow a similar story of translation (how ironic for the philosophy of language) in the book by Janik and Toulmin (Janik, A., & Toulmin, S. (1973). Wittgenstein’s Vienna. Weidenfeld and Nicolson), who argue that Wittgenstein has been generally misunderstood. Of course, because Frege did not live as adventurous a life as the superstar Wittgenstein, he never became the subject of such comprehensive books.

Formal Aphorisms

What interests me is a historical process that Frege perhaps created unintentionally, or at least contributed to. In Frege’s thought, just like his predecessors, there was an important breaking point: separating thought from the person who thinks it. Frege’s distinction between a=a and a=b says this: “The morning star is the morning star” teaches us nothing, but “The morning star is the evening star” does. Both point to the same planet (Venus), so their reference is the same. The difference lies in the route by which we arrive at it, that is, in sense. For Frege, sense is not an image in someone’s head but something objective that anyone can grasp. A thought does not depend on who thinks it.

Here lies a tension. Frege wanted meaning to be independent of any individual mind, yet he argued against the formalists of his day, for whom arithmetic could be understood as a system of meaningless symbols. For Frege, symbols had to mean something. Later developments in computing and information theory took a different direction. Turing showed how computation could be understood through mechanical operations on symbols, while Shannon developed a mathematical theory of information that deliberately put “meaning” aside. I haven’t explored these thinkers yet. 

It looks like today’s artificial intelligence combines these paths in a strange way. It produces what looks like meaning, yet it is unclear where that meaning resides, or whether it resides anywhere. In short, the attempt to think outside the “human condition,” together with the development of digital culture and technology, brought us here. Technology has increasingly nourished a non-human logic, in a way Frege himself would hardly imagined.

Design and architecture were not left outside this history. Symbolic languages, representation, computer-aided design, and similar pseudo-sciences also dragged the intellectual world of this profession into the formal logic. In the period I grew up in, there were debates about CAD. I can see that the feeling of perpetual incompleteness within us, at least in part, comes from this professional deformation. I witnessed the same thing in the criticisms of my postmodern professors when I was a student, and in the helplessness my students experience today when trying to design with Grasshopper. Interfaces, languages, and symbols lead us into a kind of “marketing myopia” about our tools: while looking at what a tool does, we fail to see what it leaves out.

In class, Zeynep gave this reading a much deeper perspective by suggesting that mathematics has been something political since the very beginning of history. I will ask her to write this down for me someday.

Frankenstein

The session we discussed with students today reached a somewhat unsettling conclusion. Frege’s project largely collapsed, but the historical tendency it helped support continues much further ahead. Artificial intelligence is not merely a new tool. It is a formal system that humanity has produced from its own ways of thinking, its language, classifications, knowledge, and contradictions, and which is now partially becoming independent of them.

Still, the idea of a logic operating outside the human is an interesting conclusion. In Mary Shelley’s novel, Frankenstein (is not the name of the monster but of its creator) is a well known example. Artificial intelligence is our “Frankenstein”: a creature born of human thought, resembling us but not belonging to us, with the responsibility remaining ours.

Actually, I don’t like writing about AI. But all the topics of this course leads there. In the end they even made me say things like “the human condition”. I also don’t want to read it dystopically, as a “history of what has befallen us.” What I do know is this: thanks to this course, together with my students, we are beginning to understand ourselves better and to rethink the history we live in.

In my view, Jeffrey Kaplan’s lecture is the best source for Frege’s central idea of sense and reference. Daniel Bonevac is also one of my favorite teachers on topics like these.