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Try to imagine words as points in a multidimensional space – each occupying a position based on its meaning and its relation to others. This concept lay at the heart of the workshop that brought together experts from various fields across UWB on Friday, June 13. Their goal was to explore whether verbal meanings can be described mathematically – using numbers and equations – and whether this could help us better understand how language, thinking, and even artificial intelligence operate.

Radek Schuster from the Department of Philosophy at the Faculty of Arts opened the discussion with his contribution titled How to Understand Vectors in the Context of Philosophy. “Vector semantics is often interpreted as an application of the linguistic distributional hypothesis which itself is derived from the philosophical concept of meaning as a type of usage, developed by later Wittgenstein,” he explained. Put simply, vector semantics is based on the idea that we understand the meaning of a word based on the way it is used and on the company of other words it keeps – a philosophical approach championed by Ludwig Wittgenstein.

Building on Schuster’s presentation, Jan Čepička and Jan Pospíšil from the Department of Mathematics at the Faculty of Applied Sciences presented the topic of words in the context of mathematics. They demonstrated how the “use of a word” can be represented numerically – as vectors in a multidimensional space.

Kamil Ekštein and Nikol Caltová from the Department of Computer Science and Engineering at the Faculty of Applied Sciences offered a practical demonstration of how a large language model – LLaMA, one of the advanced AI systems capable of generating texts in natural language –actually works. Their presentation showed how mathematical descriptions of verbal meanings are applied in modern AI: machines learn to understand expressions not through dictionary definitions, but instead through the contexts in which they appear – precisely what Wittgenstein once described. The particular model showcased was fine-tuned on a corpus of Wittgenstein’s philosophical writings. The outcome is represented by a digital imprint of the philosopher’s thinking, allowing users to engage with a chatbot on a range of topics that Wittgenstein once explored – such as his views on colors – at ludwig.fav.zcu.cz. During the workshop, researchers from various UWB departments engaged in open discussions and exchanged diverse points of view on the topic. As Radek Schuster remarked at the end of the event: “The philosophical idea that the meaning of a word is defined by its use can be modeled mathematically, which helps us understand not only how language works, but also how machines learn it.” AI and in particular large language models, it turns out, operate on principles that have deep philosophical roots. The workshop showed that even seemingly distant fields can intersect and work together to jointly contribute to a deeper understanding of how a language functions – and how its meaning can be transferred even into artificial intelligence.

The workshop was part of the UWB PRVA-25-018 interdisciplinary project.