We discuss the differences between first-order set theory and second-order logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows ...

Hallucination is fundamental to how transformer-based language models work. In fact, it's their greatest asset.

The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic (IFL) is the real ...

The entry requirement to the programmes is normally a good honours degree in mathematics or a mathematically-related discipline or an equivalent overseas qualification in a mathematical subject. As ...

Would you like to enhance your knowledge of postgraduate-level abstract mathematics and logic? Or perhaps you wish to improve you background knowledge prior to applying for a PhD by research in this ...

THE HISTORY Of computers is often told as a history of objects, from the abacus to the Babbage engine up through the code-breaking machines of World War II. In fact, it is better understood as a ...

While many people complain about the ideological biases in the California Department of Education’s proposal to revolutionize the state mathematics curriculum, that’s not the main problem. This plan ...